Positive random fields for modeling material stiffness and compliance
Hasofer, Abraham Michael; Ditlevsen, Ove Dalager; Tarp-Johansen, Niels Jacob
1998-01-01
with material properties modeled in terms of the considered random fields.The paper addsthe gamma field, the Fisher field, the beta field, and their reciprocal fields to the catalogue. These fields are all defined on the basis of sums of squares of independent standard Gaussian random variables.All the existing...... marginal moments and the correlation functions are obtained explicitly. Also an inverse Gaussian fieldis added to the catalogue. It is defined in terms of first passage times in correlated joint Brownian motions. Finally an n-dimensional random vector of positive components is defined such that it can...
Parameter estimation of hidden periodic model in random fields
何书元
1999-01-01
Two-dimensional hidden periodic model is an important model in random fields. The model is used in the field of two-dimensional signal processing, prediction and spectral analysis. A method of estimating the parameters for the model is designed. The strong consistency of the estimators is proved.
Shape Modelling Using Markov Random Field Restoration of Point Correspondences
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...
A note on moving average models for Gaussian random fields
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...
Random field distributed Heisenberg model on a thin film geometry
Akıncı, Ümit, E-mail: umit.akinci@deu.edu.tr
2014-11-15
The effects of the bimodal random field distribution on the thermal and magnetic properties of the Heisenberg thin film have been investigated by making use of a two spin cluster with the decoupling approximation. Particular attention has been devoted to the obtaining of phase diagrams and magnetization behaviors. The physical behaviors of special as well as tricritical points are discussed for a wide range of selected Hamiltonian parameters. For example, it is found that when the strength of a magnetic field increases, the locations of the special point (which is the ratio of the surface exchange interaction and the exchange interaction of the inner layers that makes the critical temperature of the film independent of the thickness) in the related plane decrease. Moreover, tricritical behavior has been obtained for higher values of the magnetic field, and influences of the varying Hamiltonian parameters on its behavior have been elucidated in detail in order to have a better understanding of the mechanism underlying the considered system. - Highlights: • Effect of bimodal random field distribution within the Heisenberg model is investigated. • Phase diagrams of the random field Heisenberg model in a thin film geometry are obtained. • Effect of the random field on the magnetic properties is obtained. • Variation of the special point with random field is determined. • Variation of the tricritical point with random field is determined.
A hybrid random field model for scalable statistical learning.
Freno, A; Trentin, E; Gori, M
2009-01-01
This paper introduces hybrid random fields, which are a class of probabilistic graphical models aimed at allowing for efficient structure learning in high-dimensional domains. Hybrid random fields, along with the learning algorithm we develop for them, are especially useful as a pseudo-likelihood estimation technique (rather than a technique for estimating strict joint probability distributions). In order to assess the generality of the proposed model, we prove that the class of pseudo-likelihood distributions representable by hybrid random fields strictly includes the class of joint probability distributions representable by Bayesian networks. Once we establish this result, we develop a scalable algorithm for learning the structure of hybrid random fields, which we call 'Markov Blanket Merging'. On the one hand, we characterize some complexity properties of Markov Blanket Merging both from a theoretical and from the experimental point of view, using a series of synthetic benchmarks. On the other hand, we evaluate the accuracy of hybrid random fields (as learned via Markov Blanket Merging) by comparing them to various alternative statistical models in a number of pattern classification and link-prediction applications. As the results show, learning hybrid random fields by the Markov Blanket Merging algorithm not only reduces significantly the computational cost of structure learning with respect to several considered alternatives, but it also leads to models that are highly accurate as compared to the alternative ones.
Stochastic geometry, spatial statistics and random fields models and algorithms
2015-01-01
Providing a graduate level introduction to various aspects of stochastic geometry, spatial statistics and random fields, this volume places a special emphasis on fundamental classes of models and algorithms as well as on their applications, for example in materials science, biology and genetics. This book has a strong focus on simulations and includes extensive codes in Matlab and R, which are widely used in the mathematical community. It can be regarded as a continuation of the recent volume 2068 of Lecture Notes in Mathematics, where other issues of stochastic geometry, spatial statistics and random fields were considered, with a focus on asymptotic methods.
Creep motion in a random-field Ising model.
Roters, L; Lübeck, S; Usadel, K D
2001-02-01
We analyze numerically a moving interface in the random-field Ising model which is driven by a magnetic field. Without thermal fluctuations the system displays a depinning phase transition, i.e., the interface is pinned below a certain critical value of the driving field. For finite temperatures the interface moves even for driving fields below the critical value. In this so-called creep regime the dependence of the interface velocity on the temperature is expected to obey an Arrhenius law. We investigate the details of this Arrhenius behavior in two and three dimensions and compare our results with predictions obtained from renormalization group approaches.
Versatility and robustness of Gaussian random fields for modelling random media
Quintanilla, John A.; Chen, Jordan T.; Reidy, Richard F.; Allen, Andrew J.
2007-06-01
One of the authors (JAQ) has recently introduced a method of modelling random materials using excursion sets of Gaussian random fields. This method uses convex quadratic programming to find the optimal admissible field autocorrelation function, providing both theoretical and computational advantages over other techniques such as simulated annealing. In this paper, we discuss the application of this algorithm to model various aerogel systems given small-angle neutron scattering data. We also present new results concerning the robustness of this method.
Ensemble renormalization group for the random-field hierarchical model.
Decelle, Aurélien; Parisi, Giorgio; Rocchi, Jacopo
2014-03-01
The renormalization group (RG) methods are still far from being completely understood in quenched disordered systems. In order to gain insight into the nature of the phase transition of these systems, it is common to investigate simple models. In this work we study a real-space RG transformation on the Dyson hierarchical lattice with a random field, which leads to a reconstruction of the RG flow and to an evaluation of the critical exponents of the model at T=0. We show that this method gives very accurate estimations of the critical exponents by comparing our results with those obtained by some of us using an independent method.
Using convex quadratic programming to model random media with Gaussian random fields
Quintanilla, John A.; Jones, W. Max
2007-04-01
Excursion sets of Gaussian random fields (GRFs) have been frequently used in the literature to model two-phase random media with measurable phase autocorrelation functions. The goal of successful modeling is finding the optimal field autocorrelation function that best approximates the prescribed phase autocorrelation function. In this paper, we present a technique which uses convex quadratic programming to find the best admissible field autocorrelation function under a prescribed discretization. Unlike previous methods, this technique efficiently optimizes over all admissible field autocorrelation functions, instead of optimizing only over a predetermined parametrized family. The results from using this technique indicate that the GRF model is significantly more versatile than observed in previous studies. An application to modeling a base-catalyzed tetraethoxysilane aerogel system given small-angle neutron scattering data is also presented
Random field Ising model and community structure in complex networks
Son, S.-W.; Jeong, H.; Noh, J. D.
2006-04-01
We propose a method to determine the community structure of a complex network. In this method the ground state problem of a ferromagnetic random field Ising model is considered on the network with the magnetic field Bs = +∞, Bt = -∞, and Bi≠s,t=0 for a node pair s and t. The ground state problem is equivalent to the so-called maximum flow problem, which can be solved exactly numerically with the help of a combinatorial optimization algorithm. The community structure is then identified from the ground state Ising spin domains for all pairs of s and t. Our method provides a criterion for the existence of the community structure, and is applicable equally well to unweighted and weighted networks. We demonstrate the performance of the method by applying it to the Barabási-Albert network, Zachary karate club network, the scientific collaboration network, and the stock price correlation network. (Ising, Potts, etc.)
Positive random fields for modeling material stiffness and compliance
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 field model reveals structure of the protein recombinational landscape.
Philip A Romero
Full Text Available We are interested in how intragenic recombination contributes to the evolution of proteins and how this mechanism complements and enhances the diversity generated by random mutation. Experiments have revealed that proteins are highly tolerant to recombination with homologous sequences (mutation by recombination is conservative; more surprisingly, they have also shown that homologous sequence fragments make largely additive contributions to biophysical properties such as stability. Here, we develop a random field model to describe the statistical features of the subset of protein space accessible by recombination, which we refer to as the recombinational landscape. This model shows quantitative agreement with experimental results compiled from eight libraries of proteins that were generated by recombining gene fragments from homologous proteins. The model reveals a recombinational landscape that is highly enriched in functional sequences, with properties dominated by a large-scale additive structure. It also quantifies the relative contributions of parent sequence identity, crossover locations, and protein fold to the tolerance of proteins to recombination. Intragenic recombination explores a unique subset of sequence space that promotes rapid molecular diversification and functional adaptation.
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.
Liouville field theory and log-correlated Random Energy Models
Cao, Xiangyu; Rosso, Alberto; Santachiara, Raoul
2016-01-01
An exact mapping is established between the $c\\geq25$ Liouville field theory (LFT) and the Gibbs measure statistics of a thermal particle in a 2D Gaussian Free Field plus a logarithmic confining potential. The probability distribution of the position of the minimum of the energy landscape is obtained exactly by combining the conformal bootstrap and one-step replica symmetry breaking methods. Operator product expansions in LFT allow to unveil novel universal behaviours of the log-correlated Random Energy class. High precision numerical tests are given.
Joint modeling of ChIP-seq data via a Markov random field model
Bao, Yanchun; Vinciotti, Veronica; Wit, Ernst; 't Hoen, Peter A C
2014-01-01
Chromatin ImmunoPrecipitation-sequencing (ChIP-seq) experiments have now become routine in biology for the detection of protein-binding sites. In this paper, we present a Markov random field model for the joint analysis of multiple ChIP-seq experiments. The proposed model naturally accounts for spat
Prediction of Geological Subsurfaces Based on Gaussian Random Field Models
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.
Phase Diagram and Tricritical Behavior of a Spin-2 Transverse Ising Model in a Random Field
LIANG Ya-Qiu; WEI Guo-Zhu; SONG Li-Li; SONG Guo-Li; ZANG Shu-Liang
2004-01-01
The phase diagrams of a spin-2 transverse Ising model with a random field on honeycomb, square, and simple-cubic lattices, respectively, are investigated within the framework of an effective-field theory with correlations.We find the behavior of the tricritical point and the reentrant phenomenon for the system with any coordination number z, when the applied random field is bimodal. The behavior of the tricritical point is also examined as a function of applied transverse field. The reentrant phenomenon comes from the competition between the transverse field and the random field.
Development of a Random Field Model for Gas Plume Detection in Multiple LWIR Images.
Heasler, Patrick G.
2008-09-30
This report develops a random field model that describes gas plumes in LWIR remote sensing images. The random field model serves as a prior distribution that can be combined with LWIR data to produce a posterior that determines the probability that a gas plume exists in the scene and also maps the most probable location of any plume. The random field model is intended to work with a single pixel regression estimator--a regression model that estimates gas concentration on an individual pixel basis.
Freno, Antonino
2011-01-01
This book presents an exciting new synthesis of directed and undirected, discrete and continuous graphical models. Combining elements of Bayesian networks and Markov random fields, the newly introduced hybrid random fields are an interesting approach to get the best of both these worlds, with an added promise of modularity and scalability. The authors have written an enjoyable book---rigorous in the treatment of the mathematical background, but also enlivened by interesting and original historical and philosophical perspectives. -- Manfred Jaeger, Aalborg Universitet The book not only marks an
Fast vectorized algorithm for the Monte Carlo Simulation of the Random Field Ising Model
Rieger, H
1992-01-01
An algoritm for the simulation of the 3--dimensional random field Ising model with a binary distribution of the random fields is presented. It uses multi-spin coding and simulates 64 physically different systems simultaneously. On one processor of a Cray YMP it reaches a speed of 184 Million spin updates per second. For smaller field strength we present a version of the algorithm that can perform 242 Million spin updates per second on the same machine.
A Markov Random Field Model for Image Segmentation of Rice Planthopper in Rice Fields
Hongwei Yue
2016-04-01
Full Text Available It is meaningful to develop the automation segmentation of rice planthopper pests based on imaging technology in precision agriculture. However, rice planthopper images affected by light and complicated backgrounds in open rice fields make the segmentation difficult. This study proposed a segmentation approach of rice planthopper images based on the Markov random field to conduct effective segmentation. First, fractional order differential was introduced into the extraction process of image texture features to gain complete texture information of rice planthopper images. Observation data modeling was established by a combination of image color features and texture features to overcome the disadvantages of insufficient image texture information. Finally, the improved potential function models, the neighborhood relationship between the pixel labels, and the attributes of pixels were defined. The segmentation results were assessed by quantitative evaluation. The experiments showed that the proposed improved approach in the study was more robust, especially with the changes in the illumination condition. This approach can effectively improve segmentation accuracy and promote vision segmentation results of rice planthopper images.
Mean-field theory of random-site q-state Potts models
van Enter, Aernout; Hemmen, Jan Leonard van; Pospiech, C.
1988-01-01
A class of random-site mean-field Potts models is introduced and solved exactly. The bifurcation properties of the resulting mean-field equations are analysed in detail. Particular emphasis is put on the relation between the solutions and the underlying symmetries of the model. It turns out that, in
van Kasteren, T.L.M.; Noulas, A.K.; Kröse, B.J.A.; Smit, G.J.M.; Epema, D.H.J.; Lew, M.S.
2008-01-01
Conditional Random Fields are a discriminative probabilistic model which recently gained popularity in applications that require modeling nonindependent observation sequences. In this work, we present the basic advantages of this model over generative models and argue about its suitability in the do
Thermodynamical Properties of Spin-3／2 Ising Model in a Longitudinal Random Field with Crystal Field
LIANGYa-Qiu; WEIGuo-Zhu; ZHANGHong; SONGGuo-Li
2004-01-01
A theoretical study of a spin-3/2 Ising model in a longitudinal random field with crystal field is studied by using of the effective-field theory with correlations. The phase diagrams and the behavior of the tricritical point are investigated numerically for the honeycomb lattice when the random field is bimodal. In particular, the specific heat and the internal energy are examined in detail for the system with a crystal-field constant in the critical region where the ground-state configuration may change from the spin-3/2 state to the spin-1/2 state. We find many interesting phenomena in the system.
Generalized Whittle-Matern random field as a model of correlated fluctuations
Lim, S C [Faculty of Engineering, Multimedia University, Jalan Multimedia, Cyberjaya, 63100, Selangor Darul Ehsan (Malaysia); Teo, L P [Faculty of Information Technology, Multimedia University, Jalan Multimedia, Cyberjaya, 63100, Selangor Darul Ehsan (Malaysia)], E-mail: sclim@mmu.edu.my, E-mail: lpteo@mmu.edu.my
2009-03-13
This paper considers a generalization of the Gaussian random field with covariance function of the Whittle-Matern family. Such a random field can be obtained as the solution to the fractional stochastic differential equation with two fractional orders. Asymptotic properties of the covariance functions belonging to this generalized Whittle-Matern family are studied, which are used to deduce the sample path properties of the random field. The Whittle-Matern field has been widely used in modeling geostatistical data such as sea beam data, wind speed, field temperature and soil data. In this paper we show that the generalized Whittle-Matern field provides a more flexible model for wind speed data.
A Markov Random Field Model for Image Segmentation of Rice Planthopper in Rice Fields
Hongwei Yue; Ken Cai; Hanhui Lin; Hong Man; Zhaofeng Zeng
2016-01-01
It is meaningful to develop the automation segmentation of rice planthopper pests based on imaging technology in precision agriculture. However, rice planthopper images affected by light and complicated backgrounds in open rice fields make the segmentation difficult. This study proposed a segmentation approach of rice planthopper images based on the Markov random field to conduct effective segmentation. First, fractional order differential was introduced into the extraction proces...
Phase Diagrams and Tricritical Behaviour of the Spin-2 Ising Model in a Longitudinal Random Field
LIANG Ya-Qiu; WEI Guo-Zhu; ZHANG Qi; SONG Guo-Li
2004-01-01
@@ Within the framework of the effective-field theory with correlations, we study the ferromagnetic spin-2 randomfield Ising model (RFIM) in the presence of a crystal field on honeycomb (z = 3), square (z = 4) and simple cubic (z = 6) lattices. The effects of the crystal field and the longitudinal random field on the phase diagrams are investigated. Some characteristic features of the phase diagrams, such as the tricritical phenomena, reentrant phenomena and existence of two tricritical points, are found.
The limiting behavior of the estimated parameters in a misspecified random field regression model
Dahl, Christian Møller; Qin, Yu
, as a consequence the random field model specification introduces non-stationarity and non-ergodicity in the misspecified model and it becomes non-trivial, relative to the existing literature, to establish the limiting behavior of the estimated parameters. The asymptotic results are obtained by applying some...... convenient new uniform convergence results that we propose. This theory may have applications beyond those presented here. Our results indicate that classical statistical inference techniques, in general, works very well for random field regression models in finite samples and that these models succesfully...
The limiting behavior of the estimated parameters in a misspecified random field regression model
Dahl, Christian Møller; Qin, Yu
convenient new uniform convergence results that we propose. This theory may have applications beyond those presented here. Our results indicate that classical statistical inference techniques, in general, works very well for random field regression models in finite samples and that these models succesfully......This paper examines the limiting properties of the estimated parameters in the random field regression model recently proposed by Hamilton (Econometrica, 2001). Though the model is parametric, it enjoys the flexibility of the nonparametric approach since it can approximate a large collection...... of nonlinear functions and it has the added advantage that there is no "curse of dimensionality."Contrary to existing literature on the asymptotic properties of the estimated parameters in random field models our results do not require that the explanatory variables are sampled on a grid. However...
Franchin, P.; Ditlevsen, Ove Dalager; Kiureghian, Armen Der
2002-01-01
The model correction factor method (MCFM) is used in conjunction with the first-order reliability method (FORM) to solve structural reliability problems involving integrals of non-Gaussian random fields. The approach replaces the limit-state function with an idealized one, in which the integrals...... are considered to be Gaussian. Conventional FORM analysis yields the linearization point of the idealized limit-state surface. A model correction factor is then introduced to push the idealized limit-state surface onto the actual limit-state surface. A few iterations yield a good approximation of the reliability...... reliability method; Model correction factor method; Nataf field integration; Non-Gaussion random field; Random field integration; Structural reliability; Pile foundation reliability...
CRITICAL BEHAVIOR OF S-3／2 ISING MODEL IN RANDOM LONGITUDINAL AND TRANSVERSE FIELDS
宋为基
1995-01-01
The phase diagrams and the other crtical properties of S-3/2 Ising model in random longitudinal and transverse fields(RLIM) are dicussed with the approximate scheme combined by mean-field renormalization group theory(MFRG) and the discretized path-integral representation(DPIR).
Synchronization in the random-field Kuramoto model on complex networks
Lopes, M. A.; Lopes, E. M.; Yoon, S.; Mendes, J. F. F.; Goltsev, A. V.
2016-07-01
We study the impact of random pinning fields on the emergence of synchrony in the Kuramoto model on complete graphs and uncorrelated random complex networks. We consider random fields with uniformly distributed directions and homogeneous and heterogeneous (Gaussian) field magnitude distribution. In our analysis, we apply the Ott-Antonsen method and the annealed-network approximation to find the critical behavior of the order parameter. In the case of homogeneous fields, we find a tricritical point above which a second-order phase transition gives place to a first-order phase transition when the network is either fully connected or scale-free with the degree exponent γ >5 . Interestingly, for scale-free networks with 2 networks, although the fields increase the critical coupling for γ >3 . Our simulations support these analytical results.
Modelling Distributed Shape Priors by Gibbs Random Fields of Second Order
Flach, Boris
2011-01-01
We analyse the potential of Gibbs Random Fields for shape prior modelling. We show that the expressive power of second order GRFs is already sufficient to express simple shapes and spatial relations between them simultaneously. This allows to model and recognise complex shapes as spatial compositions of simpler parts.
Modeling of nonlinear microscopy of localized field enhancements in random metal nanostructures
Beermann, Jonas; Bozhevolnyi, Sergey I.; Coello, Victor
2006-01-01
Nonlinear microscopy of localized field enhancements in random metal nanostructures with a tightly focused laser beam scanning over a sample surface is modeled by making use of analytic representations of the Green dyadic in the near- and far-field regions, with the latter being approximated...... by the part describing the scattering via excitation of surface plasmon polaritons. The developed approach is applied to scanning second-harmonic (SH) microscopy of small gold spheres placed randomly on a gold surface. We calculate self-consistent fundamental harmonic (FH) and SH field distributions...
Magnetic properties of a transverse spin- Ising model with random longitudinal field
Liang, Ya-Qiu; Wei, Guo-Zhu; Song, Guo-Li
2004-12-01
Within the framework of the effective-field theory with correlations, a spin- transverse Ising model in the longitudinal random-field on a honeycomb lattice is studied. The phase diagrams and the behavior of the tricritical point are examined. The possible re-entrance phenomena displayed by the system due to the competition effects that occur for the appropriate ranges of the random and transverse field are investigated. The longitudinal and transverse magnetizations, the longitudinal quadrupolar moments and internal energy are given numerically for a honeycomb lattice (z = 3).
Erhan Albayrak
2013-01-01
The spin-1 Blume-Capel model with transverse Ω and longitudinal external magnetic fields h,in addition to a longitudinal random crystal field D,is studied in the mean-field approximation.It is assumed that the crystal field is either turned on with probability p or turned off with probability 1-p on the sites of a square lattice.Phase diagrams are then calculated on the reduced temperature crystal field planes for given values of γ =-Ω/J and p at zero h.Thus,the effect of changing γ and p are illustrated on the phase diagrams in great detail and interesting results are observed.
Thermodynamical Properties of Spin-3/2 Ising Model in a Longitudinal Random Field with Crystal Field
LIANG Ya-Qiu; WEI Guo-Zhu; ZHANG Hong; SONG Guo-Li
2004-01-01
A theoretical study of a spin-3/2 Ising model in a longitudinal random field with crystal field is studiedby using of the effective-field theory with correlations. The phase diagrams and the behavior of the tricritical point areinvestigated numerically for the honeycomb lattice when the randorm field is bimodal. In particular, the specific heatand the internal energy are examined in detail for the system with a crystal-field constant in the critical region wherethe ground-state configuration may change from the spin-3/2 state to the spin-1/2 state. We find many interestingphenomena in the system.
Phase diagram of the classical Heisenberg model in a trimodal random field distribution
Santos-Filho, A.; Albuquerque, D. F. de; Santos-Filho, J. B.; Batista, T. S. Araujo
2016-11-01
The classical spin 1 / 2 Heisenberg model on a simple cubic lattice, with fluctuating bond interactions between nearest neighbors and in the presence of a random magnetic field, is investigated by effective field theory based on two-spin cluster. The random field is drawn from the asymmetric and anisotropic trimodal probability distribution. The fluctuating bond is extracted from the symmetric and anisotropic bimodal probability. We estimate the transition temperatures, and the phase diagram in the Tc- h, Tc- p and Tc - α planes. We observe that the temperature of the tricritical point decreases with the increase of disorder in exchange interactions until the system ceases to display tricritical behavior. The disorder of the interactions and reentrant phenomena depends on the trimodal distribution of the random field.
Information Extraction from Research Papers based on Conditional Random Field Model
Zhu Shuxin
2013-01-01
Full Text Available With the increasing use of CiteSeer academic search engines, the accuracy of such systems has become more and more important. The paper adopts the improved particle swarm optimization algorithm for training conditional random field model and applies it into the research papers’ title and citation retrieval. The improved particl swarm optimization algorithm brings the particle swarm aggregation to prevent particle swarm from being plunged into local convergence too early, and uses the linear inertia factor and learning factor to update particle rate. It can control algorithm in infinite iteration by the iteration between particle relative position change rate. The results of which using the standard research papers’ heads and references to evaluate the trained conditional random field model shows that compared with traditionally conditional random field model and Hidden Markov Model, the conditional random field model ,optimized and trained by improved particle swarm, has been better ameliorated in the aspect of F1 mean error and word error rate.
The van Hemmen model and effect of random crystalline anisotropy field
Morais, Denes M. de [Instituto de Física, Universidade Federal de Mato Grosso, 78060-900 Cuiabá, Mato Grosso (Brazil); Godoy, Mauricio, E-mail: mgodoy@fisica.ufmt.br [Instituto de Física, Universidade Federal de Mato Grosso, 78060-900 Cuiabá, Mato Grosso (Brazil); Arruda, Alberto S. de, E-mail: aarruda@fisica.ufmt.br [Instituto de Física, Universidade Federal de Mato Grosso, 78060-900 Cuiabá, Mato Grosso (Brazil); Silva, Jonathas N. da [Universidade Estadual Paulista, 14800-901, Araraquara, São Paulo (Brazil); Ricardo de Sousa, J. [Instituto Nacional de Sistemas Complexos, Departamento de Fisica, Universidade Federal do Amazona, 69077-000, Manaus, Amazonas (Brazil)
2016-01-15
In this work, we have presented the generalized phase diagrams of the van Hemmen model for spin S=1 in the presence of an anisotropic term of random crystalline field. In order to study the critical behavior of the phase transitions, we employed a mean-field Curie–Weiss approach, which allows calculation of the free energy and the equations of state of the model. The phase diagrams obtained here displayed tricritical behavior, with second-order phase transition lines separated from the first-order phase transition lines by a tricritical point. - Highlights: • Several phase diagrams are obtained for the model. • The influence of the random crystalline anisotropy field on the model is investigated. • Three ordered (spin-glass, ferromagnetic and mixed) phases are found. • The tricritical behavior is examined.
A Fast Variational Approach for Learning Markov Random Field Language Models
2015-01-01
our class of models. Learning undirected graphical models is challenging because of the global nor- malization constant, or partition function. We...503–528, 1989. Marcus, Mitchell P, Marcinkiewicz, Mary Ann, and San- torini, Beatrice. Building a large annotated corpus of english : The penn treebank...A Fast Variational Approach for Learning Markov Random Field Language Models Yacine Jernite JERNITE@CS.NYU.EDU CIMS, New York University, 251 Mercer
Statistical Shape Modelling and Markov Random Field Restoration (invited tutorial and exercise)
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 prov...... using Markov random field relaxation of a spectral classifier. Keywords: the Ising model, the Potts model, stochastic sampling, discriminant analysis, expectation maximization.......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...
Associative Hierarchical Random Fields.
Ladický, L'ubor; Russell, Chris; Kohli, Pushmeet; Torr, Philip H S
2014-06-01
This paper makes two contributions: the first is the proposal of a new model-The associative hierarchical random field (AHRF), and a novel algorithm for its optimization; the second is the application of this model to the problem of semantic segmentation. Most methods for semantic segmentation are formulated as a labeling problem for variables that might correspond to either pixels or segments such as super-pixels. It is well known that the generation of super pixel segmentations is not unique. This has motivated many researchers to use multiple super pixel segmentations for problems such as semantic segmentation or single view reconstruction. These super-pixels have not yet been combined in a principled manner, this is a difficult problem, as they may overlap, or be nested in such a way that the segmentations form a segmentation tree. Our new hierarchical random field model allows information from all of the multiple segmentations to contribute to a global energy. MAP inference in this model can be performed efficiently using powerful graph cut based move making algorithms. Our framework generalizes much of the previous work based on pixels or segments, and the resulting labelings can be viewed both as a detailed segmentation at the pixel level, or at the other extreme, as a segment selector that pieces together a solution like a jigsaw, selecting the best segments from different segmentations as pieces. We evaluate its performance on some of the most challenging data sets for object class segmentation, and show that this ability to perform inference using multiple overlapping segmentations leads to state-of-the-art results.
Nosedal-Sanchez, Alvaro; Jackson, Charles S.; Huerta, Gabriel
2016-07-01
A new test statistic for climate model evaluation has been developed that potentially mitigates some of the limitations that exist for observing and representing field and space dependencies of climate phenomena. Traditionally such dependencies have been ignored when climate models have been evaluated against observational data, which makes it difficult to assess whether any given model is simulating observed climate for the right reasons. The new statistic uses Gaussian Markov random fields for estimating field and space dependencies within a first-order grid point neighborhood structure. We illustrate the ability of Gaussian Markov random fields to represent empirical estimates of field and space covariances using "witch hat" graphs. We further use the new statistic to evaluate the tropical response of a climate model (CAM3.1) to changes in two parameters important to its representation of cloud and precipitation physics. Overall, the inclusion of dependency information did not alter significantly the recognition of those regions of parameter space that best approximated observations. However, there were some qualitative differences in the shape of the response surface that suggest how such a measure could affect estimates of model uncertainty.
Modeling and statistical analysis of non-Gaussian random fields with heavy-tailed distributions
Nezhadhaghighi, Mohsen Ghasemi; Nakhlband, Abbas
2017-04-01
In this paper, we investigate and develop an alternative approach to the numerical analysis and characterization of random fluctuations with the heavy-tailed probability distribution function (PDF), such as turbulent heat flow and solar flare fluctuations. We identify the heavy-tailed random fluctuations based on the scaling properties of the tail exponent of the PDF, power-law growth of q th order correlation function, and the self-similar properties of the contour lines in two-dimensional random fields. Moreover, this work leads to a substitution for the fractional Edwards-Wilkinson (EW) equation that works in the presence of μ -stable Lévy noise. Our proposed model explains the configuration dynamics of the systems with heavy-tailed correlated random fluctuations. We also present an alternative solution to the fractional EW equation in the presence of μ -stable Lévy noise in the steady state, which is implemented numerically, using the μ -stable fractional Lévy motion. Based on the analysis of the self-similar properties of contour loops, we numerically show that the scaling properties of contour loop ensembles can qualitatively and quantitatively distinguish non-Gaussian random fields from Gaussian random fluctuations.
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...
Statistical Shape Modelling and Markov Random Field Restoration (invited tutorial and exercise)
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...... themselves a generic holistic tool in various segmentation and simulation studies. Finding a basis of homologous points is a fundamental issue in PDMs which effects both alignment and decomposition of the training data, and may be aided by Markov Random Field Restoration (MRF) of the correspondence...
Random Fields and Spin Glasses
De Dominicis, Cirano; Giardina, Irene
2010-06-01
1. A brief introduction; 2. The Random Field Ising model; 3. The dynamical approach; 4. The p=2 spherical model; 5. Mean field spin glasses: one-step RSB; 6. The Sherrington-Kirkpatrick model; 7. Mean field via TAP equations; 8. Spin glass above D=6; 9. Propagators, mostly replicon; 10. Ward-Takahashi identities and Goldstone modes; 11. Alternative approaches and conclusions; Appendices; Index.
Markov Random Field Surface Reconstruction
Paulsen, Rasmus Reinhold; Bærentzen, Jakob Andreas; Larsen, Rasmus
2010-01-01
) and knowledge about data (the observation model) in an orthogonal fashion. Local models that account for both scene-specific knowledge and physical properties of the scanning device are described. Furthermore, how the optimal distance field can be computed is demonstrated using conjugate gradients, sparse......A method for implicit surface reconstruction is proposed. The novelty in this paper is the adaption of Markov Random Field regularization of a distance field. The Markov Random Field formulation allows us to integrate both knowledge about the type of surface we wish to reconstruct (the prior...
Hongyan Wang; Xiaobo Zhou
2013-01-01
By altering the electrostatic charge of histones or providing binding sites to protein recognition molecules,Chromatin marks have been proposed to regulate gene expression,a property that has motivated researchers to link these marks to cis-regulatory elements.With the help of next generation sequencing technologies,we can now correlate one specific chromatin mark with regulatory elements (e.g.enhancers or promoters) and also build tools,such as hidden Markov models,to gain insight into mark combinations.However,hidden Markov models have limitation for their character of generative models and assume that a current observation depends only on a current hidden state in the chain.Here,we employed two graphical probabilistic models,namely the linear conditional random field model and multivariate hidden Markov model,to mark gene regions with different states based on recurrent and spatially coherent character of these eight marks.Both models revealed chromatin states that may correspond to enhancers and promoters,transcribed regions,transcriptional elongation,and low-signal regions.We also found that the linear conditional random field model was more effective than the hidden Markov model in recognizing regulatory elements,such as promoter-,enhancer-,and transcriptional elongation-associated regions,which gives us a better choice.
A Modified FCM Classifier Constrained by Conditional Random Field Model for Remote Sensing Imagery
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.
Phase Diagram and Tricritical Behavior of a Spin-2 Transverse Ising Model in aRandom Field
LIANGYa-Qiu; WEIGuo-Zhu; SONGLi-Li; SONGGuo-Li; ZANGShu-Liang
2004-01-01
The phase diagrams of a spin-2 transverse Ising model with a random field on honeycomb, square, and simple-cubic lattices, respectively, are investigated within the framework of an effective-field theory with correlations.We find the behavior of the tricritical point and the reentrant phenomenon for the system with any coordination number z, when the applied random field is bimodal. The behavior of the tricritical point is also examined as a function of applied transverse field. The reentrant phenomenon comes from the competition between the transverse field and the random field.
Integrals of random fields treated by the model correction factor method
Franchin, P.; Ditlevsen, Ove Dalager; Kiureghian, Armen Der
2002-01-01
The model correction factor method (MCFM) is used in conjunction with the first-order reliability method (FORM) to solve structural reliability problems involving integrals of non-Gaussian random fields. The approach replaces the limit-state function with an idealized one, in which the integrals...... are considered to be Gaussian. Conventional FORM analysis yields the linearization point of the idealized limit-state surface. A model correction factor is then introduced to push the idealized limit-state surface onto the actual limit-state surface. A few iterations yield a good approximation of the reliability...
Random-field Ising model: Insight from zero-temperature simulations
P.E. Theodorakis
2014-12-01
Full Text Available We enlighten some critical aspects of the three-dimensional (d=3 random-field Ising model (RFIM from simulations performed at zero temperature. We consider two different, in terms of the field distribution, versions of model, namely a Gaussian RFIM and an equal-weight trimodal RFIM. By implementing a computational approach that maps the ground-state of the system to the maximum-flow optimization problem of a network, we employ the most up-to-date version of the push-relabel algorithm and simulate large ensembles of disorder realizations of both models for a broad range of random-field values and systems sizes V=LxLxL, where L denotes linear lattice size and Lmax=156. Using as finite-size measures the sample-to-sample fluctuations of various quantities of physical and technical origin, and the primitive operations of the push-relabel algorithm, we propose, for both types of distributions, estimates of the critical field hmax and the critical exponent ν of the correlation length, the latter clearly suggesting that both models share the same universality class. Additional simulations of the Gaussian RFIM at the best-known value of the critical field provide the magnetic exponent ratio β/ν with high accuracy and clear out the controversial issue of the critical exponent α of the specific heat. Finally, we discuss the infinite-limit size extrapolation of energy- and order-parameter-based noise to signal ratios related to the self-averaging properties of the model, as well as the critical slowing down aspects of the algorithm.
Risk Prediction Modeling of Sequencing Data Using a Forward Random Field Method.
Wen, Yalu; He, Zihuai; Li, Ming; Lu, Qing
2016-02-19
With the advance in high-throughput sequencing technology, it is feasible to investigate the role of common and rare variants in disease risk prediction. While the new technology holds great promise to improve disease prediction, the massive amount of data and low frequency of rare variants pose great analytical challenges on risk prediction modeling. In this paper, we develop a forward random field method (FRF) for risk prediction modeling using sequencing data. In FRF, subjects' phenotypes are treated as stochastic realizations of a random field on a genetic space formed by subjects' genotypes, and an individual's phenotype can be predicted by adjacent subjects with similar genotypes. The FRF method allows for multiple similarity measures and candidate genes in the model, and adaptively chooses the optimal similarity measure and disease-associated genes to reflect the underlying disease model. It also avoids the specification of the threshold of rare variants and allows for different directions and magnitudes of genetic effects. Through simulations, we demonstrate the FRF method attains higher or comparable accuracy over commonly used support vector machine based methods under various disease models. We further illustrate the FRF method with an application to the sequencing data obtained from the Dallas Heart Study.
Multi-fidelity modelling via recursive co-kriging and Gaussian–Markov random fields
Perdikaris, P.; Venturi, D.; Royset, J. O.; Karniadakis, G. E.
2015-01-01
We propose a new framework for design under uncertainty based on stochastic computer simulations and multi-level recursive co-kriging. The proposed methodology simultaneously takes into account multi-fidelity in models, such as direct numerical simulations versus empirical formulae, as well as multi-fidelity in the probability space (e.g. sparse grids versus tensor product multi-element probabilistic collocation). We are able to construct response surfaces of complex dynamical systems by blending multiple information sources via auto-regressive stochastic modelling. A computationally efficient machine learning framework is developed based on multi-level recursive co-kriging with sparse precision matrices of Gaussian–Markov random fields. The effectiveness of the new algorithms is demonstrated in numerical examples involving a prototype problem in risk-averse design, regression of random functions, as well as uncertainty quantification in fluid mechanics involving the evolution of a Burgers equation from a random initial state, and random laminar wakes behind circular cylinders. PMID:26345079
Potts q-color field theory and scaling random cluster model
Delfino, Gesualdo
2011-01-01
We study structural properties of the q-color Potts field theory which, for real values of q, describes the scaling limit of the random cluster model. We show that the number of independent n-point Potts spin correlators coincides with that of independent n-point cluster connectivities and is given by generalized Bell numbers. Only a subset of these spin correlators enters the determination of the Potts magnetic properties for q integer. The structure of the operator product expansion of the spin fields for generic q is also identified. For the two-dimensional case, we analyze the duality relation between spin and kink field correlators, both for the bulk and boundary cases, obtaining in particular a sum rule for the kink-kink elastic scattering amplitudes.
Theory of Distribution Estimation of Hyperparameters in Markov Random Field Models
Sakamoto, Hirotaka; Nakanishi-Ohno, Yoshinori; Okada, Masato
2016-06-01
We investigated the performance of distribution estimation of hyperparameters in Markov random field models proposed by Nakanishi-Ohno et al., http://doi.org/10.1088/1751-8113/47/4/045001, J. Phys. A 47, 045001 (2014) when used to evaluate the confidence of data. We analytically calculated the configurational average, with respect to data, of the negative logarithm of the posterior distribution, which is called free energy based on an analogy with statistical mechanics. This configurational average of free energy shrinks as the amount of data increases. Our results theoretically confirm the numerical results from that previous study.
ITAC volume assessment through a Gaussian hidden Markov random field model-based algorithm.
Passera, Katia M; Potepan, Paolo; Brambilla, Luca; Mainardi, Luca T
2008-01-01
In this paper, a semi-automatic segmentation method for volume assessment of Intestinal-type adenocarcinoma (ITAC) is presented and validated. The method is based on a Gaussian hidden Markov random field (GHMRF) model that represents an advanced version of a finite Gaussian mixture (FGM) model as it encodes spatial information through the mutual influences of neighboring sites. To fit the GHMRF model an expectation maximization (EM) algorithm is used. We applied the method to a magnetic resonance data sets (each of them composed by T1-weighted, Contrast Enhanced T1-weighted and T2-weighted images) for a total of 49 tumor-contained slices. We tested GHMRF performances with respect to FGM by both a numerical and a clinical evaluation. Results show that the proposed method has a higher accuracy in quantifying lesion area than FGM and it can be applied in the evaluation of tumor response to therapy.
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
Integrating BC & GC Models In Computing Stereo Disparity As Markov Random Field
Hongsheng Zhang
2006-11-01
Full Text Available Belief propagation and graph cuts have emerged as powerful tools for computing efficient approximate solution to stereo disparity field modelled as the Markov random field (MRF. These algorithms have provided the best performance based on results on a standard data set. However, employment of the brightness constancy (BC assumption severely limits the range of their applications. Previously, augmenting the BC with gradient constancy (GC assumption has shown to produce a more robust optical flow algorithm. In this paper, these constraints are integrated within the MRF framework to devise an enhanced global method that broadens the application domains for stereo computation. Results of experiments with both semi-synthetic data and more challenging ocean images are presented to illustrate that the proposed method generally outperforms earlier dense optical flow and stereo algorithms.
Correlation functions of the one-dimensional random field Ising model at zero temperature
Farhi, E; Farhi, Edward; Gutmann, Sam
1993-01-01
We consider the one-dimensional random field Ising model, where the spin-spin coupling, $J$, is ferromagnetic and the external field is chosen to be $+h$ with probability $p$ and $-h$ with probability $1-p$. At zero temperature, we calculate an exact expression for the correlation length of the quenched average of the correlation function $\\langle s_0 s_n \\rangle - \\langle s_0 \\rangle \\langle s_n \\rangle$ in the case that $2J/h$ is not an integer. The result is a discontinuous function of $2J/h$. When $p = {1 \\over 2}$, we also place a bound on the correlation length of the quenched average of the correlation function $\\langle s_0 s_n \\rangle$.
Adaptive Multi-GPU Exchange Monte Carlo for the 3D Random Field Ising Model
Navarro, C A; Deng, Youjin
2015-01-01
The study of disordered spin systems through Monte Carlo simulations has proven to be a hard task due to the adverse energy landscape present at the low temperature regime, making it difficult for the simulation to escape from a local minimum. Replica based algorithms such as the Exchange Monte Carlo (also known as parallel tempering) are effective at overcoming this problem, reaching equilibrium on disordered spin systems such as the Spin Glass or Random Field models, by exchanging information between replicas of neighbor temperatures. In this work we present a multi-GPU Exchange Monte Carlo method designed for the simulation of the 3D Random Field Model. The implementation is based on a two-level parallelization scheme that allows the method to scale its performance in the presence of faster and GPUs as well as multiple GPUs. In addition, we modified the original algorithm by adapting the set of temperatures according to the exchange rate observed from short trial runs, leading to an increased exchange rate...
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.
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.
Quantum Phase Transition in the Two-Dimensional Random Transverse-Field Ising Model
Pich, C.; Young, A. P.
1998-03-01
We study the quantum phase transition in the random transverse-field Ising model by Monte Carlo simulations. In one-dimension it has been established that this system has the following striking behavior: (i) the dynamical exponent is infinite, and (ii) the exponents for the divergence of the average and typical correlation lengths are different. An important issue is whether this behavior is special to one-dimension or whether similar behavior persists in higher dimensions. Here we attempt to answer this question by studies of the two-dimensional model. Our simulations use the Wolff cluster algorithm and the results are analyzed by anisotropic finite size scaling, paying particular attention to the Binder ratio of moments of the order parameter distribution and the distribution of the spin-spin correlation functions for various distances.
A Markov Random Field Model-Based Approach to Natural Image Matting
Sheng-You Lin; Jiao-Ying Shi
2007-01-01
This paper proposes a Markov Random Field (MRF) model-based approach to natural image matting with complex scenes.After the trimap for matting is given manually, the unknown region is roughly segmented into several joint sub-regions.In each sub-region, we partition the colors of neighboring background or foreground pixels into several clusters in RGB color space and assign matting label to each unknown pixel.All the labels are modelled as an MRF and the matting problem is then formulated as a maximum a posteriori (MAP) estimation problem.Simulated annealing is used to find the optimal MAP estimation.The better results can be obtained under the same user-interactions when images are complex.Results of natural image matting experiments performed on complex images using this approach are shown and compared in this paper.
Hadjiagapiou, Ioannis A.
2014-03-01
The magnetic systems with disorder form an important class of systems, which are under intensive studies, since they reflect real systems. Such a class of systems is the spin glass one, which combines randomness and frustration. The Sherrington-Kirkpatrick Ising spin glass with random couplings in the presence of a random magnetic field is investigated in detail within the framework of the replica method. The two random variables (exchange integral interaction and random magnetic field) are drawn from a joint Gaussian probability density function characterized by a correlation coefficient ρ. The thermodynamic properties and phase diagrams are studied with respect to the natural parameters of both random components of the system contained in the probability density. The de Almeida-Thouless line is explored as a function of temperature, ρ and other system parameters. The entropy for zero temperature as well as for non zero temperatures is partly negative or positive, acquiring positive branches as h0 increases.
A Tutorial of the Poisson Random Field Model in Population Genetics
Praveen Sethupathy
2008-01-01
Full Text Available Population genetics is the study of allele frequency changes driven by various evolutionary forces such as mutation, natural selection, and random genetic drift. Although natural selection is widely recognized as a bona-fide phenomenon, the extent to which it drives evolution continues to remain unclear and controversial. Various qualitative techniques, or so-called “tests of neutrality”, have been introduced to detect signatures of natural selection. A decade and a half ago, Stanley Sawyer and Daniel Hartl provided a mathematical framework, referred to as the Poisson random field (PRF, with which to determine quantitatively the intensity of selection on a particular gene or genomic region. The recent availability of large-scale genetic polymorphism data has sparked widespread interest in genome-wide investigations of natural selection. To that end, the original PRF model is of particular interest for geneticists and evolutionary genomicists. In this article, we will provide a tutorial of the mathematical derivation of the original Sawyer and Hartl PRF model.
Markov random field modelling for fluid distributions from the seismic velocity structures
Kuwatani, T.; Nagata, K.; Okada, M.; Toriumi, M.
2011-12-01
Recent development of geophysical observations, such as seismic tomography, seismic reflection method and geomagnetic method, provide us detailed images of the earth's interior. However, it has still been difficult to interpret these data geologically, including predicting lithology and fluid distributions, mainly because (1) available data usually have large noise and uncertainty, and (2) the number of observable parameters is usually smaller than the number of target parameters. Therefore, the statistical analyses of geophysical data sets are essential for the objective and quantitative geological interpretation. We propose the use of Markov random field (MRF) model to geophysical image data as an alternative to classical deterministic approaches. The MRF model is a Bayesian stochastic model using a generalized form of Markov Chains, and is often applied to the analysis of images, particularly in the detection of visual patterns or textures. The MRF model assumes that the spatial gradients of physical properties are relatively small compared to the observational noises. By hyperparameter estimation, the variances of noises can be appropriately estimated only from available data sets without prior information about observational noises. In this study, we try to image the fluid distributions based on the seismic velocity structure by using the Markov random field model. According to Nakajima et al. (2005), seismic velocities (Vp and Vs) are expressed as functions of porosity and pore geometry using the unified formulation proposed by Takei (2002). Additionally, the spatial continuity of porosity and pore geometry is incorporated by Gaussian Markov Chains as prior probabilities. The most probable estimation can be obtained by maximizing the posterior probability of the fluid distribution given the observed velocity structures. In the present study, the steepest descent method was implemented in order to minimize the free energy (i.e. maximize the posterior
Depinning transition and thermal fluctuations in the random-field Ising model.
Roters, L; Hucht, A; Lübeck, S; Nowak, U; Usadel, K D
1999-11-01
We analyze the depinning transition of a driven interface in the three-dimensional (3D) random field Ising model (RFIM) with quenched disorder by means of Monte Carlo simulations. The interface initially built into the system is perpendicular to the [111] direction of a simple cubic lattice. We introduce an algorithm which is capable of simulating such an interface independent of the considered dimension and time scale. This algorithm is applied to the 3D RFIM to study both the depinning transition and the influence of thermal fluctuations on this transition. It turns out that in the RFIM characteristics of the depinning transition depend crucially on the existence of overhangs. Our analysis yields critical exponents of the interface velocity, the correlation length, and the thermal rounding of the transition. We find numerical evidence for a scaling relation for these exponents and the dimension d of the system.
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.
Contextual Hierarchical Part-Driven Conditional Random Field Model for Object Category Detection
Lizhen Wu
2012-01-01
Full Text Available Even though several promising approaches have been proposed in the literature, generic category-level object detection is still challenging due to high intraclass variability and ambiguity in the appearance among different object instances. From the view of constructing object models, the balance between flexibility and discrimination must be taken into consideration. Motivated by these demands, we propose a novel contextual hierarchical part-driven conditional random field (CRF model, which is based on not only individual object part appearance but also model contextual interactions of the parts simultaneously. By using a latent two-layer hierarchical formulation of labels and a weighted neighborhood structure, the model can effectively encode the dependencies among object parts. Meanwhile, beta-stable local features are introduced as observed data to ensure the discriminative and robustness of part description. The object category detection problem can be solved in a probabilistic framework using a supervised learning method based on maximum a posteriori (MAP estimation. The benefits of the proposed model are demonstrated on the standard dataset and satellite images.
Language Recognition Using Latent Dynamic Conditional Random Field Model with Phonological Features
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.
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.
Super-rough glassy phase of the random field XY model in two dimensions.
Perret, Anthony; Ristivojevic, Zoran; Le Doussal, Pierre; Schehr, Grégory; Wiese, Kay J
2012-10-12
We study both analytically, using the renormalization group (RG) to two loop order, and numerically, using an exact polynomial algorithm, the disorder-induced glass phase of the two-dimensional XY model with quenched random symmetry-breaking fields and without vortices. In the super-rough glassy phase, i.e., below the critical temperature T(c), the disorder and thermally averaged correlation function B(r) of the phase field θ(x), B(r)=([θ(x)-θ(x+r)](2)) behaves, for r > a, as B(r) is approximately equal to A(τ)ln(2)(r/a) where r=|r| and a is a microscopic length scale. We derive the RG equations up to cubic order in τ=(T(c)-T)/T(c) and predict the universal amplitude A(τ)=2τ(2)-2τ(3)+O(τ(4)). The universality of A(τ) results from nontrivial cancellations between nonuniversal constants of RG equations. Using an exact polynomial algorithm on an equivalent dimer version of the model we compute A(τ) numerically and obtain a remarkable agreement with our analytical prediction, up to τ≈0.5.
A Deep-Structured Conditional Random Field Model for Object Silhouette Tracking.
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.
Wang, Zhiyong; Xu, Jinbo
2011-07-01
Accurate tertiary structures are very important for the functional study of non-coding RNA molecules. However, predicting RNA tertiary structures is extremely challenging, because of a large conformation space to be explored and lack of an accurate scoring function differentiating the native structure from decoys. The fragment-based conformation sampling method (e.g. FARNA) bears shortcomings that the limited size of a fragment library makes it infeasible to represent all possible conformations well. A recent dynamic Bayesian network method, BARNACLE, overcomes the issue of fragment assembly. In addition, neither of these methods makes use of sequence information in sampling conformations. Here, we present a new probabilistic graphical model, conditional random fields (CRFs), to model RNA sequence-structure relationship, which enables us to accurately estimate the probability of an RNA conformation from sequence. Coupled with a novel tree-guided sampling scheme, our CRF model is then applied to RNA conformation sampling. Experimental results show that our CRF method can model RNA sequence-structure relationship well and sequence information is important for conformation sampling. Our method, named as TreeFolder, generates a much higher percentage of native-like decoys than FARNA and BARNACLE, although we use the same simple energy function as BARNACLE. zywang@ttic.edu; j3xu@ttic.edu Supplementary data are available at Bioinformatics online.
Destruction of first-order phase transition in a random-field Ising model
Crokidakis, Nuno; Nobre, Fernando D [Centro Brasileiro de Pesquisas Fisicas, Rua Xavier Sigaud 150, 22290-180, Rio de Janeiro-RJ (Brazil)], E-mail: nuno@if.uff.br, E-mail: fdnobre@cbpf.br
2008-04-09
The phase transitions that occur in an infinite-range-interaction Ising ferromagnet in the presence of a double Gaussian random magnetic field are analyzed. Such random fields are defined as a superposition of two Gaussian distributions, presenting the same width {sigma}. It is argued that this distribution is more appropriate for a theoretical description of real systems than other simpler cases, i.e. the bimodal ({sigma} = 0) and single Gaussian distributions. It is shown that a low-temperature first-order phase transition may be destroyed for increasing values of {sigma}, similarly to what happens in the compound Fe{sub x}Mg{sub 1-x}Cl{sub 2}, whose finite-temperature first-order phase transition is presumably destroyed by an increase in the field randomness.
Zhang, Yifan
2016-08-18
For face naming in TV series or movies, a typical way is using subtitles/script alignment to get the time stamps of the names, and tagging them to the faces. We study the problem of face naming in videos when subtitles are not available. To this end, we divide the problem into two tasks: face clustering which groups the faces depicting a certain person into a cluster, and name assignment which associates a name to each face. Each task is formulated as a structured prediction problem and modeled by a hidden conditional random field (HCRF) model. We argue that the two tasks are correlated problems whose outputs can provide prior knowledge of the target prediction for each other. The two HCRFs are coupled in a unified graphical model called coupled HCRF where the joint dependence of the cluster labels and face name association is naturally embedded in the correlation between the two HCRFs. We provide an effective algorithm to optimize the two HCRFs iteratively and the performance of the two tasks on real-world data set can be both improved.
Human fixation detection model in video compressed domain based on Markov random field
Li, Yongjun; Li, Yunsong; Liu, Weijia; Hu, Jing; Ge, Chiru
2017-01-01
Recently, research on and applications of human fixation detection in video compressed domain have gained increasing attention. However, prediction accuracy and computational complexity still remain a challenge. This paper addresses the problem of compressed domain fixations detection in the videos based on residual discrete cosine transform coefficients norm (RDCN) and Markov random field (MRF). RDCN feature is directly extracted from the compressed video with partial decoding and is normalized. After spatial-temporal filtering, the normalized map [Smoothed RDCN (SRDCN) map] is taken to the MRF model, and the optimal binary label map is obtained. Based on the label map and the center saliency map, saliency enhancement and nonsaliency inhibition are done for the SRDCN map, and the final SRDCN-MRF salient map is obtained. Compared with the similar models, we enhance the available energy functions and introduce an energy function that indicates the positional information of the saliency. The procedure is advantageous for improving prediction accuracy and reducing computational complexity. The validation and comparison are made by several accuracy metrics on two ground truth datasets. Experimental results show that the proposed saliency detection model achieves superior performances over several state-of-the-art compressed-domain and pixel-domain algorithms on evaluation metrics. Computationally, our algorithm reduces 26% more computational complexity with comparison to similar algorithms.
Jin, Ick Hoon; Yuan, Ying; Bandyopadhyay, Dipankar
2016-01-01
Research in dental caries generates data with two levels of hierarchy: that of a tooth overall and that of the different surfaces of the tooth. The outcomes often exhibit spatial referencing among neighboring teeth and surfaces, i.e., the disease status of a tooth or surface might be influenced by the status of a set of proximal teeth/surfaces. Assessments of dental caries (tooth decay) at the tooth level yield binary outcomes indicating the presence/absence of teeth, and trinary outcomes at the surface level indicating healthy, decayed, or filled surfaces. The presence of these mixed discrete responses complicates the data analysis under a unified framework. To mitigate complications, we develop a Bayesian two-level hierarchical model under suitable (spatial) Markov random field assumptions that accommodates the natural hierarchy within the mixed responses. At the first level, we utilize an autologistic model to accommodate the spatial dependence for the tooth-level binary outcomes. For the second level and conditioned on a tooth being non-missing, we utilize a Potts model to accommodate the spatial referencing for the surface-level trinary outcomes. The regression models at both levels were controlled for plausible covariates (risk factors) of caries, and remain connected through shared parameters. To tackle the computational challenges in our Bayesian estimation scheme caused due to the doubly-intractable normalizing constant, we employ a double Metropolis-Hastings sampler. We compare and contrast our model performances to the standard non-spatial (naive) model using a small simulation study, and illustrate via an application to a clinical dataset on dental caries. PMID:27807470
Random-field Potts model for the polar domains of lead magnesium niobate and lead scandium tantalate
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.
Recognition of 3-D objects based on Markov random field models
HUANG Ying; DING Xiao-qing; WANG Sheng-jin
2006-01-01
The recognition of 3-D objects is quite a difficult task for computer vision systems.This paper presents a new object framework,which utilizes densely sampled grids with different resolutions to represent the local information of the input image.A Markov random field model is then created to model the geometric distribution of the object key nodes.Flexible matching,which aims to find the accurate correspondence map between the key points of two images,is performed by combining the local similarities and the geometric relations together using the highest confidence first method.Afterwards,a global similarity is calculated for object recognition. Experimental results on Coil-100 object database,which consists of 7 200 images of 100 objects,are presented.When the numbers of templates vary from 4,8,18 to 36 for each object,and the remaining images compose the test sets,the object recognition rates are 95.75 %,99.30 %,100.0 % and 100.0 %,respectively.The excellent recognition performance is much better than those of the other cited references,which indicates that our approach is well-suited for appearance-based object recognition.
Automatic lung tumor segmentation on PET/CT images using fuzzy Markov random field model.
Guo, Yu; Feng, Yuanming; Sun, Jian; Zhang, Ning; Lin, Wang; Sa, Yu; Wang, Ping
2014-01-01
The combination of positron emission tomography (PET) and CT images provides complementary functional and anatomical information of human tissues and it has been used for better tumor volume definition of lung cancer. This paper proposed a robust method for automatic lung tumor segmentation on PET/CT images. The new method is based on fuzzy Markov random field (MRF) model. The combination of PET and CT image information is achieved by using a proper joint posterior probability distribution of observed features in the fuzzy MRF model which performs better than the commonly used Gaussian joint distribution. In this study, the PET and CT simulation images of 7 non-small cell lung cancer (NSCLC) patients were used to evaluate the proposed method. Tumor segmentations with the proposed method and manual method by an experienced radiation oncologist on the fused images were performed, respectively. Segmentation results obtained with the two methods were similar and Dice's similarity coefficient (DSC) was 0.85 ± 0.013. It has been shown that effective and automatic segmentations can be achieved with this method for lung tumors which locate near other organs with similar intensities in PET and CT images, such as when the tumors extend into chest wall or mediastinum.
Automatic Lung Tumor Segmentation on PET/CT Images Using Fuzzy Markov Random Field Model
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.
Min Chen
2011-04-01
Full Text Available Genome-wide association studies (GWAS examine a large number of markers across the genome to identify associations between genetic variants and disease. Most published studies examine only single markers, which may be less informative than considering multiple markers and multiple genes jointly because genes may interact with each other to affect disease risk. Much knowledge has been accumulated in the literature on biological pathways and interactions. It is conceivable that appropriate incorporation of such prior knowledge may improve the likelihood of making genuine discoveries. Although a number of methods have been developed recently to prioritize genes using prior biological knowledge, such as pathways, most methods treat genes in a specific pathway as an exchangeable set without considering the topological structure of a pathway. However, how genes are related with each other in a pathway may be very informative to identify association signals. To make use of the connectivity information among genes in a pathway in GWAS analysis, we propose a Markov Random Field (MRF model to incorporate pathway topology for association analysis. We show that the conditional distribution of our MRF model takes on a simple logistic regression form, and we propose an iterated conditional modes algorithm as well as a decision theoretic approach for statistical inference of each gene's association with disease. Simulation studies show that our proposed framework is more effective to identify genes associated with disease than a single gene-based method. We also illustrate the usefulness of our approach through its applications to a real data example.
Singular-potential random-matrix model arising in mean-field glassy systems.
Akemann, Gernot; Villamaina, Dario; Vivo, Pierpaolo
2014-06-01
We consider an invariant random matrix ensemble where the standard Gaussian potential is distorted by an additional single pole of arbitrary fixed order. Potentials with first- and second-order poles have been considered previously and found applications in quantum chaos and number theory. Here we present an application to mean-field glassy systems. We derive and solve the loop equation in the planar limit for the corresponding class of potentials. We find that the resulting mean or macroscopic spectral density is generally supported on two disconnected intervals lying on the two sides of the repulsive pole, whose edge points can be completely determined imposing the additional constraint of traceless matrices on average. For an unbounded potential with an attractive pole, we also find a possible one-cut solution for certain values of the couplings, which is ruled out when the traceless condition is imposed. Motivated by the calculation of the distribution of the spin-glass susceptibility in the Sherrington-Kirkpatrick spin-glass model, we consider in detail a second-order pole for a zero-trace model and provide the most explicit solution in this case. In the limit of a vanishing pole, we recover the standard semicircle. Working in the planar limit, our results apply to matrices with orthogonal, unitary, and symplectic invariance. Numerical simulations and an independent analytical Coulomb fluid calculation for symmetric potentials provide an excellent confirmation of our results.
Singular-potential random-matrix model arising in mean-field glassy systems
Akemann, Gernot; Villamaina, Dario; Vivo, Pierpaolo
2014-06-01
We consider an invariant random matrix ensemble where the standard Gaussian potential is distorted by an additional single pole of arbitrary fixed order. Potentials with first- and second-order poles have been considered previously and found applications in quantum chaos and number theory. Here we present an application to mean-field glassy systems. We derive and solve the loop equation in the planar limit for the corresponding class of potentials. We find that the resulting mean or macroscopic spectral density is generally supported on two disconnected intervals lying on the two sides of the repulsive pole, whose edge points can be completely determined imposing the additional constraint of traceless matrices on average. For an unbounded potential with an attractive pole, we also find a possible one-cut solution for certain values of the couplings, which is ruled out when the traceless condition is imposed. Motivated by the calculation of the distribution of the spin-glass susceptibility in the Sherrington-Kirkpatrick spin-glass model, we consider in detail a second-order pole for a zero-trace model and provide the most explicit solution in this case. In the limit of a vanishing pole, we recover the standard semicircle. Working in the planar limit, our results apply to matrices with orthogonal, unitary, and symplectic invariance. Numerical simulations and an independent analytical Coulomb fluid calculation for symmetric potentials provide an excellent confirmation of our results.
Random-field Ising model on isometric lattices: Ground states and non-Porod scattering
Bupathy, Arunkumar; Banerjee, Varsha; Puri, Sanjay
2016-01-01
We use a computationally efficient graph cut method to obtain ground state morphologies of the random-field Ising model (RFIM) on (i) simple cubic (SC), (ii) body-centered cubic (BCC), and (iii) face-centered cubic (FCC) lattices. We determine the critical disorder strength Δc at zero temperature with high accuracy. For the SC lattice, our estimate (Δc=2.278 ±0.002 ) is consistent with earlier reports. For the BCC and FCC lattices, Δc=3.316 ±0.002 and 5.160 ±0.002 , respectively, which are the most accurate estimates in the literature to date. The small-r behavior of the correlation function exhibits a cusp regime characterized by a cusp exponent α signifying fractal interfaces. In the paramagnetic phase, α =0.5 ±0.01 for all three lattices. In the ferromagnetic phase, the cusp exponent shows small variations due to the lattice structure. Consequently, the interfacial energy Ei(L ) for an interface of size L is significantly different for the three lattices. This has important implications for nonequilibrium properties.
da Silva, W. P.; de Arruda, P. H. Z.; Tunes, T. M.; Godoy, M.; de Arruda, A. S.
2017-01-01
We have studied the effects of the random single-ion anisotropy and random magnetic field in the phase diagram and in the thermodynamic properties of the spin-3/2 Blume-Capel model via Curie-Weiss mean-field approximation. The phase diagrams were built in the planes temperature versus single-ion anisotropy, temperature versus magnetic field, temperature versus random parameters and the dependencies of magnetization were plotted versus temperature and single-ion anisotropy. These diagrams show that, in the space (D / J - T / J) , the type (first- or second-order) of the phase transition between the ferromagnetic and paramagnetic phases is dependent on the random parameters. Therefore, within these conditions the model presents tricritical behavior. For large values, and a certain critical value of the random parameters, the phase transition is only of second-order, but it is of first-order within the ordered phase, between the phase with m = 1 / 2 and m = 3 / 2 , which ends in a terminal critical point.
Morais, C. V.; Zimmer, F. M.; Lazo, M. J.; Magalhães, S. G.; Nobre, F. D.
2016-06-01
The behavior of the nonlinear susceptibility χ3 and its relation to the spin-glass transition temperature Tf in the presence of random fields are investigated. To accomplish this task, the Sherrington-Kirkpatrick model is studied through the replica formalism, within a one-step replica-symmetry-breaking procedure. In addition, the dependence of the Almeida-Thouless eigenvalue λAT (replicon) on the random fields is analyzed. Particularly, in the absence of random fields, the temperature Tf can be traced by a divergence in the spin-glass susceptibility χSG, which presents a term inversely proportional to the replicon λAT. As a result of a relation between χSG and χ3, the latter also presents a divergence at Tf, which comes as a direct consequence of λAT=0 at Tf. However, our results show that, in the presence of random fields, χ3 presents a rounded maximum at a temperature T* which does not coincide with the spin-glass transition temperature Tf (i.e., T*>Tf for a given applied random field). Thus, the maximum value of χ3 at T* reflects the effects of the random fields in the paramagnetic phase instead of the nontrivial ergodicity breaking associated with the spin-glass phase transition. It is also shown that χ3 still maintains a dependence on the replicon λAT, although in a more complicated way as compared with the case without random fields. These results are discussed in view of recent observations in the LiHoxY1 -xF4 compound.
Adaptive multi-GPU Exchange Monte Carlo for the 3D Random Field Ising Model
Navarro, Cristóbal A.; Huang, Wei; Deng, Youjin
2016-08-01
This work presents an adaptive multi-GPU Exchange Monte Carlo approach for the simulation of the 3D Random Field Ising Model (RFIM). The design is based on a two-level parallelization. The first level, spin-level parallelism, maps the parallel computation as optimal 3D thread-blocks that simulate blocks of spins in shared memory with minimal halo surface, assuming a constant block volume. The second level, replica-level parallelism, uses multi-GPU computation to handle the simulation of an ensemble of replicas. CUDA's concurrent kernel execution feature is used in order to fill the occupancy of each GPU with many replicas, providing a performance boost that is more notorious at the smallest values of L. In addition to the two-level parallel design, the work proposes an adaptive multi-GPU approach that dynamically builds a proper temperature set free of exchange bottlenecks. The strategy is based on mid-point insertions at the temperature gaps where the exchange rate is most compromised. The extra work generated by the insertions is balanced across the GPUs independently of where the mid-point insertions were performed. Performance results show that spin-level performance is approximately two orders of magnitude faster than a single-core CPU version and one order of magnitude faster than a parallel multi-core CPU version running on 16-cores. Multi-GPU performance is highly convenient under a weak scaling setting, reaching up to 99 % efficiency as long as the number of GPUs and L increase together. The combination of the adaptive approach with the parallel multi-GPU design has extended our possibilities of simulation to sizes of L = 32 , 64 for a workstation with two GPUs. Sizes beyond L = 64 can eventually be studied using larger multi-GPU systems.
Albert, Lena; Rottensteiner, Franz; Heipke, Christian
2017-08-01
We propose a new approach for the simultaneous classification of land cover and land use considering spatial as well as semantic context. We apply a Conditional Random Fields (CRF) consisting of a land cover and a land use layer. In the land cover layer of the CRF, the nodes represent super-pixels; in the land use layer, the nodes correspond to objects from a geospatial database. Intra-layer edges of the CRF model spatial dependencies between neighbouring image sites. All spatially overlapping sites in both layers are connected by inter-layer edges, which leads to higher order cliques modelling the semantic relation between all land cover and land use sites in the clique. A generic formulation of the higher order potential is proposed. In order to enable efficient inference in the two-layer higher order CRF, we propose an iterative inference procedure in which the two classification tasks mutually influence each other. We integrate contextual relations between land cover and land use in the classification process by using contextual features describing the complex dependencies of all nodes in a higher order clique. These features are incorporated in a discriminative classifier, which approximates the higher order potentials during the inference procedure. The approach is designed for input data based on aerial images. Experiments are carried out on two test sites to evaluate the performance of the proposed method. The experiments show that the classification results are improved compared to the results of a non-contextual classifier. For land cover classification, the result is much more homogeneous and the delineation of land cover segments is improved. For the land use classification, an improvement is mainly achieved for land use objects showing non-typical characteristics or similarities to other land use classes. Furthermore, we have shown that the size of the super-pixels has an influence on the level of detail of the classification result, but also on the
Xi F. XU
2015-01-01
The Green-function-based multiscale stochastic finite element method （MSFEM） has been formulated based on the stochastic variational principle. In this study a fast computing procedure based on the MSFEM is developed to solve random field geotechnical problems with a typical coefficient of variance less than 1. A unique fast computing advantage of the procedure enables computation performed only on those locations of interest, therefore saving a lot of computation. The numerical example on soil settlement shows that the procedure achieves significant computing efficiency compared with Monte Carlo method.
Mixed spin Ising model with four-spin interaction and random crystal field
Benayad, N., E-mail: n.benayad@fsac.ac.ma [Groupe de Mecanique Statistique, Laboratoire de physique theorique et appliquee, Faculte des sciences-Aien Chock, Universite Hassan II-Casablanca, B.P 5366 Maarif, Casablanca 20100 (Morocco); Laboratoire de physique des hautes energies et de la matiere condensee, Faculte des sciences-Aien Chock, Universite Hassan II-Casablanca, B.P 5366 Maarif, Casablanca 20100 (Morocco); Ghliyem, M. [Groupe de Mecanique Statistique, Laboratoire de physique theorique et appliquee, Faculte des sciences-Aien Chock, Universite Hassan II-Casablanca, B.P 5366 Maarif, Casablanca 20100 (Morocco); Laboratoire de physique des hautes energies et de la matiere condensee, Faculte des sciences-Aien Chock, Universite Hassan II-Casablanca, B.P 5366 Maarif, Casablanca 20100 (Morocco)
2012-01-01
The effects of fluctuations of the crystal field on the phase diagram of the mixed spin-1/2 and spin-1 Ising model with four-spin interactions are investigated within the finite cluster approximation based on a single-site cluster theory. The state equations are derived for the two-dimensional square lattice. It has been found that the system exhibits a variety of interesting features resulting from the fluctuation of the crystal field interactions. In particular, for low mean value D of the crystal field, the critical temperature is not very sensitive to fluctuations and all transitions are of second order for any value of the four-spin interactions. But for relatively high D, the transition temperature depends on the fluctuation of the crystal field, and the system undergoes tricritical behaviour for any strength of the four-spin interactions. We have also found that the model may exhibit reentrance for appropriate values of the system parameters.
Hartford, Edward John
This position-space renormalization-group study focuses on two systems with quenched disorder: the Ising spin glass and the asymmetric random-field Ising model. We have employed the Migdal-Kadanoff approach to determine local recursion relations and have retained the full correlated probability distribution of interactions and fields at each iteration in a series of histograms. We find an equilibrium spin-glass phase in three dimensions, but not in two. The spin glass is characterized by a distribution of effective interactions that broadens under iteration, signaling both the long-range order of the phase and the importance of competing interactions on all length scales. We have introduced a method to calculate the distribution of local properties by differentiating the free energy with respect to a particular magnetic field or interaction. Within the spin-glass phase, the nearest neighbor correlation ranges from negative one to one, showing the strong correlations and the local variation within the phase. The spin-glass-to-paramagnet phase transition is second order, with a smooth specific heat indicated by a negative critical exponent alpha. The multicritical point separating the spin-glass, paramagnetic, and ferromagnetic phases lies along the Nishimori line and also has a nondivergent specific heat. When the system undergoes quenched dilution, the resulting critical and multicritical behaviors are identical to those of the undiluted system. Even the addition of an infinitesimal magnetic field destroys the long-range spin-glass order; however, the characteristic broadening of the distribution continues for several iterations for small fields and low temperatures, suggesting the persistence of sizable spin-glass domains. Our study of the asymmetric random-field Ising model is motivated by recent experiments on phase transitions in porous media and mean-field treatments, which suggest that new critical behavior could occur when the distribution of fields is
Iacobelli, Giulio; Kuelske, Christof
We consider a general class of disordered mean-field models where both the spin variables and disorder variables eta take finitely many values. To investigate the size-dependence in the phase-transition regime we construct the metastate describing the probabilities to find a large system close to a
Brouard, Olivier; Delannay, Fabrice; Ricordel, Vincent; Barba, Dominique
2008-01-01
International audience; In this paper, we proposed a Markov Random field sequence segmentation and regions tracking model, which aims at combining color, texture, and motion features. First a motion-based segmentation is realized. The global motion of the video sequence is estimated and compensated. From the remaining motion information, the motion segmentation is achieved. Then, we use a Markovian approach to update and track over time the video objects. By video object, we mean typically, a...
A Markov random field approach for modeling spatio-temporal evolution of microstructures
Acar, Pinar; Sundararaghavan, Veera
2016-10-01
The following problem is addressed: ‘Can one synthesize microstructure evolution over a large area given experimental movies measured over smaller regions?’ Our input is a movie of microstructure evolution over a small sample window. A Markov random field (MRF) algorithm is developed that uses this data to estimate the evolution of microstructure over a larger region. Unlike the standard microstructure reconstruction problem based on stationary images, the present algorithm is also able to reconstruct time-evolving phenomena such as grain growth. Such an algorithm would decrease the cost of full-scale microstructure measurements by coupling mathematical estimation with targeted small-scale spatiotemporal measurements. The grain size, shape and orientation distribution statistics of synthesized polycrystalline microstructures at different times are compared with the original movie to verify the method.
Roters, L; Lübeck, S; Usadel, K D
2002-12-01
We investigate the depinning transition for driven interfaces in the random-field Ising model for various dimensions. We consider the order parameter as a function of the control parameter (driving field) and examine the effect of thermal fluctuations. Although thermal fluctuations drive the system away from criticality, the order parameter obeys a certain scaling law for sufficiently low temperatures and the corresponding exponents are determined. Our results suggest that the so-called upper critical dimension of the depinning transition is five and that the systems belongs to the universality class of the quenched Edward-Wilkinson equation.
Fu, Chuan-Ji; Zhu, Qin-Sheng; Wu, Shao-Yi
2010-06-01
Based on algebraic dynamics and the concept of the concurrence of the entanglement, we investigate the evolutive properties of the two-qubit entanglement that formed by Heisenberg XXX models under a time-depending external held. For this system, the property of the concurrence that is only dependent on the coupling constant J and total values of the external field is proved. Furthermore, we found that the thermal concurrence of the system under a static random external field is a function of the coupling constant J, temperature T, and the magnitude of external held.
The random field model of the spatial distribution of heavy vehicle loads on long-span bridges
Chen, Zhicheng; Bao, Yuequan; Li, Hui
2016-04-01
A stochastic model based on Markov random field is proposed to model the spatial distribution of vehicle loads on longspan bridges. The bridge deck is divided into a finite set of discrete grid cells, each cell has two states according to whether the cell is occupied by the heavy vehicle load or not, then a four-neighbor lattice-structured undirected graphical model with each node corresponding to a cell state variable is proposed to model the location distribution of heavy vehicle loads on the bridge deck. The node potential is defined to quantitatively describe the randomness of node state, and the edge potential is defined to quantitatively describe the correlation of the connected node pair. The junction tree algorithm is employed to obtain the systematic solutions of inference problems of the graphical model. A marked random variable is assigned to each node to represent the amplitude of the total weight of vehicle applied on the corresponding cell of the bridge deck. The rationality of the model is validated by a Monte Carlo simulation of a learned model based on monitored data of a cable-stayed bridge.
APLIKASI MARKOV RANDOM FIELD PADA MASALAH INDUSTRI
Siana Halim
2002-01-01
Full Text Available Markov chain in the stochastic process is widely used in the industrial problems particularly in the problem of determining the market share of products. In this paper we are going to extend the one in the random field so called the Markov Random Field and applied also in the market share problem with restriction the market is considered as a discrete lattice and Pott's models are going to be used as the potential function. Metropolis sampler is going to be used to determine the stability condition. Abstract in Bahasa Indonesia : Rantai Markov dalam proses stokastik seringkali digunakan dalam penyelesaian masalah industri khususnya dalam masalah penentuan market share. Dalam artikel ini akan dibahas perluasan Rantai Markov tesebut ke dalam sebuah random field yang disebut sebagai Markov Random Field (MRF yang juga akan diaplikasikan pada masalah market share dengan batasan daerah pemasarannya dianggap sebagai sebuah lattice diskrit dan fungsi potensial yang akan digunakan adalah Potts models. Akan digunakan Metropolis sampler untuk menentukan kondisi stabil. Kata kunci: proses stokastik, Markov Random Field, Gibbs Random Field, Potts model, Metropolis sampling.
Bayesian edge detector for SAR imagery using discontinuity-adaptive Markov random field modeling
Yuan Zhan; He You; Cai Fuqing
2013-01-01
Synthetic aperture radar (SAR) image is severely affected by multiplicative speckle noise, which greatly complicates the edge detection. In this paper, by incorporating the discontinuity-adaptive Markov random field (DAMRF) and maximum a posteriori (MAP) estimation criterion into edge detection, a Bayesian edge detector for SAR imagery is accordingly developed. In the pro-posed detector, the DAMRF is used as the a priori distribution of the local mean reflectivity, and a maximum a posteriori estimation of it is thus obtained by maximizing the posteriori energy using gradient-descent method. Four normalized ratios constructed in different directions are computed, based on which two edge strength maps (ESMs) are formed. The final edge detection result is achieved by fusing the results of two thresholded ESMs. The experimental results with synthetic and real SAR images show that the proposed detector could efficiently detect edges in SAR images, and achieve better performance than two popular detectors in terms of Pratt’s figure of merit and visual evaluation in most cases.
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.
Sumedha; Jana, Nabin Kumar
2017-01-01
In this paper we solve the Blume-Capel model on a complete graph in the presence of random crystal field with a distribution, P≤ft({{ Δ }i}\\right)=pδ ≤ft({{ Δ }i}- Δ \\right)+(1-p)δ ≤ft({{ Δ }i}+ Δ \\right) , using large deviation techniques. We find that the first order transition of the pure system is destroyed for 0.046 0.954) even at zero temperature.
Brémaud, Pierre
2017-01-01
The emphasis in this book is placed on general models (Markov chains, random fields, random graphs), universal methods (the probabilistic method, the coupling method, the Stein-Chen method, martingale methods, the method of types) and versatile tools (Chernoff's bound, Hoeffding's inequality, Holley's inequality) whose domain of application extends far beyond the present text. Although the examples treated in the book relate to the possible applications, in the communication and computing sciences, in operations research and in physics, this book is in the first instance concerned with theory. The level of the book is that of a beginning graduate course. It is self-contained, the prerequisites consisting merely of basic calculus (series) and basic linear algebra (matrices). The reader is not assumed to be trained in probability since the first chapters give in considerable detail the background necessary to understand the rest of the book. .
Random field estimation approach to robot dynamics
Rodriguez, Guillermo
1990-01-01
The difference equations of Kalman filtering and smoothing recursively factor and invert the covariance of the output of a linear state-space system driven by a white-noise process. Here it is shown that similar recursive techniques factor and invert the inertia matrix of a multibody robot system. The random field models are based on the assumption that all of the inertial (D'Alembert) forces in the system are represented by a spatially distributed white-noise model. They are easier to describe than the models based on classical mechanics, which typically require extensive derivation and manipulation of equations of motion for complex mechanical systems. With the spatially random models, more primitive locally specified computations result in a global collective system behavior equivalent to that obtained with deterministic models. The primary goal of applying random field estimation is to provide a concise analytical foundation for solving robot control and motion planning problems.
Stochastic modeling and vibration analysis of rotating beams considering geometric random fields
Choi, Chan Kyu; Yoo, Hong Hee
2017-02-01
Geometric parameters such as the thickness and width of a beam are random for various reasons including manufacturing tolerance and operation wear. Due to these random parameter properties, the vibration characteristics of the structure are also random. In this paper, we derive equations of motion to conduct stochastic vibration analysis of a rotating beam using the assumed mode method and stochastic spectral method. The accuracy of the proposed method is first verified by comparing analysis results to those obtained with Monte-Carlo simulation (MCS). The efficiency of the proposed method is then compared to that of MCS. Finally, probability densities of various modal and transient response characteristics of rotating beams are obtained with the proposed method.
Analysis, Simulation and Prediction of Multivariate Random Fields with Package RandomFields
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.
Xu, Jun; Monaco, James P; Madabhushi, Anant
2010-01-01
In this paper we present a Markov random field (MRF) driven region-based active contour model (MaRACel) for medical image segmentation. State-of-the-art region-based active contour (RAC) models assume that every spatial location in the image is statistically independent of the others, thereby ignoring valuable contextual information. To address this shortcoming we incorporate a MRF prior into the AC model, further generalizing Chan & Vese's (CV) and Rousson and Deriche's (RD) AC models. This incorporation requires a Markov prior that is consistent with the continuous variational framework characteristic of active contours; consequently, we introduce a continuous analogue to the discrete Potts model. To demonstrate the effectiveness of MaRACel, we compare its performance to those of the CV and RD AC models in the following scenarios: (1) the qualitative segmentation of a cancerous lesion in a breast DCE-MR image and (2) the qualitative and quantitative segmentations of prostatic acini (glands) in 200 histopathology images. Across the 200 prostate needle core biopsy histology images, MaRACel yielded an average sensitivity, specificity, and positive predictive value of 71%, 95%, 74% with respect to the segmented gland boundaries; the CV and RD models have corresponding values of 19%, 81%, 20% and 53%, 88%, 56%, respectively.
Robinson, Sean; Guyon, Laurent; Nevalainen, Jaakko; Toriseva, Mervi
2015-01-01
Organotypic, three dimensional (3D) cell culture models of epithelial tumour types such as prostate cancer recapitulate key aspects of the architecture and histology of solid cancers. Morphometric analysis of multicellular 3D organoids is particularly important when additional components such as the extracellular matrix and tumour microenvironment are included in the model. The complexity of such models has so far limited their successful implementation. There is a great need for automatic, accurate and robust image segmentation tools to facilitate the analysis of such biologically relevant 3D cell culture models. We present a segmentation method based on Markov random fields (MRFs) and illustrate our method using 3D stack image data from an organotypic 3D model of prostate cancer cells co-cultured with cancer-associated fibroblasts (CAFs). The 3D segmentation output suggests that these cell types are in physical contact with each other within the model, which has important implications for tumour biology. Segmentation performance is quantified using ground truth labels and we show how each step of our method increases segmentation accuracy. We provide the ground truth labels along with the image data and code. Using independent image data we show that our segmentation method is also more generally applicable to other types of cellular microscopy and not only limited to fluorescence microscopy. PMID:26630674
Sean Robinson
Full Text Available Organotypic, three dimensional (3D cell culture models of epithelial tumour types such as prostate cancer recapitulate key aspects of the architecture and histology of solid cancers. Morphometric analysis of multicellular 3D organoids is particularly important when additional components such as the extracellular matrix and tumour microenvironment are included in the model. The complexity of such models has so far limited their successful implementation. There is a great need for automatic, accurate and robust image segmentation tools to facilitate the analysis of such biologically relevant 3D cell culture models. We present a segmentation method based on Markov random fields (MRFs and illustrate our method using 3D stack image data from an organotypic 3D model of prostate cancer cells co-cultured with cancer-associated fibroblasts (CAFs. The 3D segmentation output suggests that these cell types are in physical contact with each other within the model, which has important implications for tumour biology. Segmentation performance is quantified using ground truth labels and we show how each step of our method increases segmentation accuracy. We provide the ground truth labels along with the image data and code. Using independent image data we show that our segmentation method is also more generally applicable to other types of cellular microscopy and not only limited to fluorescence microscopy.
Conditional Random Fields for Image Labeling
Tong Liu
2016-01-01
Full Text Available With the rapid development and application of CRFs (Conditional Random Fields in computer vision, many researchers have made some outstanding progress in this domain because CRFs solve the classical version of the label bias problem with respect to MEMMs (maximum entropy Markov models and HMMs (hidden Markov models. This paper reviews the research development and status of object recognition with CRFs and especially introduces two main discrete optimization methods for image labeling with CRFs: graph cut and mean field approximation. This paper describes graph cut briefly while it introduces mean field approximation more detailedly which has a substantial speed of inference and is researched popularly in recent years.
Markov Random Field Restoration of Point Correspondences for Active Shape Modelling
Hilger, Klaus Baggesen; Paulsen, Rasmus Reinhold; Larsen, Rasmus
2004-01-01
In this paper it is described how to build a statistical shape model using a training set with a sparse of landmarks. A well defined model mesh is selected and fitted to all shapes in the training set using thin plate spline warping. This is followed by a projection of the points of the warped...
Language Recognition Using Latent Dynamic Conditional Random Field Model with Phonological Features
Sirinoot Boonsuk; Atiwong Suchato; Proadpran Punyabukkana; Chai Wutiwiwatchai; Nattanun Thatphithakkul
2014-01-01
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 apply...
Gaussian Markov random fields theory and applications
Rue, Havard
2005-01-01
Gaussian Markov Random Field (GMRF) models are most widely used in spatial statistics - a very active area of research in which few up-to-date reference works are available. This is the first book on the subject that provides a unified framework of GMRFs with particular emphasis on the computational aspects. This book includes extensive case-studies and, online, a c-library for fast and exact simulation. With chapters contributed by leading researchers in the field, this volume is essential reading for statisticians working in spatial theory and its applications, as well as quantitative researchers in a wide range of science fields where spatial data analysis is important.
T. Novack
2015-03-01
Full Text Available In this work we focused on the classification of Urban Settlement Types (USTs based on two datasets from the TerraSAR-X satellite acquired at ascending and descending look directions. These data sets comprise the intensity, amplitude and coherence images from the ascending and descending datasets. In accordance to most official UST maps, the urban blocks of our study site were considered as the elements to be classified. The considered USTs classes in this paper are: Vegetated Areas, Single-Family Houses and Commercial and Residential Buildings. Three different groups of image attributes were utilized, namely: Relative Areas, Histogram of Oriented Gradients and geometrical and contextual attributes extracted from the nodes of a Max-Tree Morphological Profile. These image attributes were submitted to three powerful soft multi-class classification algorithms. In this way, each classifier output a membership value to each of the classes. This membership values were then treated as the potentials of the unary factors of a Conditional Random Fields (CRFs model. The pairwise factors of the CRFs model were parameterised with a Potts function. The reclassification performed with the CRFs model enabled a slight increase of the classification’s accuracy from 76% to 79% out of 1926 urban blocks.
Novack, T.; Stilla, U.
2015-03-01
In this work we focused on the classification of Urban Settlement Types (USTs) based on two datasets from the TerraSAR-X satellite acquired at ascending and descending look directions. These data sets comprise the intensity, amplitude and coherence images from the ascending and descending datasets. In accordance to most official UST maps, the urban blocks of our study site were considered as the elements to be classified. The considered USTs classes in this paper are: Vegetated Areas, Single-Family Houses and Commercial and Residential Buildings. Three different groups of image attributes were utilized, namely: Relative Areas, Histogram of Oriented Gradients and geometrical and contextual attributes extracted from the nodes of a Max-Tree Morphological Profile. These image attributes were submitted to three powerful soft multi-class classification algorithms. In this way, each classifier output a membership value to each of the classes. This membership values were then treated as the potentials of the unary factors of a Conditional Random Fields (CRFs) model. The pairwise factors of the CRFs model were parameterised with a Potts function. The reclassification performed with the CRFs model enabled a slight increase of the classification's accuracy from 76% to 79% out of 1926 urban blocks.
Yisu Lu
2014-01-01
Full Text Available Brain-tumor segmentation is an important clinical requirement for brain-tumor diagnosis and radiotherapy planning. It is well-known that the number of clusters is one of the most important parameters for automatic segmentation. However, it is difficult to define owing to the high diversity in appearance of tumor tissue among different patients and the ambiguous boundaries of lesions. In this study, a nonparametric mixture of Dirichlet process (MDP model is applied to segment the tumor images, and the MDP segmentation can be performed without the initialization of the number of clusters. Because the classical MDP segmentation cannot be applied for real-time diagnosis, a new nonparametric segmentation algorithm combined with anisotropic diffusion and a Markov random field (MRF smooth constraint is proposed in this study. Besides the segmentation of single modal brain-tumor images, we developed the algorithm to segment multimodal brain-tumor images by the magnetic resonance (MR multimodal features and obtain the active tumor and edema in the same time. The proposed algorithm is evaluated using 32 multimodal MR glioma image sequences, and the segmentation results are compared with other approaches. The accuracy and computation time of our algorithm demonstrates very impressive performance and has a great potential for practical real-time clinical use.
Kumar, Manoj; Banerjee, Varsha; Puri, Sanjay
2017-01-01
We perform comprehensive Monte Carlo (MC) simulations to study ordering dynamics in the random field Ising model with conserved order parameter (C-RFIM) in d=2,3 . The observations from this study are: a) For a fixed value of the disorder Δ, the correlation function C(r,t;Δ) exhibits dynamical scaling. b) The scaling function is not robust with respect to Δ, i.e., super-universality (SU) is violated by C(r,t;Δ) . c) At early times, the domains follow the algebraic growth with a disorder-dependent exponent: L(t,Δ)∼ t1/\\bar{z(Δ)} . At late times, there is a crossover to logarithmic growth: L(t,Δ) ∼ (\\ln t)1/\\varphi , where φ is a disorder-independent exponent. d) The small-r behavior of the correlation function exhibits a cusp singularity: 1-C(r) ∼ rα(Δ) , where α is the cusp exponent signifying rough fractal interfaces. e) The corresponding structure factor exhibits a non-Porod tail: S(k,t;Δ)∼ k-(d+α) , and obeys a generalized Tomita sum rule \\int_0^∞ {d}p p1-α≤ft[pd+αf(p)-C\\right]=0 , where f(p) is the appropriate scaling function, and C is a constant.
Large deviations of the finite-time magnetization of the Curie-Weiss random-field Ising model
Paga, Pierre; Kühn, Reimer
2017-08-01
We study the large deviations of the magnetization at some finite time in the Curie-Weiss random field Ising model with parallel updating. While relaxation dynamics in an infinite-time horizon gives rise to unique dynamical trajectories [specified by initial conditions and governed by first-order dynamics of the form mt +1=f (mt) ] , we observe that the introduction of a finite-time horizon and the specification of terminal conditions can generate a host of metastable solutions obeying second-order dynamics. We show that these solutions are governed by a Newtonian-like dynamics in discrete time which permits solutions in terms of both the first-order relaxation ("forward") dynamics and the backward dynamics mt +1=f-1(mt) . Our approach allows us to classify trajectories for a given final magnetization as stable or metastable according to the value of the rate function associated with them. We find that in analogy to the Freidlin-Wentzell description of the stochastic dynamics of escape from metastable states, the dominant trajectories may switch between the two types (forward and backward) of first-order dynamics. Additionally, we show how to compute rate functions when uncertainty in the quenched disorder is introduced.
基于MRF场的SAR图像分割方法%SAR Image Segmentation Based On Markov Random Field Model
张翠; 郦苏丹; 王正志
2001-01-01
In this paper, we propose a SAR image segmentation algorithmbased on Markov Random Field Model. The model captures the image contextual information by making the assumption that the properties of a pixel are dependent upon nearby pixels and are independent of distant pixels. A two-order neighborhood system is used in this paper. The segmentation result is obtained by applying ICM（Iterative Conditional Mode）algorithm. The ICM is an iterative algorithm. During the iteration sequence, each pixel is labeled according to the MAP（maximum a posteriori）criterion. After each pixel labeling step, the parameters of each segmentation class' probability density function are re-estimated from current set of pixel labels. The influence of speckle noise is further reduced by an outlier rejection method. Using this method, outlier pixels are excluded from current pixels' neighborhood. The algorithm is applied to SAR imagery from the MSTAR（Moving and Stationary Target Acquisition and Recognition）datasets. The result shows that this algorithm can efficiently reduce the influence of speckle noise, and segment the image into three parts of target, shadow and background. The experimental results are very satisfactory.%提出了一种基于MRF（Markov Randomfield）模型的SAR（Synthetic ApertureRadar）图像分割算法。本算法利用ICM（Iterative Conditional Mode）局部优化方法，获得MAP（maximum a posteriori）准则下的图像分割结果，并引入了剔除外层数据的机制。用MSTAR（Movingand Stationary Target Acquisitionand Recognition）数据进行实验，结果表明，算法能有效减少斑点噪声的影响，将图像分割为目标、阴影、背景三部分，实验结果是令人满意的。
Sampling Strategies for Fast Updating of Gaussian Markov Random Fields
Brown, D. Andrew; McMahan, Christopher S.
2017-01-01
Gaussian Markov random fields (GMRFs) are popular for modeling temporal or spatial dependence in large areal datasets due to their ease of interpretation and computational convenience afforded by conditional independence and their sparse precision matrices needed for random variable generation. Using such models inside a Markov chain Monte Carlo algorithm requires repeatedly simulating random fields. This is a nontrivial issue, especially when the full conditional precision matrix depends on ...
Sensing Random Electromagnetic Fields and Applications
2015-06-23
AFRL-OSR-VA-TR-2015-0172 SENSING RANDOM ELECTROMAGNETIC FIELDS AND APPLICATIONS Aristide Dogariu UNIVERSITY OF CENTRAL FLORIDA Final Report 06/23... Electromagnetic Fields and Applications 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK...14. ABSTRACT Random electromagnetic fields (REF) exist in all forms and one common origin is a result of the interaction of coherent fields with
Persistent Homology for Random Fields and Complexes
Adler, Robert J; Borman, Matthew S; Subag, Eliran; Weinberger, Shmuel
2010-01-01
We discuss and review recent developments in the area of applied algebraic topology, such as persistent homology and barcodes. In particular, we discuss how these are related to understanding more about manifold learning from random point cloud data, the algebraic structure of simplicial complexes determined by random vertices, and, in most detail, the algebraic topology of the excursion sets of random fields.
Efficient Incorporation of Markov Random Fields in Change Detection
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...
Approximating a harmonizable isotropic random field
Randall J. Swift
2001-01-01
Full Text Available The class of harmonizable fields is a natural extension of the class of stationary fields. This paper considers a stochastic series approximation of a harmonizable isotropic random field. This approximation is useful for numerical simulation of such a field.
Exponential random graph models
Fronczak, Agata
2012-01-01
Nowadays, exponential random graphs (ERGs) are among the most widely-studied network models. Different analytical and numerical techniques for ERG have been developed that resulted in the well-established theory with true predictive power. An excellent basic discussion of exponential random graphs addressed to social science students and researchers is given in [Anderson et al., 1999][Robins et al., 2007]. This essay is intentionally designed to be more theoretical in comparison with the well-known primers just mentioned. Given the interdisciplinary character of the new emerging science of complex networks, the essay aims to give a contribution upon which network scientists and practitioners, who represent different research areas, could build a common area of understanding.
Uniform dimension results for Gaussian random fields
2009-01-01
Let X = {X(t),t ∈ RN} be a Gaussian random field with values in Rd defined by X(t) =(X1(t),...,Xd(t)), t ∈ RN.(1) The properties of space and time anisotropy of X and their connections to uniform Hausdorff dimension results are discussed.It is shown that in general the uniform Hausdorff dimension result does not hold for the image sets of a space-anisotropic Gaussian random field X.When X is an(N,d)-Gaussian random field as in(1),where X1,...,Xd are independent copies of a real valued,centered Gaussian random field X0 which is anisotropic in the time variable.We establish uniform Hausdorff dimension results for the image sets of X.These results extend the corresponding results on one-dimensional Brownian motion,fractional Brownian motion and the Brownian sheet.
Concentration inequalities for random fields via coupling
Chazottes, J. R.; Collet, P.; Kuelske, C.; Redig, F.
We present a new and simple approach to concentration inequalities in the context of dependent random processes and random fields. Our method is based on coupling and does not use information inequalities. In case one has a uniform control on the coupling, one obtains exponential concentration
The Griffiths Singularity Random Field
Enter, Aernout van; Maes, Christian; Schonmann, Roberto H.; Shlosman, Senya
2000-01-01
We consider a spin system on sites of a d-dimensional cubic lattice (d ≥ 2), with the values 0, 1 or -1. It is built over the Bernoulli site percolation model, with spins taking the value 0 on empty sites, and taking values ±1 on occupied sites according to the ferromagnetic Ising model distribution
STAVREV, A.
2013-03-01
The uncertainty of geometric imperfections in a series of nominally equal I-beams leads to a variability of corresponding buckling loads. Its analysis requires a stochastic imperfection model, which can be derived either by the simple variation of the critical eigenmode with a scalar random variable, or with the help of the more advanced theory of random fields. The present paper first provides a concise review of the two different modeling approaches, covering theoretical background, assumptions and calibration, and illustrates their integration into commercial finite element software to conduct stochastic buckling analyses with the Monte-Carlo method. The stochastic buckling behavior of an example beam is then simulated with both stochastic models, calibrated from corresponding imperfection measurements. The simulation results show that for different load cases, the response statistics of the buckling load obtained with the eigenmode-based and the random field-based models agree very well. A comparison of our simulation results with corresponding Eurocode 3 limit loads indicates that the design standard is very conservative for compression dominated load cases. © 2013 World Scientific Publishing Company.
Nonlinear smoothing for random fields
Aihara, Shin Ichi; Bagchi, Arunabha
1995-01-01
Stochastic nonlinear elliptic partial differential equations with white noise disturbances are studied in the countably additive measure set up. Introducing the Onsager-Machlup function to the system model, the smoothing problem for maximizing the modified likelihood functional is solved and the exp
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.
Blanchet, Juliette; Vignes, Matthieu
2009-03-01
The different measurement techniques that interrogate biological systems provide means for monitoring the behavior of virtually all cell components at different scales and from complementary angles. However, data generated in these experiments are difficult to interpret. A first difficulty arises from high-dimensionality and inherent noise of such data. Organizing them into meaningful groups is then highly desirable to improve our knowledge of biological mechanisms. A more accurate picture can be obtained when accounting for dependencies between components (e.g., genes) under study. A second difficulty arises from the fact that biological experiments often produce missing values. When it is not ignored, the latter issue has been solved by imputing the expression matrix prior to applying traditional analysis methods. Although helpful, this practice can lead to unsound results. We propose in this paper a statistical methodology that integrates individual dependencies in a missing data framework. More explicitly, we present a clustering algorithm dealing with incomplete data in a Hidden Markov Random Field context. This tackles the missing value issue in a probabilistic framework and still allows us to reconstruct missing observations a posteriori without imposing any pre-processing of the data. Experiments on synthetic data validate the gain in using our method, and analysis of real biological data shows its potential to extract biological knowledge.
Properties and simulation of α-permanental random fields
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...
Subquantum nonlocal correlations induced by the background random field
Khrennikov, Andrei
2011-10-01
We developed a purely field model of microphenomena—prequantum classical statistical field theory (PCSFT). This model not only reproduces important probabilistic predictions of quantum mechanics (QM) including correlations for entangled systems, but also gives a possibility to go beyond QM, i.e. to make predictions of phenomena that could be observed at the subquantum level. In this paper, we discuss one such prediction—the existence of nonlocal correlations between prequantum random fields corresponding to all quantum systems. (And by PCSFT, quantum systems are represented by classical Gaussian random fields and quantum observables by quadratic forms of these fields.) The source of these correlations is the common background field. Thus all prequantum random fields are 'entangled', but in the sense of classical signal theory. On the one hand, PCSFT demystifies quantum nonlocality by reducing it to nonlocal classical correlations based on the common random background. On the other hand, it demonstrates total generality of such correlations. They exist even for distinguishable quantum systems in factorizable states (by PCSFT terminology—for Gaussian random fields with covariance operators corresponding to factorizable quantum states).
Bandiera, Rino
2016-01-01
The maps of intensity and polarization of the radio synchrotron emission from shell-type supernova remnants (SNRs) contain a considerable amount of information, although of not easy interpretation. With the aim of deriving constraints on the 3-D spatial distribution of the emissivity, as well as on the structure of both ordered and random magnetic fields (MFs), we present here a scheme to model maps of the emission and polarization in SNRs. We first generalize the classical treatment of the synchrotron emission to the case in which the MF is composed by an ordered MF plus an isotropic random component, with arbitrary relative strengths. In the case of a power-law particle energy distribution, we derive analytic formulae that formally resemble those for the classical case. We also treat the case of a shock compression of a fully random upstream field and we predict that the polarization fraction in this case should be higher than typically measured in SNRs. We implement the above treatment into a code, which s...
Entropy estimates for simple random fields
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...
Relativistic diffusive motion in random electromagnetic fields
Haba, Z, E-mail: zhab@ift.uni.wroc.pl [Institute of Theoretical Physics, University of Wroclaw, 50-204 Wroclaw, Plac Maxa Borna 9 (Poland)
2011-08-19
We show that the relativistic dynamics in a Gaussian random electromagnetic field can be approximated by the relativistic diffusion of Schay and Dudley. Lorentz invariant dynamics in the proper time leads to the diffusion in the proper time. The dynamics in the laboratory time gives the diffusive transport equation corresponding to the Juettner equilibrium at the inverse temperature {beta}{sup -1} = mc{sup 2}. The diffusion constant is expressed by the field strength correlation function (Kubo's formula).
Aging in the two-dimensional random-field systems
Cheng, Xiang; Ma, Tianyu; Urazhdin, Sergei; Boettcher, Stefan
Random fields introduced into the classical Ising and Heisenberg spin models can roughen the energy landscape, leading to complex nonequilibrium dynamics. The effects of random fields on magnetism have been previously studied in the context of dilute antiferromagnets (AF), impure substrates, and magnetic alloys [ 1 ] . We utilized random-field spin models to simulate the observed magnetic aging in thin-film ferromagnet/antiferromagnet (F/AF) bilayers. Our experiments show extremely slow cooperative relaxation over a wide range of temperatures and magnetic fields [ 2 ] . In our simulations, the experimental system is coarse-grained into a random field Ising model on a 2D square lattice. Monte Carlo simulations indicate that aging processes may be associated with the glassy evolution of the magnetic domain walls, due to the pinning by the random fields. The scaling of the simulated aging agrees well with experiments. Both are consistent with either a small power-law or logarithmic dependence on time. We further discuss the topological effects on aging due to the dimensional crossover from the Ising to the Heisenberg regime. Supported through NSF grant DMR-1207431.
Interfaces in Random Field Ising Systems
Seppälä, Eira
2001-03-01
Domain walls are studied in random field Ising magnets at T=0 in two and three dimensions using exact ground state calculations. In 2D below the random field strength dependent length scale Lb the walls exhibit a super-rough behavior with a roughness exponent greater than unity ζ ~= 1.20 ± 0.05. The nearest-neighbor height difference probability distribution depends on the system size below L_b. Above Lb domains become fractal, ζ ~= 1.(E. T. Seppälä, V. Petäjä, and M. J. Alava, Phys. Rev. E 58), R5217 (1998). The energy fluctuation exponent has a value θ=1, contradicting the exponent relation θ = 2ζ -1 due to the broken scale-invariance, below Lb and vanishes for system sizes above L_b. The broken scale-invariance should be manifest also in Kardar-Parisi-Zhang problem with random-field noise.(E. Frey, U. C. Täuber, and H. K. Janssen, Europhys. Lett. 47), 14 (1999). In 3D there exists a transition between ferromagnetic and paramagnetic phases at the critical random field strength (Δ/J)_c. Below (Δ/J)c the roughness exponent is also greater ζ ~= 0.73 ± 0.03 than the functional-renormalization-group calculation result ζ = (5-d)/3.(D. Fisher, Phys. Rev. Lett. 56), 1964 (1986).(P. Chauve, P. Le Doussal, and K. Wiese, cond-mat/0006056.) The height differences are system size dependent in 3D, as well. The behavior of the domain walls in 2D below Lb with a constant external field, i.e., the random-bulk wetting, is demonstrated.(E. T. Seppälä, I. Sillanpää, and M. J. Alava, unpublished.)
Saldanha Filho, Paulo Carlos
1998-02-01
Stochastic simulation has been employed in petroleum reservoir characterization as a modeling tool able to reconcile information from several different sources. It has the ability to preserve the variability of the modeled phenomena and permits transference of geological knowledge to numerical models of flux, whose predictions on reservoir constitute the main basis for reservoir management decisions. Several stochastic models have been used and/or suggested, depending on the nature of the phenomena to be described. Markov Random Fields (MRFs) appear as an alternative for the modeling of discrete variables, mainly reservoirs with mosaic architecture of facies. In this dissertation, the reader is introduced to the stochastic modeling by MRFs in a generic sense. The main aspects of the technique are reviewed. MRF Conceptual Background is described: its characterization through the Markovian property and the equivalence to Gibbs distributions. The framework for generic modeling of MRFs is described. The classical models of Ising and Potts-Strauss are specific in this context and are related to models of Ising and Potts-Strauss are specific in this context and are related to models used in petroleum reservoir characterization. The problem of parameter estimation is discussed. The maximum pseudolikelihood estimators for some models are presented. Estimators for two models useful for reservoir characterization are developed, and represent a new contribution to the subject. Five algorithms for the Conditional Simulation of MRFs are described: the Metropolis algorithm, the algorithm of German and German (Gibbs sampler), the algorithm of Swendsen-Wang, the algorithm of Wolff, and the algorithm of Flinn. Finally, examples of simulation for some of the models discussed are presented, along with their implications on the modelling of petroleum reservoirs. (author)
Recent progress on the Random Conductance Model
Biskup, Marek
2011-01-01
Recent progress on the understanding of the Random Conductance Model is reviewed and commented. A particular emphasis is on the results on the scaling limit of the random walk among random conductances for almost every realization of the environment, observations on the behavior of the effective resistance as well as the scaling limit of certain models of gradient fields with non-convex interactions. The text is an expanded version of the lecture notes for a course delivered at the 2011 Cornell Summer School on Probability.
Ergodicity and Gaussianity for Spherical Random Fields
Marinucci, Domenico
2009-01-01
We investigate the relationship between ergodicity and asymptotic Gaussianity of isotropic spherical random fields, in the high-resolution (or high-frequency) limit. In particular, our results suggest that under a wide variety of circumstances the two conditions are equivalent, i.e. the sample angular power spectrum may converge to the population value if and only if the underlying field is asymptotically Gaussian, in the high frequency sense. These findings may shed some light on the role of Cosmic Variance in Cosmic Microwave Background (CMB) radiation data analysis.
Guoying Liu
2015-01-01
Full Text Available This paper presents a variation of the fuzzy local information c-means clustering (FLICM algorithm that provides color texture image clustering. The proposed algorithm incorporates region-level spatial, spectral, and structural information in a novel fuzzy way. The new algorithm, called RFLICM, combines FLICM and region-level Markov random field model (RMRF together to make use of large scale interactions between image patches instead of pixels. RFLICM can overcome the weakness of FLICM when dealing with textured images and at the same time enhances the clustering performance. The major characteristic of RFLICM is the use of a region-level fuzzy factor, aiming to guarantee texture homogeneity and preserve region boundaries. Experiments performed on synthetic and remote sensing images show that RFLICM is effective in providing accuracy to color texture images.
Infinite conditional random fields for human behavior analysis
Bousmalis, Konstantinos; Zafeiriou, Stefanos; Morency, Louis-Philippe; Pantic, Maja
2013-01-01
Hidden conditional random fields (HCRFs) are discriminative latent variable models that have been shown to successfully learn the hidden structure of a given classification problem (provided an appropriate validation of the number of hidden states). In this brief, we present the infinite HCRF (iHCRF
Variational Hidden Conditional Random Fields with Coupled Dirichlet Process Mixtures
Bousmalis, K.; Zafeiriou, S.; Morency, L.P.; Pantic, Maja; Ghahramani, Z.
2013-01-01
Hidden Conditional Random Fields (HCRFs) are discriminative latent variable models which have been shown to successfully learn the hidden structure of a given classification problem. An infinite HCRF is an HCRF with a countably infinite number of hidden states, which rids us not only of the necessit
Field and intensity correlation in random media
Sebbah; Pnini; Genack
2000-11-01
We have obtained the spectral and spatial field correlation functions, C(E)(Deltaomega) and C(E)(Deltax), respectively, from measurement of the microwave field spectrum at a series of points along a line on the output of a random dielectric medium. C(E)(Deltaomega) and C(E)(Deltax) are shown to be the Fourier transforms, respectively, of the time of flight distribution, obtained from pulsed measurements, and of the specific intensity. Unlike C(E)(Deltaomega), the imaginary part of C(E)(Deltax) is shown to vanish as a result of the isotropy of the correlation function in the output plane. The complex square of the field correlation function gives the short-range or C1 contribution to the intensity correlation function C. Longer-range contributions to the intensity correlation function are obtained directly by subtracting C1 from C and are in good agreement with theory.
Field-theoretic simulations of random copolymers with structural rigidity.
Mao, Shifan; MacPherson, Quinn; Qin, Jian; Spakowitz, Andrew J
2017-04-12
Copolymers play an important role in a range of soft-materials applications and biological phenomena. Prevalent works on block copolymer phase behavior use flexible chain models and incorporate interactions using a mean-field approximation. However, when phase separation takes place on length scales comparable to a few monomers, the structural rigidity of the monomers becomes important. In addition, concentration fluctuations become significant at short length scales, rendering the mean-field approximation invalid. In this work, we use simulation to address the role of finite monomer rigidity and concentration fluctuations in microphase segregation of random copolymers. Using a field-theoretic Monte-Carlo simulation of semiflexible polymers with random chemical sequences, we generate phase diagrams for random copolymers. We find that the melt morphology of random copolymers strongly depends on chain flexibility and chemical sequence correlation. Chemically anti-correlated copolymers undergo first-order phase transitions to local lamellar structures. With increasing degree of chemical correlation, this first-order phase transition is softened, and melts form microphases with irregular shaped domains. Our simulations in the homogeneous phase exhibit agreement with the density-density correlation from mean-field theory. However, conditions near a phase transition result in deviations between simulation and mean-field theory for the density-density correlation and the critical wavemode. Chain rigidity and sequence randomness lead to frustration in the segregated phase, introducing heterogeneity in the resulting morphologies.
Three-dimensional extinction mapping using Gaussian random fields
Sale, S E
2014-01-01
We present a scheme for using stellar catalogues to map the three-dimensional distributions of extinction and dust within our Galaxy. Extinction is modelled as a Gaussian random field, whose covariance function is set by a simple physical model of the ISM that assumes a Kolmogorov-like power spectrum of turbulent fluctuations. As extinction is modelled as a random field, the spatial resolution of the resulting maps is set naturally by the data available; there is no need to impose any spatial binning. We verify the validity of our scheme by testing it on simulated extinction fields and show that its precision is significantly improved over previous dust-mapping efforts. The approach we describe here can make use of any photometric, spectroscopic or astrometric data; it is not limited to any particular survey. Consequently, it can be applied to a wide range of data from both existing and future surveys.
Fytas, Nikolaos G; Martín-Mayor, Víctor
2016-06-01
It was recently shown [Phys. Rev. Lett. 110, 227201 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.227201] that the critical behavior of the random-field Ising model in three dimensions is ruled by a single universality class. This conclusion was reached only after a proper taming of the large scaling corrections of the model by applying a combined approach of various techniques, coming from the zero- and positive-temperature toolboxes of statistical physics. In the present contribution we provide a detailed description of this combined scheme, explaining in detail the zero-temperature numerical scheme and developing the generalized fluctuation-dissipation formula that allowed us to compute connected and disconnected correlation functions of the model. We discuss the error evolution of our method and we illustrate the infinite limit-size extrapolation of several observables within phenomenological renormalization. We present an extension of the quotients method that allows us to obtain estimates of the critical exponent α of the specific heat of the model via the scaling of the bond energy and we discuss the self-averaging properties of the system and the algorithmic aspects of the maximum-flow algorithm used.
Ashraf, Ahmed B; Gavenonis, Sara; Daye, Dania; Mies, Carolyn; Feldman, Michael; Rosen, Mark; Kontos, Despina
2011-01-01
We present a multichannel extension of Markov random fields (MRFs) for incorporating multiple feature streams in the MRF model. We prove that for making inference queries, any multichannel MRF can be reduced to a single channel MRF provided features in different channels are conditionally independent given the hidden variable, Using this result we incorporate kinetic feature maps derived from breast DCE MRI into the observation model of MRF for tumor segmentation. Our algorithm achieves an ROC AUC of 0.97 for tumor segmentation, We present a comparison against the commonly used approach of fuzzy C-means (FCM) and the more recent method of running FCM on enhancement variance features (FCM-VES). These previous methods give a lower AUC of 0.86 and 0.60 respectively, indicating the superiority of our algorithm. Finally, we investigate the effect of superior segmentation on predicting breast cancer recurrence using kinetic DCE MRI features from the segmented tumor regions. A linear prediction model shows significant prediction improvement when segmenting the tumor using the proposed method, yielding a correlation coefficient r = 0.78 (p < 0.05) to validated cancer recurrence probabilities, compared to 0.63 and 0.45 when using FCM and FCM-VES respectively.
Simulation of heterogeneous two-phase media using random fields and level sets
George STEFANOU[1,2
2015-01-01
The accurate and efficient simulation of random heterogeneous media is important in the framework of modeling and design of complex materials across multiple length scales. It is usually assumed that the morphology of a random microstructure can be described as a non-Gaussian random field that is completely defined by its multivariate distribution. A particular kind of non-Gaussian random fields with great practical importance is that of translation fields resulting from a simple memory-less transformation of an underlying Gaussian field with known second-order statistics. This paper provides a critical examination of existing random field models of heterogeneous two-phase media with emphasis on level-cut random fields which are a special case of translation fields. The case of random level sets, often used to represent the geometry of physical systems, is also examined. Two numerical examples are provided to illustrate the basic features of the different approaches.
Tail Approximations of Integrals of Gaussian Random Fields
Liu, Jingchen
2010-01-01
This paper develops asymptotic approximations of $P(\\int_T e^{f(t)}dt > b)$ as $b\\rightarrow \\infty$ for homogeneous smooth Gaussian random field, $f$, living on a compact $d$-dimensional Jordan measurable set $T$. The integral of exponent of Gaussian random field is an important random variable for many generic models in spatial point processes, portfolio risk analysis, asset pricing and so forth. The analysis technique consists of two steps: 1. evaluate the tail probability $P(\\int_\\Delta e^{f(t)}dt > b)$ over a small domain $\\Delta$ depending on $b$, where $mes(\\Delta) \\rightarrow 0$ as $b\\rightarrow \\infty$ and $mes(\\cdot)$ is the Lebesgue measure; 2. with $\\Delta$ appropriately chosen, we show that $P(\\int_T e^{f(t)}dt > b) =(1+o(1)) mes(T) mes^{-1}(\\Delta) P(\\int_\\Delta e^{f(t)}dt > b)$.
Hu, B.; Li, P.
2013-07-01
Markov random field (MRF) is an effective method for description of local spatial-temporal dependence of image and has been widely used in land cover classification and change detection. However, existing studies only use pair-point clique (PPC) to describe spatial dependence of neighbouring pixels, which may not fully quantify complex spatial relations, particularly in high spatial resolution images. In this study, multi-point clique (MPC) is adopted in MRF model to quantitatively express spatial dependence among pixels. A modified least squares fit (LSF) method based on robust estimation is proposed to calculate potential parameters for MRF models with different types. The proposed MPC-MRF method is evaluated and quantitatively compared with traditional PPCMRF in urban land cover classification using high resolution hyperspectral HYDICE data of Washington DC. The experimental results revealed that the proposed MPC-MRF method outperformed the traditional PPC-MRF method in terms of classification details. The MPC-MRF provides a sophisticated way of describing complex spatial dependence for relevant applications.
Nonstationary random acoustic and electromagnetic fields as wave diffusion processes
Arnaut, L R
2007-01-01
We investigate the effects of relatively rapid variations of the boundaries of an overmoded cavity on the stochastic properties of its interior acoustic or electromagnetic field. For quasi-static variations, this field can be represented as an ideal incoherent and statistically homogeneous isotropic random scalar or vector field, respectively. A physical model is constructed showing that the field dynamics can be characterized as a generalized diffusion process. The Langevin--It\\^{o} and Fokker--Planck equations are derived and their associated statistics and distributions for the complex analytic field, its magnitude and energy density are computed. The energy diffusion parameter is found to be proportional to the square of the ratio of the standard deviation of the source field to the characteristic time constant of the dynamic process, but is independent of the initial energy density, to first order. The energy drift vanishes in the asymptotic limit. The time-energy probability distribution is in general n...
Segmentation of RGB-D indoor scenes by stacking random forests and conditional random fields
Thøgersen, Mikkel; Guerrero, Sergio Escalera; Gonzàlez, Jordi
2016-01-01
on stacked classifiers; the benefits are two fold: on one hand, the system scales well to consider different types of complex features and, on the other hand, the use of stacked classifiers makes the performance of the proposed technique more accurate. The proposed method consists of a random forest using...... a stacked random forest which gives the final predictions. The model is tested on the renown NYU-v2 dataset and the recently available SUNRGBD dataset. The approach shows that simple multimodal features with the power of using multi-class multi-scale stacked sequential learners (MMSSL) can achieve slight...... random offset features in combination with a conditional random field (CRF) acting on a simple linear iterative clustering (SLIC) superpixel segmentation. The predictions of the CRF are filtered spatially by a multi-scale decomposition before merging it with the original feature set and applying...
Conditional random field-based gesture recognition with depth information
Chung, Hyunsook; Yang, Hee-Deok
2013-01-01
Gesture recognition is useful for human-computer interaction. The difficulty of gesture recognition is that instances of gestures vary both in motion and shape in three-dimensional (3-D) space. We use depth information generated using Microsoft's Kinect in order to detect 3-D human body components and apply a threshold model with a conditional random field in order to recognize meaningful gestures using continuous motion information. Body gesture recognition is achieved through a framework consisting of two steps. First, a human subject is described by a set of features, encoding the angular relationship between body components in 3-D space. Second, a feature vector is recognized using a threshold model with a conditional random field. In order to show the performance of the proposed method, we use a public data set, the Microsoft Research Cambridge-12 Kinect gesture database. The experimental results demonstrate that the proposed method can efficiently and effectively recognize body gestures automatically.
Glassy behaviour of random field Ising spins on Bethe lattice in external magnetic field
Khalid Bannora; Galal Ismail; Wafaa Hassan
2011-01-01
The thermodynamics and the phase diagram of random field Ising model (RFIM) on Bethe lattice are studied by using a replica trick. This lattice is placed in an external magnetic field (B). A Gaussian distribution of random field (hi) with zero mean and variance = H2RF is considered. The free-energy (F), the magnetization (M) and the order parameter (q) are investigated for several values of coordination number (z). The phase diagram shows several interesting behaviours and presents tricritical point at critical temperature TC = J/k and when HRF = 0 for finite z. The free-energy (F) values increase as T increases for different intensities of random field (HRF) and finite z. The internal energy (U) has a similar behaviour to that obtained from the Monte Carlo simulations. The ground state of magnetization decreases as the intensity of random field HRF increases. The ferromagnetic (FM)-paramagnetic (PM) phase boundary is clearly observed only when z →∞. While FM-PM-spin glass (SG) phase boundaries are present for finite z. The magnetic susceptibility (X) shows a sharp cusp at TC in a small random field for finite z and rounded different peaks on increasing HRF.
Random Intercept and Random Slope 2-Level Multilevel Models
Rehan Ahmad Khan
2012-11-01
Full Text Available Random intercept model and random intercept & random slope model carrying two-levels of hierarchy in the population are presented and compared with the traditional regression approach. The impact of students’ satisfaction on their grade point average (GPA was explored with and without controlling teachers influence. The variation at level-1 can be controlled by introducing the higher levels of hierarchy in the model. The fanny movement of the fitted lines proves variation of student grades around teachers.
The XXZ Heisenberg model on random surfaces
Ambjørn, J., E-mail: ambjorn@nbi.dk [The Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, DK-2100 Copenhagen (Denmark); Institute for Mathematics, Astrophysics and Particle Physics (IMAPP), Radbaud University Nijmegen, Heyendaalseweg 135, 6525 AJ, Nijmegen (Netherlands); Sedrakyan, A., E-mail: sedrak@nbi.dk [The Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, DK-2100 Copenhagen (Denmark); Yerevan Physics Institute, Br. Alikhanyan str. 2, Yerevan-36 (Armenia)
2013-09-21
We consider integrable models, or in general any model defined by an R-matrix, on random surfaces, which are discretized using random Manhattan lattices. The set of random Manhattan lattices is defined as the set dual to the lattice random surfaces embedded on a regular d-dimensional lattice. They can also be associated with the random graphs of multiparticle scattering nodes. As an example we formulate a random matrix model where the partition function reproduces the annealed average of the XXZ Heisenberg model over all random Manhattan lattices. A technique is presented which reduces the random matrix integration in partition function to an integration over their eigenvalues.
The XXZ Heisenberg model on random surfaces
Ambjorn, J
2013-01-01
We consider integrable models, or in general any model defined by an $R$-matrix, on random surfaces, which are discretized using random Manhattan lattices. The set of random Manhattan lattices is defined as the set dual to the lattice random surfaces embedded on a regular d-dimensional lattice. They can also be associated with the random graphs of multiparticle scattering nodes. As an example we formulate a random matrix model where the partition function reproduces the annealed average of the XXZ Heisenberg model over all random Manhattan lattices. A technique is presented which reduces the random matrix integration in partition function to an integration over their eigenvalues.
Precise Asymptotics for Random Matrices and Random Growth Models
Zhong Gen SU
2008-01-01
The author considers the largest eigenvalues of random matrices from Gaussian unitary ensemble and Laguerre unitary ensemble, and the rightmost charge in certain random growth models.We obtain some precise asymptotics results, which are in a sense similar to the precise asymptotics for sums of independent random variables in the context of the law of large numbers and complete convergence. Our proofs depend heavily upon the upper and lower tail estimates for random matrices and random growth models. The Tracy-Widom distribution plays a central role as well.
Infinite Random Graphs as Statistical Mechanical Models
Durhuus, Bergfinnur Jøgvan; Napolitano, George Maria
2011-01-01
We discuss two examples of infinite random graphs obtained as limits of finite statistical mechanical systems: a model of two-dimensional dis-cretized quantum gravity defined in terms of causal triangulated surfaces, and the Ising model on generic random trees. For the former model we describe...... a relation to the so-called uniform infinite tree and results on the Hausdorff and spectral dimension of two-dimensional space-time obtained in B. Durhuus, T. Jonsson, J.F. Wheater, J. Stat. Phys. 139, 859 (2010) are briefly outlined. For the latter we discuss results on the absence of spontaneous...... magnetization and argue that, in the generic case, the values of the Hausdorff and spectral dimension of the underlying infinite trees are not influenced by the coupling to an Ising model in a constant magnetic field (B. Durhuus, G.M. Napolitano, in preparation)...
Weger, R. C.; Lee, J.; Zhu, Tianri; Welch, R. M.
1992-01-01
The current controversy existing in reference to the regularity vs. clustering in cloud fields is examined by means of analysis and simulation studies based upon nearest-neighbor cumulative distribution statistics. It is shown that the Poisson representation of random point processes is superior to pseudorandom-number-generated models and that pseudorandom-number-generated models bias the observed nearest-neighbor statistics towards regularity. Interpretation of this nearest-neighbor statistics is discussed for many cases of superpositions of clustering, randomness, and regularity. A detailed analysis is carried out of cumulus cloud field spatial distributions based upon Landsat, AVHRR, and Skylab data, showing that, when both large and small clouds are included in the cloud field distributions, the cloud field always has a strong clustering signal.
Heterogeneous Web Data Extraction Algorithm Based On Modified Hidden Conditional Random Fields
Cui Cheng
2014-01-01
As it is of great importance to extract useful information from heterogeneous Web data, in this paper, we propose a novel heterogeneous Web data extraction algorithm using a modified hidden conditional random fields model. Considering the traditional linear chain based conditional random fields can not effectively solve the problem of complex and heterogeneous Web data extraction, we modify the standard hidden conditional random fields in three aspects, which are 1) Using the hidden Markov mo...
Random Dieudonne modules, random p-divisible groups, and random curves over finite fields
Cais, Bryden; Zureick-Brown, David
2012-01-01
We describe a probability distribution on isomorphism classes of principally quasi-polarized p-divisible groups over a finite field k of characteristic p which can reasonably be thought of as "uniform distribution," and we compute the distribution of various statistics (p-corank, a-number, etc.) of p-divisible groups drawn from this distribution. It is then natural to ask to what extent the p-divisible groups attached to a randomly chosen hyperelliptic curve (resp. curve, resp. abelian variety) over k are uniformly distributed in this sense. For instance, one can ask whether the proportion of genus-g curves over F_p whose Jacobian is ordinary approaches the limit that such a heuristic would predict. This heuristic is analogous to conjectures of Cohen-Lenstra type for fields k of characteristic other than p, in which case the random p-divisible group is defined by a random matrix recording the action of Frobenius. Extensive numerical investigation reveals some cases of agreement with the heuristic and some int...
Firmani, C
2013-01-01
In order to attain a statistical description of the evolution of cosmic density fluctuations in agreement with results from the numerical simulations, we introduce a probability conditional formalism (CF) based on an inventory of isolated overdense regions in a density random field. This formalism is a useful tool for describing at the same time the mass function (MF) of dark haloes, their mass aggregation histories (MAHs) and merging rates (MRs). The CF focuses on virialized regions in a self-consistent way rather than in mass elements, and it offers an economical description for a variety of random fields. Within the framework of the CF, we confirm that, for a Gaussian field, it is not possible to reproduce at the same time the MF, MAH, and MR of haloes, both for a constant and moving barrier. Then, we develop an inductive method for constraining the cumulative conditional probability from a given halo MF description, and thus, using the CF, we calculate the halo MAHs and MRs. By applying this method to the...
Grammatical-Restrained Hidden Conditional Random Fields for Bioinformatics applications
Martelli Pier
2009-10-01
Full Text Available Abstract Background Discriminative models are designed to naturally address classification tasks. However, some applications require the inclusion of grammar rules, and in these cases generative models, such as Hidden Markov Models (HMMs and Stochastic Grammars, are routinely applied. Results We introduce Grammatical-Restrained Hidden Conditional Random Fields (GRHCRFs as an extension of Hidden Conditional Random Fields (HCRFs. GRHCRFs while preserving the discriminative character of HCRFs, can assign labels in agreement with the production rules of a defined grammar. The main GRHCRF novelty is the possibility of including in HCRFs prior knowledge of the problem by means of a defined grammar. Our current implementation allows regular grammar rules. We test our GRHCRF on a typical biosequence labeling problem: the prediction of the topology of Prokaryotic outer-membrane proteins. Conclusion We show that in a typical biosequence labeling problem the GRHCRF performs better than CRF models of the same complexity, indicating that GRHCRFs can be useful tools for biosequence analysis applications. Availability GRHCRF software is available under GPLv3 licence at the website http://www.biocomp.unibo.it/~savojard/biocrf-0.9.tar.gz.
Fuzzy Markov random fields versus chains for multispectral image segmentation.
Salzenstein, Fabien; Collet, Christophe
2006-11-01
This paper deals with a comparison of recent statistical models based on fuzzy Markov random fields and chains for multispectral image segmentation. The fuzzy scheme takes into account discrete and continuous classes which model the imprecision of the hidden data. In this framework, we assume the dependence between bands and we express the general model for the covariance matrix. A fuzzy Markov chain model is developed in an unsupervised way. This method is compared with the fuzzy Markovian field model previously proposed by one of the authors. The segmentation task is processed with Bayesian tools, such as the well-known MPM (Mode of Posterior Marginals) criterion. Our goal is to compare the robustness and rapidity for both methods (fuzzy Markov fields versus fuzzy Markov chains). Indeed, such fuzzy-based procedures seem to be a good answer, e.g., for astronomical observations when the patterns present diffuse structures. Moreover, these approaches allow us to process missing data in one or several spectral bands which correspond to specific situations in astronomy. To validate both models, we perform and compare the segmentation on synthetic images and raw multispectral astronomical data.
Reducing RANS Model Error Using Random Forest
Wang, Jian-Xun; Wu, Jin-Long; Xiao, Heng; Ling, Julia
2016-11-01
Reynolds-Averaged Navier-Stokes (RANS) models are still the work-horse tools in the turbulence modeling of industrial flows. However, the model discrepancy due to the inadequacy of modeled Reynolds stresses largely diminishes the reliability of simulation results. In this work we use a physics-informed machine learning approach to improve the RANS modeled Reynolds stresses and propagate them to obtain the mean velocity field. Specifically, the functional forms of Reynolds stress discrepancies with respect to mean flow features are trained based on an offline database of flows with similar characteristics. The random forest model is used to predict Reynolds stress discrepancies in new flows. Then the improved Reynolds stresses are propagated to the velocity field via RANS equations. The effects of expanding the feature space through the use of a complete basis of Galilean tensor invariants are also studied. The flow in a square duct, which is challenging for standard RANS models, is investigated to demonstrate the merit of the proposed approach. The results show that both the Reynolds stresses and the propagated velocity field are improved over the baseline RANS predictions. SAND Number: SAND2016-7437 A
A Mixed Effects Randomized Item Response Model
Fox, J.-P.; Wyrick, Cheryl
2008-01-01
The randomized response technique ensures that individual item responses, denoted as true item responses, are randomized before observing them and so-called randomized item responses are observed. A relationship is specified between randomized item response data and true item response data. True item response data are modeled with a (non)linear…
Wiegelmann, Thomas; Petrie, Gordon J. D.; Riley, Pete
2017-09-01
Coronal magnetic field models use photospheric field measurements as boundary condition to model the solar corona. We review in this paper the most common model assumptions, starting from MHD-models, magnetohydrostatics, force-free and finally potential field models. Each model in this list is somewhat less complex than the previous one and makes more restrictive assumptions by neglecting physical effects. The magnetohydrostatic approach neglects time-dependent phenomena and plasma flows, the force-free approach neglects additionally the gradient of the plasma pressure and the gravity force. This leads to the assumption of a vanishing Lorentz force and electric currents are parallel (or anti-parallel) to the magnetic field lines. Finally, the potential field approach neglects also these currents. We outline the main assumptions, benefits and limitations of these models both from a theoretical (how realistic are the models?) and a practical viewpoint (which computer resources to we need?). Finally we address the important problem of noisy and inconsistent photospheric boundary conditions and the possibility of using chromospheric and coronal observations to improve the models.
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...
Parabolic Anderson Model in a Dynamic Random Environment: Random Conductances
Erhard, D.; den Hollander, F.; Maillard, G.
2016-06-01
The parabolic Anderson model is defined as the partial differential equation ∂ u( x, t)/ ∂ t = κ Δ u( x, t) + ξ( x, t) u( x, t), x ∈ ℤ d , t ≥ 0, where κ ∈ [0, ∞) is the diffusion constant, Δ is the discrete Laplacian, and ξ is a dynamic random environment that drives the equation. The initial condition u( x, 0) = u 0( x), x ∈ ℤ d , is typically taken to be non-negative and bounded. The solution of the parabolic Anderson equation describes the evolution of a field of particles performing independent simple random walks with binary branching: particles jump at rate 2 d κ, split into two at rate ξ ∨ 0, and die at rate (- ξ) ∨ 0. In earlier work we looked at the Lyapunov exponents λ p(κ ) = limlimits _{tto ∞} 1/t log {E} ([u(0,t)]p)^{1/p}, quad p in {N} , qquad λ 0(κ ) = limlimits _{tto ∞} 1/2 log u(0,t). For the former we derived quantitative results on the κ-dependence for four choices of ξ : space-time white noise, independent simple random walks, the exclusion process and the voter model. For the latter we obtained qualitative results under certain space-time mixing conditions on ξ. In the present paper we investigate what happens when κΔ is replaced by Δ𝓚, where 𝓚 = {𝓚( x, y) : x, y ∈ ℤ d , x ˜ y} is a collection of random conductances between neighbouring sites replacing the constant conductances κ in the homogeneous model. We show that the associated annealed Lyapunov exponents λ p (𝓚), p ∈ ℕ, are given by the formula λ p({K} ) = {sup} {λ p(κ ) : κ in {Supp} ({K} )}, where, for a fixed realisation of 𝓚, Supp(𝓚) is the set of values taken by the 𝓚-field. We also show that for the associated quenched Lyapunov exponent λ 0(𝓚) this formula only provides a lower bound, and we conjecture that an upper bound holds when Supp(𝓚) is replaced by its convex hull. Our proof is valid for three classes of reversible ξ, and for all 𝓚
Measuring marine oil spill extent by Markov Random Fields
Moctezuma, Miguel; Parmiggiani, Flavio; Lopez Lopez, Ludwin
2014-10-01
The Deepwater Horizon oil spill of the Gulf of Mexico in the spring of 2010 was the largest accidental marine oil spill in the history of the petroleum industry. An immediate request, after the accident, was to detect the oil slick and to measure its extent: SAR images were the obvious tool to be employed for the task. This paper presents a processing scheme based on Markov Random Fields (MRF) theory. MRF theory describes the global information by probability terms involving local neighborhood representations of the SAR backscatter data. The random degradation introduced by speckle noise is dealt with a pre-processing stage which applies a nonlinear diffusion filter. Spatial context attributes are structured by the Bayes equation derived from a Maximum-A-Posteriori (MAP) estimation. The probability terms define an objective function of a MRF model whose goal is to detect contours and fine structures. The markovian segmentation problem is solved with a numerical optimization method. The scheme was applied to an Envisat/ASAR image over the Gulf of Mexico of May 9, 2010, when the oil spill was already fully developed. The final result was obtained with 51 recursion cycles, where, at each step, the segmentation consists of a 3-class label field (open sea and two oil slick thicknesses). Both the MRF model and the parameters of the stochastic optimization procedure will be provided, together with the area measurement of the two kinds of oil slick.
Realization of random-field Ising ferromagnetism in a molecular magnet
Wen, Bo; Subedi, P.; Bo, Lin; Yeshurun, Y.; Sarachik, M. P.; Kent, A. D.; Millis, A. J.; Lampropoulos, C.; Christou, G.
2010-07-01
The longitudinal magnetic susceptibility of single crystals of the molecular magnet Mn12 -acetate obeys a Curie-Weiss law, indicating a transition to a ferromagnetic phase at ˜0.9K . With increasing magnetic field applied transverse to the easy axis, a marked change is observed in the temperature dependence of the susceptibility, and the suppression of ferromagnetism is considerably more rapid than predicted by mean-field theory for an ordered single crystal. Our results can instead be fit by a Hamiltonian for a random-field Ising ferromagnet in a transverse magnetic field, where the randomness derives from the intrinsic distribution of locally tilted magnetic easy axes known to exist in Mn12 -acetate crystals, suggesting that Mn12 -acetate is a realization of the random-field Ising model in which the random field may be tuned by a field applied transverse to the easy axis.
Generalization of Random Intercept Multilevel Models
Rehan Ahmad Khan
2013-10-01
Full Text Available The concept of random intercept models in a multilevel model developed by Goldstein (1986 has been extended for k-levels. The random variation in intercepts at individual level is marginally split into components by incorporating higher levels of hierarchy in the single level model. So, one can control the random variation in intercepts by incorporating the higher levels in the model.
CLOUD IMAGE DETECTION BASED ON MARKOV RANDOM FIELD
Xu Xuemei; Guo Yuanwei; Wang Zhenfei
2012-01-01
In order to overcome the disadvantages of low accuracy rate,high complexity and poor robustness to image noise in many traditional algorithms of cloud image detection,this paper proposed a novel algorithm on the basis of Markov Random Field (MRF) modeling.This paper first defined algorithm model and derived the core factors affecting the performance of the algorithm,and then,the solving of this algorithm was obtained by the use of Belief Propagation (BP) algorithm and Iterated Conditional Modes (ICM) algorithm.Finally,experiments indicate that this algorithm for the cloud image detection has higher average accuracy rate which is about 98.76％ and the average result can also reach 96.92％ for different type of image noise.
Hidden Conditional Random Fields for Action Recognition
Chen, L.; van der Aa, N.P.; Tan, R.T.; Veltkamp, R.C.
2014-01-01
In the field of action recognition, the design of features has been explored extensively, but the choice of action classification methods is limited. Commonly used classification methods like k-Nearest Neighbors and Support Vector Machines assume conditional independency between features. In contras
A dissipative random velocity field for fully developed fluid turbulence
Chevillard, Laurent; Pereira, Rodrigo; Garban, Christophe
2016-11-01
We investigate the statistical properties, based on numerical simulations and analytical calculations, of a recently proposed stochastic model for the velocity field of an incompressible, homogeneous, isotropic and fully developed turbulent flow. A key step in the construction of this model is the introduction of some aspects of the vorticity stretching mechanism that governs the dynamics of fluid particles along their trajectory. An additional further phenomenological step aimed at including the long range correlated nature of turbulence makes this model depending on a single free parameter that can be estimated from experimental measurements. We confirm the realism of the model regarding the geometry of the velocity gradient tensor, the power-law behaviour of the moments of velocity increments, including the intermittent corrections, and the existence of energy transfers across scales. We quantify the dependence of these basic properties of turbulent flows on the free parameter and derive analytically the spectrum of exponents of the structure functions in a simplified non dissipative case. A perturbative expansion shows that energy transfers indeed take place, justifying the dissipative nature of this random field.
Bi-Spectrum Scattering Model for Conducting Randomly Rough Surface
刘宁; 李宗谦
2002-01-01
A scattering model is developed to predict the scattering coefficient of a conducting randomly rough surface by analyzing the randomly rough surface in the spectral domain using the bi-spectrum method. For common randomly rough surfaces without obvious two-scale characteristics, a scale-compression filter can divide the auto-correlation spectrum into two parts with different correlation lengths. The Kirchhoff approximation and the small perturbation method are used to obtain the surface field, then a bistatic scattering model, the bi-spectrum model (BSM), is used to derive an explicit expression from the surface field. Examples using the integral equation model (IEM), finite difference of the time domain (FDTD) method, and BSM show that the BSM accuracy is acceptable and its range of validity is similar to IEM. BSM can also be extended to a scattering model for dielectric randomly rough surfaces.
The parabolic Anderson model random walk in random potential
König, Wolfgang
2016-01-01
This is a comprehensive survey on the research on the parabolic Anderson model – the heat equation with random potential or the random walk in random potential – of the years 1990 – 2015. The investigation of this model requires a combination of tools from probability (large deviations, extreme-value theory, e.g.) and analysis (spectral theory for the Laplace operator with potential, variational analysis, e.g.). We explain the background, the applications, the questions and the connections with other models and formulate the most relevant results on the long-time behavior of the solution, like quenched and annealed asymptotics for the total mass, intermittency, confinement and concentration properties and mass flow. Furthermore, we explain the most successful proof methods and give a list of open research problems. Proofs are not detailed, but concisely outlined and commented; the formulations of some theorems are slightly simplified for better comprehension.
Random Effect and Latent Variable Model Selection
Dunson, David B
2008-01-01
Presents various methods for accommodating model uncertainty in random effects and latent variable models. This book focuses on frequentist likelihood ratio and score tests for zero variance components. It also focuses on Bayesian methods for random effects selection in linear mixed effects and generalized linear mixed models
Infinite Random Graphs as Statistical Mechanical Models
Durhuus, Bergfinnur Jøgvan; Napolitano, George Maria
2011-01-01
We discuss two examples of infinite random graphs obtained as limits of finite statistical mechanical systems: a model of two-dimensional dis-cretized quantum gravity defined in terms of causal triangulated surfaces, and the Ising model on generic random trees. For the former model we describe...
Distributed estimation of a parametric field with random sensor placements
Alkhweldi, Marwan; Cao, Zhicheng; Schmid, Natalia A.
2015-05-01
This paper considers a problem of distributed function estimation in the case when sensor locations are modeled as Gaussian random variables. We consider a scenario where sensors are deployed in clusters with cluster centers known a priori (or estimated by a high performance GPS) and the average quadratic spread of sensors around the cluster center also known. Distributed sensors make noisy observations about an unknown parametric field generated by a physical object of interest (for example, magnetic field generated by a ferrous object and sensed by a network of magnetometers). Each sensor then performs local signal processing of its noisy observation and sends it to a central processor (called fusion center) in the wireless sensor network over parallel channels corrupted by fading and additive noise. The central processor combines the set of received signals to form an estimate of the unknown parametric field. In our numerical analysis, we involve a field shaped as a Gaussian bell. We experiment with the size of sensor clusters and with their number. A mean square error between the estimated parameters of the field and the true parameters used in simulations is involved as a performance measure. It can be shown that a relatively good estimate of the field can be obtained with only a small number of clusters. As the number of clusters increases, the estimation performance steadily improves. The results also indicate that, on the average, the number of clusters has more impact on the performance than the number of sensors per cluster, given the same size of the total network.
Gaussian conditional random fields for regression in remote sensing
Radosavljevic, Vladan
In recent years many remote sensing instruments of various properties have been employed in an attempt to better characterize important geophysical phenomena. Satellite instruments provide an exceptional opportunity for global long-term observations of the land, the biosphere, the atmosphere, and the oceans. The collected data are used for estimation and better understanding of geophysical parameters such as land cover type, atmospheric properties, or ocean temperature. Achieving accurate estimations of such parameters is an important requirement for development of models able to predict global climate changes. One of the most challenging climate research problems is estimation of global composition, load, and variability of aerosols, small airborne particles that reflect and absorb incoming solar radiation. The existing algorithm for aerosol prediction from satellite observations is deterministic and manually tuned by domain scientist. In contrast to domain-driven method, we show that aerosol prediction is achievable by completely data-driven approaches. These statistical methods consist of learning of nonlinear regression models to predict aerosol load using the satellite observations as inputs. Measurements from unevenly distributed ground-based sites over the world are used as proxy to ground-truth outputs. Although statistical methods achieve better accuracy than deterministic method this setup is appropriate when data are independently and identically distributed (IID). The IID assumption is often violated in remote sensing where data exhibit temporal, spatial, or spatio-temporal dependencies. In such cases, the traditional supervised learning approaches could result in a model with degraded accuracy. Conditional random fields (CRF) are widely used for predicting output variables that have some internal structure. Most of the CRF research has been done on structured classification where the outputs are discrete. We propose a CRF model for continuous outputs
Gaussian Random Field: Physical Origin of Sersic Profiles
Cen, Renyue
2014-01-01
While the Sersic profile family provide adequate fits for the surface brightness profiles of observed galaxies, the physical origin is unknown. We show that, if the cosmological density field are seeded by random gaussian fluctuations, as in the standard cold dark matter model, galaxies with steep central profiles have simultaneously extended envelopes of shallow profiles in the outskirts, whereas galaxies with shallow central profiles are accompanied by steep density profiles in the outskirts. These properties are in accord with those of the Sersic profile family. Moreover, galaxies with steep central profiles form their central regions in smaller denser subunits that possibly merge subsequently, which naturally leads to formation of bulges. In contrast, galaxies with shallow central profiles form their central regions in a coherent fashion without significant substructure, a necessary condition for disk galaxy formation. Thus, the scenario is self-consistent with respect to the correlation between observed ...
DUAL RANDOM MODEL OF INCREASING ANNUITY
HeWenjiong; ZhangYi
2001-01-01
The dual random models about the life insurance and social pension insurance have received considerable attention in the recent articles on actuarial theory and applications. This paper discusses a general kind of increasing annuity based on its force of interest accumulationfunction as a general random process. The dual random model of the present value of the benefits of the increasing annuity has been set, and their moments have been calculated under certainconditions.
Quantum Coherence and Random Fields at Mesoscopic Scales
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.
Correlation Models for Temperature Fields
North, Gerald R.
2011-05-16
This paper presents derivations of some analytical forms for spatial correlations of evolving random fields governed by a white-noise-driven damped diffusion equation that is the analog of autoregressive order 1 in time and autoregressive order 2 in space. The study considers the two-dimensional plane and the surface of a sphere, both of which have been studied before, but here time is introduced to the problem. Such models have a finite characteristic length (roughly the separation at which the autocorrelation falls to 1/e) and a relaxation time scale. In particular, the characteristic length of a particular temporal Fourier component of the field increases to a finite value as the frequency of the particular component decreases. Some near-analytical formulas are provided for the results. A potential application is to the correlation structure of surface temperature fields and to the estimation of large area averages, depending on how the original datastream is filtered into a distribution of Fourier frequencies (e.g., moving average, low pass, or narrow band). The form of the governing equation is just that of the simple energy balance climate models, which have a long history in climate studies. The physical motivation provided by the derivation from a climate model provides some heuristic appeal to the approach and suggests extensions of the work to nonuniform cases.
Metastable minima of the Heisenberg spin glass in a random magnetic field
Sharma, Auditya; Yeo, Joonhyun; Moore, M. A.
2016-11-01
We have studied zero-temperature metastable minima in classical m -vector component spin glasses in the presence of m -component random fields for two models, the Sherrington-Kirkpatrick (SK) model and the Viana-Bray (VB) model. For the SK model we have calculated analytically its complexity (the log of the number of minima) for both the annealed case where one averages the number of minima before taking the log and the quenched case where one averages the complexity itself, both for fields above and below the de Almeida-Thouless (AT) field, which is finite for m >2 . We have done numerical quenches starting from a random initial state (infinite temperature state) by putting spins parallel to their local fields until there is no further decrease of the energy and found that in zero field it always produces minima that have zero overlap with each other. For the m =2 and m =3 cases in the SK model the final energy reached in the quench is very close to the energy Ec at which the overlap of the states would acquire replica symmetry-breaking features. These minima have marginal stability and will have long-range correlations between them. In the SK limit we have analytically studied the density of states ρ (λ ) of the Hessian matrix in the annealed approximation. Despite the fact that in the presence of a random field there are no continuous symmetries, the spectrum extends down to zero with the usual √{λ } form for the density of states for fields below the AT field. However, when the random field is larger than the AT field, there is a gap in the spectrum, which closes up as the AT field is approached. The VB model behaves differently and seems rather similar to studies of the three-dimensional Heisenberg spin glass in a random vector field.
Conditional Random Fields for Pattern Recognition Applied to Structured Data
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.
Bearing Fault Classification Based on Conditional Random Field
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.
Bridges in the random-cluster model
Eren Metin Elçi
2016-02-01
Full Text Available The random-cluster model, a correlated bond percolation model, unifies a range of important models of statistical mechanics in one description, including independent bond percolation, the Potts model and uniform spanning trees. By introducing a classification of edges based on their relevance to the connectivity we study the stability of clusters in this model. We prove several exact relations for general graphs that allow us to derive unambiguously the finite-size scaling behavior of the density of bridges and non-bridges. For percolation, we are also able to characterize the point for which clusters become maximally fragile and show that it is connected to the concept of the bridge load. Combining our exact treatment with further results from conformal field theory, we uncover a surprising behavior of the (normalized variance of the number of (non-bridges, showing that it diverges in two dimensions below the value 4cos2(π/3=0.2315891⋯ of the cluster coupling q. Finally, we show that a partial or complete pruning of bridges from clusters enables estimates of the backbone fractal dimension that are much less encumbered by finite-size corrections than more conventional approaches.
Magalhaes, S. G.; Zimmer, F. M.; Coqblin, B.
2012-12-01
We study here the influence of a random applied magnetic field on the competition between the Kondo effect, the spin glass phase and a ferromagnetic order in disordered cerium systems such as CeNi1-xCux. The model used here takes an intrasite Kondo coupling and an intersite random coupling; both the intersite random coupling and the random magnetic field are described within the Sherrington-Kirkpatrick model and the one-step replica symmetry breaking procedure is also used here. We present phase diagrams giving Temperature versus the Kondo exchange parameter and the random magnetic field makes decrease particularly the importance of the spin glass and ferromagnetic phases.
Sums of random matrices and the Potts model on random planar maps
Atkin, Max R.; Niedner, Benjamin; Wheater, John F.
2016-05-01
We compute the partition function of the q-states Potts model on a random planar lattice with p≤slant q allowed, equally weighted colours on a connected boundary. To this end, we employ its matrix model representation in the planar limit, generalising a result by Voiculescu for the addition of random matrices to a situation beyond free probability theory. We show that the partition functions with p and q - p colours on the boundary are related algebraically. Finally, we investigate the phase diagram of the model when 0≤slant q≤slant 4 and comment on the conformal field theory description of the critical points.
Random Walk Smooth Transition Autoregressive Models
2004-01-01
This paper extends the family of smooth transition autoregressive (STAR) models by proposing a specification in which the autoregressive parameters follow random walks. The random walks in the parameters can capture structural change within a regime switching framework, but in contrast to the time varying STAR (TV-STAR) speciifcation recently introduced by Lundbergh et al (2003), structural change in our random walk STAR (RW-STAR) setting follows a stochastic process rather than a determinist...
Glaucoma progression detection using nonlocal Markov random field prior.
Belghith, Akram; Bowd, Christopher; Medeiros, Felipe A; Balasubramanian, Madhusudhanan; Weinreb, Robert N; Zangwill, Linda M
2014-10-01
Glaucoma is neurodegenerative disease characterized by distinctive changes in the optic nerve head and visual field. Without treatment, glaucoma can lead to permanent blindness. Therefore, monitoring glaucoma progression is important to detect uncontrolled disease and the possible need for therapy advancement. In this context, three-dimensional (3-D) spectral domain optical coherence tomography (SD-OCT) has been commonly used in the diagnosis and management of glaucoma patients. We present a new framework for detection of glaucoma progression using 3-D SD-OCT images. In contrast to previous works that use the retinal nerve fiber layer thickness measurement provided by commercially available instruments, we consider the whole 3-D volume for change detection. To account for the spatial voxel dependency, we propose the use of the Markov random field (MRF) model as a prior for the change detection map. In order to improve the robustness of the proposed approach, a nonlocal strategy was adopted to define the MRF energy function. To accommodate the presence of false-positive detection, we used a fuzzy logic approach to classify a 3-D SD-OCT image into a "non-progressing" or "progressing" glaucoma class. We compared the diagnostic performance of the proposed framework to the existing methods of progression detection.
Random walk models for top-N recommendation task
Yin ZHANG; Jiang-qin WU; Yue-ting ZHUANG
2009-01-01
Recently there has been an increasing interest in applying random walk based methods to recommender systems.We employ a Gaussian random field to model the top-N recommendation task as a semi-supervised learning problem.taking into account the degree of each node on the user-item bipartite graph,and induce an effective absorbing random walk (ARW) algorithm for the top-N recommendation task.Our random walk approach directly generates the top-N recommendations for individuals,rather than predicting the ratings of the recommendations.Experimental results on the two real data sets show that our random walk algorithm significantly outperforms the state-of-the-art random walk based personalized ranking algorithm as well as the popular item-based collaborative filtering method.
Two Dimensional Honeycomb Materials: Random Fields, Dissipation and Fluctuations
Frederico, T.; Oliveira, O.; de Paula, W.; Hussein, M. S.; Cardoso, T. R.
2017-02-01
In this paper, we propose a method to describe the many-body problem of electrons in honeycomb materials via the introduction of random fields which are coupled to the electrons and have a Gaussian distribution. From a one-body approach to the problem, after integrating exactly the contribution of the random fields, one builds a non-hermitian and dissipative effective Hamiltonian with two-body interactions. Our approach introduces besides the usual average over the electron field a second average over the random fields. The interplay of two averages enables the definition of various types of Green's functions which allow the investigation of fluctuation-dissipation characteristics of the interactions that are a manifestation of the many-body problem. In the current work, we study only the dissipative term, through the perturbative analysis of the dynamics associated the effective Hamiltonian generated by two different kinds of couplings. For the cases analyzed, the eigenstates of the effective Hamiltonian are complex and, therefore, some of the states have a finite life time. Moreover, we also investigate, in the mean field approximation, the most general parity conserving coupling to the random fields and compute the width of charge carriers Γ as a function of the Fermi energy E F . The theoretical prediction for Γ( E F ) is compared to the available experimental data for graphene. The good agreement between Γ t h e o and Γ e x p suggests that description of the many-body problem associated to the electrons in honeycomb materials can indeed be done via the introduction of random fields.
Generating Functionals for Quantum Field Theories with Random Potentials
Jain, Mudit
2015-01-01
We consider generating functionals for computing correlators in quantum field theories with random potentials. Examples of such theories include condensed matter systems with quenched disorder (e.g. spin glass) or cosmological systems in context of the string theory landscape (e.g. cosmic inflation). We use the so-called replica trick to define two different generating functionals for calculating correlators of the quantum fields averaged over a given distribution of random potentials. The first generating functional is appropriate for calculating averaged (in-out) amplitudes and involves a single replica of fields, but the replica limit is taken to an (unphysical) negative one number of fields outside of the path integral. When the number of replicas is doubled the generating functional can also be used for calculating averaged probabilities (squared amplitudes) using the in-in construction. The second generating functional involves an infinite number of replicas, but can be used for calculating both in-out ...
Magnetic properties of mixed Ising system with random field
Liang Ya-Qiu; Wei Guo-Zhu; Zhang Qi; Qiu Wei; Zang Shu-Liang
2004-01-01
A spin-1/2 and spin-3/2 mixed Ising system in a random field is studied by the use of effective-field theory with correlations. The phase diagrams and thermal behaviours of magnetizations are investigated numerically for the honeycomb lattice (z=3) and square lattice (z=4) respectively. The tricritical behaviours for both honeycomb and square lattices, as well as the reentrant behaviour for the square lattice are found.
IMAGE SEGMENTATION BASED ON MARKOV RANDOM FIELD AND WATERSHED TECHNIQUES
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.
Magnetic Field Line Random Walk in Isotropic Turbulence with Zero Mean Field
Sonsrettee, W.; Subedi, P.; Ruffolo, D.; Matthaeus, W. H.; Snodin, A. P.; Wongpan, P.; Chuychai, P.
2015-01-01
In astrophysical plasmas, magnetic field lines often guide the motions of thermal and non-thermal particles. The field line random walk (FLRW) is typically considered to depend on the Kubo number R = (b/B 0)(l∥/l) for rms magnetic fluctuation b, large-scale mean field B 0, and parallel and perpendicular coherence scales l∥ and l, respectively. Here we examine the FLRW when R → ∞ by taking B 0 → 0 for finite bz (fluctuation component along B 0), which differs from the well-studied route with bz = 0 or bz Lt B 0 as the turbulence becomes quasi-two-dimensional (quasi-2D). Fluctuations with B 0 = 0 are typically isotropic, which serves as a reasonable model of interstellar turbulence. We use a non-perturbative analytic framework based on Corrsin's hypothesis to determine closed-form solutions for the asymptotic field line diffusion coefficient for three versions of the theory, which are directly related to the k -1 or k -2 moment of the power spectrum. We test these theories by performing computer simulations of the FLRW, obtaining the ratio of diffusion coefficients for two different parameterizations of a field line. Comparing this with theoretical ratios, the random ballistic decorrelation version of the theory agrees well with the simulations. All results exhibit an analog to Bohm diffusion. In the quasi-2D limit, previous works have shown that Corrsin-based theories deviate substantially from simulation results, but here we find that as B 0 → 0, they remain in reasonable agreement. We conclude that their applicability is limited not by large R, but rather by quasi-two-dimensionality.
MAGNETIC FIELD LINE RANDOM WALK IN ISOTROPIC TURBULENCE WITH ZERO MEAN FIELD
Sonsrettee, W.; Ruffolo, D.; Snodin, A. P.; Wongpan, P. [Department of Physics, Faculty of Science, Mahidol University, Bangkok 10400 (Thailand); Subedi, P.; Matthaeus, W. H. [Bartol Research Institute, University of Delaware, Newark, DE 19716 (United States); Chuychai, P., E-mail: bturbulence@gmail.com, E-mail: david.ruf@mahidol.ac.th, E-mail: andrew.snodin@gmail.com, E-mail: pat.wongpan@postgrad.otago.ac.nz, E-mail: piyanate@gmail.com, E-mail: prasub@udel.edu, E-mail: whm@udel.edu [Thailand Center of Excellence in Physics, CHE, Ministry of Education, Bangkok 10400 (Thailand)
2015-01-01
In astrophysical plasmas, magnetic field lines often guide the motions of thermal and non-thermal particles. The field line random walk (FLRW) is typically considered to depend on the Kubo number R = (b/B {sub 0})(ℓ{sub ∥}/ℓ ) for rms magnetic fluctuation b, large-scale mean field B {sub 0}, and parallel and perpendicular coherence scales ℓ{sub ∥} and ℓ , respectively. Here we examine the FLRW when R → ∞ by taking B {sub 0} → 0 for finite b{sub z} (fluctuation component along B {sub 0}), which differs from the well-studied route with b{sub z} = 0 or b{sub z} << B {sub 0} as the turbulence becomes quasi-two-dimensional (quasi-2D). Fluctuations with B {sub 0} = 0 are typically isotropic, which serves as a reasonable model of interstellar turbulence. We use a non-perturbative analytic framework based on Corrsin's hypothesis to determine closed-form solutions for the asymptotic field line diffusion coefficient for three versions of the theory, which are directly related to the k {sup –1} or k {sup –2} moment of the power spectrum. We test these theories by performing computer simulations of the FLRW, obtaining the ratio of diffusion coefficients for two different parameterizations of a field line. Comparing this with theoretical ratios, the random ballistic decorrelation version of the theory agrees well with the simulations. All results exhibit an analog to Bohm diffusion. In the quasi-2D limit, previous works have shown that Corrsin-based theories deviate substantially from simulation results, but here we find that as B {sub 0} → 0, they remain in reasonable agreement. We conclude that their applicability is limited not by large R, but rather by quasi-two-dimensionality.
Carrozza, Sylvain; Tanasa, Adrian
2016-11-01
We define in this paper a class of three-index tensor models, endowed with {O(N)^{⊗ 3}} invariance ( N being the size of the tensor). This allows to generate, via the usual QFT perturbative expansion, a class of Feynman tensor graphs which is strictly larger than the class of Feynman graphs of both the multi-orientable model (and hence of the colored model) and the U( N) invariant models. We first exhibit the existence of a large N expansion for such a model with general interactions. We then focus on the quartic model and we identify the leading and next-to-leading order (NLO) graphs of the large N expansion. Finally, we prove the existence of a critical regime and we compute the critical exponents, both at leading order and at NLO. This is achieved through the use of various analytic combinatorics techniques.
Closed form maximum likelihood estimator of conditional random fields
Zhu, Zhemin; Hiemstra, Djoerd; Apers, Peter M.G.; Wombacher, Andreas
2013-01-01
Training Conditional Random Fields (CRFs) can be very slow for big data. In this paper, we present a new training method for CRFs called {\\em Empirical Training} which is motivated by the concept of co-occurrence rate. We show that the standard training (unregularized) can have many maximum likeliho
Anisotropic Fractional Brownian Random Fields as White Noise Functionals
Zhi-yuan Huang; Chu-jin Li
2005-01-01
This investigation aims at a new construction of anisotropic fractional Brownisn random fields by the white noise approach. Moreover, we investigate its distribution and sample properties (stationariness of increments, self-similarity, sample continuity) which will furnish some useful views to future applications.
吴秦; 胡丽娟; 梁久祯
2014-01-01
Traditional methods for Web information extraction are mainly based on linear conditional random fields model,which firstly converts the two dimensional structure of Web pages into a one dimensional sequence and then extract information.One of the shortcomings of this type of methods is that the two dimensional dependence of Web obj ects is overlooked,which may influence the effectiveness of Web information extraction.In this paper,a Web in-formation extraction method is proposed based on the block importance model and two-dimensional conditional random fields(2D CRFs).The proposed method firstly applies the vision-based page segmentation algorithm to divide the Web page into different blocks.Then support vector machine are used to learn the importance of different blocks.Unimportant blocks are removed so that Web object could be identified more accurately.Finally,the 2D CRFs model is applied to extract information from the Web page.Comparing with linear conditional random fields model, 2D CRFs model fits the two dimensional structure of Web page blocks better,which also improves the accuracy of Web information extraction.Experiments are presented on two datasets and the results show that the proposed method performs excellently on Web information extraction.%网页分块方法使得 Web信息抽取的单位由原来的页面缩小为分块。结合分块重要度模型与二维条件随机场的优点，提出一种 Web对象信息抽取方法。该方法利用分块重要度模型对网页分块进行重要度标注，过滤掉大量与主题无关信息，更加准确的定位待抽取信息的位置。二维条件随机场模型相比传统的线性条件随机场模型更好的适应了网页分块的二维结构，有效的提高信息抽取准确率。实验结果表明，该方法对 Web 对象信息抽取具有良好的效果。
Kernel conditional ordinal random fields for temporal segmentation of facial action units
Rudovic, Ognjen; Pavlovic, Vladimir; Pantic, Maja
2012-01-01
We consider the problem of automated recognition of temporal segments (neutral, onset, apex and offset) of Facial Action Units. To this end, we propose the Laplacian-regularized Kernel Conditional Ordinal Random Field model. In contrast to standard modeling approaches to recognition of AUs’ temporal
Driving a Superconductor to Insulator Transition with Random Gauge Fields
Nguyen, H. Q.; Hollen, S. M.; Shainline, J.; Xu, J. M.; Valles, J. M.
2016-11-01
Typically the disorder that alters the interference of particle waves to produce Anderson localization is potential scattering from randomly placed impurities. Here we show that disorder in the form of random gauge fields that act directly on particle phases can also drive localization. We present evidence of a superfluid bose glass to insulator transition at a critical level of this gauge field disorder in a nano-patterned array of amorphous Bi islands. This transition shows signs of metallic transport near the critical point characterized by a resistance , indicative of a quantum phase transition. The critical disorder depends on interisland coupling in agreement with recent Quantum Monte Carlo simulations. We discuss how this disorder tuned SIT differs from the common frustration tuned SIT that also occurs in magnetic fields. Its discovery enables new high fidelity comparisons between theoretical and experimental studies of disorder effects on quantum critical systems.
Modelling population processes with random initial conditions.
Pollett, P K; Dooley, A H; Ross, J V
2010-02-01
Population dynamics are almost inevitably associated with two predominant sources of variation: the first, demographic variability, a consequence of chance in progenitive and deleterious events; the second, initial state uncertainty, a consequence of partial observability and reporting delays and errors. Here we outline a general method for incorporating random initial conditions in population models where a deterministic model is sufficient to describe the dynamics of the population. Additionally, we show that for a large class of stochastic models the overall variation is the sum of variation due to random initial conditions and variation due to random dynamics, and thus we are able to quantify the variation not accounted for when random dynamics are ignored. Our results are illustrated with reference to both simulated and real data.
基于二维混合条件随机场的Web记录抽取模型%Web Records Extraction Model Based on 2D Mixed Conditional Random Fields
卓林; 杨舟; 赵朋朋; 崔志明
2011-01-01
This paper presents a model of two-dimensional Mix Conditional Random Fields(MCRF) which are used for the extraction of Web records.It overcomes the shortcomings of linear-chain conditional random that it can not take full advantage of dependencies between the various elements of Web entities.Meanwhile, it solves the problem that training CRF model often requires large number of hand-labeling sample data.In the experiment, it tries to extract 742 data records from Dangdang online, and compared with other models under the same conditions.Experimental results show a more superior performance during extracting TDS.%提出一种基于混合二维条件随机场的Web记录抽取模型,以克服线性链条件随机场不能充分利用Web实体间二维依赖关系的缺点,且训练条件随机场模型时无需大量手工标注的样本数据.对当当网上的742个数据记录进行抽取,对比同等情况下的其他模型.实验结果表明,混合二维条件随机场模型在抽取TDS数据集时展现了更优越的性能.
MRFalign: protein homology detection through alignment of Markov random fields.
Ma, Jianzhu; Wang, Sheng; Wang, Zhiyong; Xu, Jinbo
2014-03-01
Sequence-based protein homology detection has been extensively studied and so far the most sensitive method is based upon comparison of protein sequence profiles, which are derived from multiple sequence alignment (MSA) of sequence homologs in a protein family. A sequence profile is usually represented as a position-specific scoring matrix (PSSM) or an HMM (Hidden Markov Model) and accordingly PSSM-PSSM or HMM-HMM comparison is used for homolog detection. This paper presents a new homology detection method MRFalign, consisting of three key components: 1) a Markov Random Fields (MRF) representation of a protein family; 2) a scoring function measuring similarity of two MRFs; and 3) an efficient ADMM (Alternating Direction Method of Multipliers) algorithm aligning two MRFs. Compared to HMM that can only model very short-range residue correlation, MRFs can model long-range residue interaction pattern and thus, encode information for the global 3D structure of a protein family. Consequently, MRF-MRF comparison for remote homology detection shall be much more sensitive than HMM-HMM or PSSM-PSSM comparison. Experiments confirm that MRFalign outperforms several popular HMM or PSSM-based methods in terms of both alignment accuracy and remote homology detection and that MRFalign works particularly well for mainly beta proteins. For example, tested on the benchmark SCOP40 (8353 proteins) for homology detection, PSSM-PSSM and HMM-HMM succeed on 48% and 52% of proteins, respectively, at superfamily level, and on 15% and 27% of proteins, respectively, at fold level. In contrast, MRFalign succeeds on 57.3% and 42.5% of proteins at superfamily and fold level, respectively. This study implies that long-range residue interaction patterns are very helpful for sequence-based homology detection. The software is available for download at http://raptorx.uchicago.edu/download/. A summary of this paper appears in the proceedings of the RECOMB 2014 conference, April 2-5.
Sample to sample fluctuations in the random energy model
Derrida, B. (Service de Physique Theorique, CEN Saclay, 91 - Gif-sur-Yvette (France)); Toulouse, G. (E.S.P.C.I., 75 - Paris (France))
1985-03-15
In the spin glass phase, mean field theory says that the weights of the valleys vary from sample to sample. Exact expressions for the probability laws of these fluctuations are derived, from the random energy model, without recourse to the replica method.
Cosmological fluctuations of a random field and radiation fluid
Bastero-Gil, Mar [Departamento de Física Teórica y del Cosmos, Campus de Fuentenueva, Universidad de Granada, Granada, 18071 (Spain); Berera, Arjun [SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh, EH9 3JZ (United Kingdom); Moss, Ian G. [School of Mathematics and Statistics, Newcastlle University, Newcastle upon Tyne, NE1 7RU (United Kingdom); Ramos, Rudnei O., E-mail: mbg@ugr.es, E-mail: ab@ph.ed.ac.uk, E-mail: ian.moss@ncl.ac.uk, E-mail: rudnei@uerj.br [Departamento de Física Teórica, Universidade do Estado do Rio de Janeiro, Rio de Janeiro, RJ, 20550-013 Brazil (Brazil)
2014-05-01
A generalization of the random fluid hydrodynamic fluctuation theory due to Landau and Lifshitz is applied to describe cosmological fluctuations in systems with radiation and scalar fields. The viscous pressures, parametrized in terms of the bulk and shear viscosity coefficients, and the respective random fluctuations in the radiation fluid are combined with the stochastic and dissipative scalar evolution equation. This results in a complete set of equations describing the perturbations in both scalar and radiation fluids. These derived equations are then studied, as an example, in the context of warm inflation. Similar treatments can be done for other cosmological early universe scenarios involving thermal or statistical fluctuations.
Gaussian Random Field: Physical Origin of Sersic Profiles
Cen, Renyue
2014-08-01
While the Sersic profile family provides adequate fits for the surface brightness profiles of observed galaxies, its physical origin is unknown. We show that if the cosmological density field is seeded by random Gaussian fluctuations, as in the standard cold dark matter model, galaxies with steep central profiles have simultaneously extended envelopes of shallow profiles in the outskirts, whereas galaxies with shallow central profiles are accompanied by steep density profiles in the outskirts. These properties are in accord with those of the Sersic profile family. Moreover, galaxies with steep central profiles form their central regions in smaller denser subunits that possibly merge subsequently, which naturally leads to the formation of bulges. In contrast, galaxies with shallow central profiles form their central regions in a coherent fashion without significant substructure, a necessary condition for disk galaxy formation. Thus, the scenario is self-consistent with respect to the correlation between observed galaxy morphology and the Sersic index. We further predict that clusters of galaxies should display a similar trend, which should be verifiable observationally.
Reduction of the Random Variables of the Turbulent Wind Field
Sichani, Mahdi Teimouri; Nielsen, Søren R.K.
2012-01-01
of the integral domain; this becomes increasingly difficult as the dimensions of the integral domain increase. On the other hand efficiency of the AMC methods is closely dependent on the design points of the problem. Presence of many random variables may increase the number of the design points, hence affects......Applicability of the Probability Density Evolution Method (PDEM) for realizing evolution of the probability density for the wind turbines has rather strict bounds on the basic number of the random variables involved in the model. The efficiency of most of the Advanced Monte Carlo (AMC) methods, i.......e. Importance Sampling (IS) or Subset Simulation (SS), will be deteriorated on problems with many random variables. The problem with PDEM is that a multidimensional integral has to be carried out over the space defined by the random variables of the system. The numerical procedure requires discretization...
Boroomand, Ameneh; Khalvati, Farzad; Haider, Masoom A; Wong, Alexander
2015-01-01
Diffusion weighted magnetic resonance imaging (DW-MRI) is a powerful tool in imaging-based prostate cancer (PCa) screening and detection. Endorectal coils are commonly used in DW-MRI to improve the signal-to-noise ratio (SNR) of the acquisition, at the expense of significant intensity inhomogeneities (bias field) that worsens as we move away from the endorectal coil. The presence of bias field can have a significant negative impact on the accuracy of different image analysis tasks, as well as the accuracy of PCa tumor localization, thus leading to increased inter- and intra-observer variability. The previously proposed bias field correction methods often suffer from undesired noise amplification that can reduce the image quality of the resulting bias-corrected DW-MRI data. Here, we propose a unified data reconstruction approach that enables joint compensation of bias field as well as data noise in diffusion weighted endorectal magnetic resonance (DW-EMR) imaging. The proposed noise-compensated, bias-corrected...
Random matrix model approach to chiral symmetry
Verbaarschot, J J M
1996-01-01
We review the application of random matrix theory (RMT) to chiral symmetry in QCD. Starting from the general philosophy of RMT we introduce a chiral random matrix model with the global symmetries of QCD. Exact results are obtained for universal properties of the Dirac spectrum: i) finite volume corrections to valence quark mass dependence of the chiral condensate, and ii) microscopic fluctuations of Dirac spectra. Comparisons with lattice QCD simulations are made. Most notably, the variance of the number of levels in an interval containing $n$ levels on average is suppressed by a factor $(\\log n)/\\pi^2 n$. An extension of the random matrix model model to nonzero temperatures and chemical potential provides us with a schematic model of the chiral phase transition. In particular, this elucidates the nature of the quenched approximation at nonzero chemical potential.
Computer simulations of the random barrier model
Schrøder, Thomas; Dyre, Jeppe
2002-01-01
A brief review of experimental facts regarding ac electronic and ionic conduction in disordered solids is given followed by a discussion of what is perhaps the simplest realistic model, the random barrier model (symmetric hopping model). Results from large scale computer simulations are presented......, focusing on universality of the ac response in the extreme disorder limit. Finally, some important unsolved problems relating to hopping models for ac conduction are listed....
A Dexterous Optional Randomized Response Model
Tarray, Tanveer A.; Singh, Housila P.; Yan, Zaizai
2017-01-01
This article addresses the problem of estimating the proportion Pi[subscript S] of the population belonging to a sensitive group using optional randomized response technique in stratified sampling based on Mangat model that has proportional and Neyman allocation and larger gain in efficiency. Numerically, it is found that the suggested model is…
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.
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
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.
Random-anisotropy Blume-Emery-Griffiths model
Maritan, Amos; Cieplak, Marek; Swift, Michael R.; Toigo, Flavio; Banavar, Jayanth R.
1992-01-01
The results are described of studies of a random-anisotropy Blume-Emery-Griffiths spin-1 Ising model using mean-field theory, transfer-matrix calculations, and position-space renormalization-group calculations. The interplay between the quenched randomness of the anisotropy and the annealed disorder introduced by the spin-1 model leads to a rich phase diagram with a variety of phase transitions and reentrant behavior. The results may be relevant to the study of the phase separation of He-3 - He-4 mixtures in porous media in the vicinity of the superfluid transition.
Random-anisotropy Blume-Emery-Griffiths model
Maritan, Amos; Cieplak, Marek; Swift, Michael R.; Toigo, Flavio; Banavar, Jayanth R.
1992-01-01
The results are described of studies of a random-anisotropy Blume-Emery-Griffiths spin-1 Ising model using mean-field theory, transfer-matrix calculations, and position-space renormalization-group calculations. The interplay between the quenched randomness of the anisotropy and the annealed disorder introduced by the spin-1 model leads to a rich phase diagram with a variety of phase transitions and reentrant behavior. The results may be relevant to the study of the phase separation of He-3 - He-4 mixtures in porous media in the vicinity of the superfluid transition.
Random-anisotropy Blume-Emery-Griffiths model
Maritan, Amos; Cieplak, Marek; Swift, Michael R.; Toigo, Flavio; Banavar, Jayanth R.
1992-10-01
We describe the results of studies of a random-anisotropy Blume-Emery-Griffiths spin-1 Ising model using mean-field theory, transfer-matrix calculations, and position-space renormalization-group calculations. The interplay between the quenched randomness of the anisotropy and the annealed disorder introduced by the spin-1 model leads to a rich phase diagram with a variety of phase transitions and reentrant behavior. Our results may be relevant to the study of the phase separation of 3He-4He mixtures in porous media in the vicinity of the superfluid transition.
Randomly Stopped Sums: Models and Psychological Applications
Michael eSmithson
2014-11-01
Full Text Available This paper describes an approach to modeling the sums of a continuous random variable over a number of measurement occasions when the number of occasions also is a random variable. A typical example is summing the amounts of time spent attending to pieces of information in an information search task leading to a decision to obtain the total time taken to decide. Although there is a large literature on randomly stopped sums in financial statistics, it is largely absent from psychology. The paper begins with the standard modeling approaches used in financial statistics, and then extends them in two ways. First, the randomly stopped sums are modeled as ``life distributions'' such as the gamma or log-normal distribution. A simulation study investigates Type I error rate accuracy and power for gamma and log-normal versions of this model. Second, a Bayesian hierarchical approach is used for constructing an appropriate general linear model of the sums. Model diagnostics are discussed, and three illustrations are presented from real datasets.
Critical properties of random Potts models
Kinzel, Wolfgang; Domany, Eytan
1981-04-01
The critical properties of Potts models with random bonds are considered in two dimensions. A position-space renormalization-group procedure, based on the Migdal-Kadanoff method, is developed. While all previous position-space calculations satisfied the Harris criterion and the resulting scaling relation only approximately, we found conditions under which these relations are exactly satisfied, and constructed our renormalization-group procedure accordingly. Numerical results for phase diagrams and thermodynamic functions for various random-bond Potts models are presented. In addition, some exact results obtained using a duality transformation, as well as an heuristic derivation of scaling properties that correspond to the percolation problem are given.
Duality between random trap and barrier models
Jack, Robert L [Department of Chemistry, University of California at Berkeley, Berkeley, CA 94720 (United States); Sollich, Peter [Department of Mathematics, King' s College London, London WC2R 2LS (United Kingdom)
2008-08-15
We discuss the physical consequences of a duality between two models with quenched disorder, in which particles propagate in one dimension among random traps or across random barriers. We derive an exact relation between their diffusion fronts at fixed disorder and deduce from this that their disorder-averaged diffusion fronts are exactly equal. We use effective dynamics schemes to isolate the different physical processes by which particles propagate in the models and discuss how the duality arises from a correspondence between the rates for these different processes.
Visibility graphs of random scalar fields and spatial data
Lacasa, Lucas; Iacovacci, Jacopo
2017-07-01
We extend the family of visibility algorithms to map scalar fields of arbitrary dimension into graphs, enabling the analysis of spatially extended data structures as networks. We introduce several possible extensions and provide analytical results on the topological properties of the graphs associated to different types of real-valued matrices, which can be understood as the high and low disorder limits of real-valued scalar fields. In particular, we find a closed expression for the degree distribution of these graphs associated to uncorrelated random fields of generic dimension. This result holds independently of the field's marginal distribution and it directly yields a statistical randomness test, applicable in any dimension. We showcase its usefulness by discriminating spatial snapshots of two-dimensional white noise from snapshots of a two-dimensional lattice of diffusively coupled chaotic maps, a system that generates high dimensional spatiotemporal chaos. The range of potential applications of this combinatorial framework includes image processing in engineering, the description of surface growth in material science, soft matter or medicine, and the characterization of potential energy surfaces in chemistry, disordered systems, and high energy physics. An illustration on the applicability of this method for the classification of the different stages involved in carcinogenesis is briefly discussed.
Two-Stage Modelling Of Random Phenomena
Barańska, Anna
2015-12-01
The main objective of this publication was to present a two-stage algorithm of modelling random phenomena, based on multidimensional function modelling, on the example of modelling the real estate market for the purpose of real estate valuation and estimation of model parameters of foundations vertical displacements. The first stage of the presented algorithm includes a selection of a suitable form of the function model. In the classical algorithms, based on function modelling, prediction of the dependent variable is its value obtained directly from the model. The better the model reflects a relationship between the independent variables and their effect on the dependent variable, the more reliable is the model value. In this paper, an algorithm has been proposed which comprises adjustment of the value obtained from the model with a random correction determined from the residuals of the model for these cases which, in a separate analysis, were considered to be the most similar to the object for which we want to model the dependent variable. The effect of applying the developed quantitative procedures for calculating the corrections and qualitative methods to assess the similarity on the final outcome of the prediction and its accuracy, was examined by statistical methods, mainly using appropriate parametric tests of significance. The idea of the presented algorithm has been designed so as to approximate the value of the dependent variable of the studied phenomenon to its value in reality and, at the same time, to have it "smoothed out" by a well fitted modelling function.
Improving randomness characterization through Bayesian model selection
R., Rafael Díaz-H; Martínez, Alí M Angulo; U'Ren, Alfred B; Hirsch, Jorge G; Marsili, Matteo; Castillo, Isaac Pérez
2016-01-01
Nowadays random number generation plays an essential role in technology with important applications in areas ranging from cryptography, which lies at the core of current communication protocols, to Monte Carlo methods, and other probabilistic algorithms. In this context, a crucial scientific endeavour is to develop effective methods that allow the characterization of random number generators. However, commonly employed methods either lack formality (e.g. the NIST test suite), or are inapplicable in principle (e.g. the characterization derived from the Algorithmic Theory of Information (ATI)). In this letter we present a novel method based on Bayesian model selection, which is both rigorous and effective, for characterizing randomness in a bit sequence. We derive analytic expressions for a model's likelihood which is then used to compute its posterior probability distribution. Our method proves to be more rigorous than NIST's suite and the Borel-Normality criterion and its implementation is straightforward. We...
Exponential Distribution for the Occurrence of Rare Patterns in Gibbsian Random Fields
Abadi, M.; Chazottes, J.-R.; Redig, F.; Verbitskiy, E.
2004-01-01
We study the distribution of the occurrence of rare patterns in sufficiently mixing Gibbs random fields on the lattice Z^d, d ≥ 2. A typical example is the high temperature Ising model. This distribution is shown to converge to an exponential law as the size of the pattern diverges. Our analysis not
Mean field theory of directed polymers with random complex weights
Derrida, B.; Evans, M. R.; Speer, E. R.
1993-09-01
We show that for the problem of directed polymers on a tree with i.i.d. random complex weights on each bond, three possible phases can exist; the phase of a particular system is determined by the distribution ρ of the random weights. For each of these three phases, we give the expression of the free energy per unit length in the limit of infinitely long polymers. Our proofs require several hypotheses on the distribution ρ, most importantly, that the amplitude and the phase of each complex weight be statistically independent. The main steps of our proofs use bounds on noninteger moments of the partition function and self averaging properties of the free energy. We illustrate our results by some examples and discuss possible generalizations to a larger class of distributions, to Random Energy Models, and to the finite dimensional case. We note that our results are not in agreement with the predictions of a recent replica approach to a similar problem.
A Markov random field-based approach to speckle reduction
Lankoande, Ousseini
One of the major factors plaguing the performance of any coherent imaging system in general, and synthetic-aperture-radar (SAR) and ultrasound-medical-imaging systems in particular, is the presence of signal-dependent speckle noise. Grainy in appearance, speckle noise is primarily due to the phase fluctuations of the electromagnetic returned signals. Existing multiplicative models for speckle noise do not possess the level of generality required to capture and exploit the inherent spatial-correlation characteristics of speckle noise. The capability of Markov random fields (MRFs) to model spatially correlated and signal-dependent phenomena makes them an excellent choice for modeling speckled images without the need to adopt a multiplicative-noise model. In addition, a MRF framework can lend itself to many image-processing strategies that are not predicated on any multiplicative- or additive-noise assumptions. We propose a new mathematical framework for modeling and mitigating speckle noise that combines the flexibility and generality of a MRF with the physical properties of speckle noise drawn from the statistical optics principles. In particular, Goodman's conditional probability density function (cpdf) of the intensity of any two points in the speckled image and the associated correlation function are used to derive the cpdf of any center pixel intensity given its four neighbors. An important parameter of the cpdf, the coherence factor, characterizes the spatial correlation between two given pixels. For the first-order MRF model used in this dissertation, the coherence factor is restricted to only one value, which is estimated from the data using a pseudo-likelihood method. Equipped with the cpdf, the Hammersley-Clifford theorem is utilized to derive a convex Gibbs energy function that characterizes the MRF. Based on the proposed model, we introduce two speckle-reduction algorithms. The first algorithm, termed the simulated-annealing-MRF (SAMRF), is based on
Random effect selection in generalised linear models
Denwood, Matt; Houe, Hans; Forkman, Björn;
We analysed abattoir recordings of meat inspection codes with possible relevance to onfarm animal welfare in cattle. Random effects logistic regression models were used to describe individual-level data obtained from 461,406 cattle slaughtered in Denmark. Our results demonstrate that the largest...
Tests of Hypotheses Arising In the Correlated Random Coefficient Model.
Heckman, James J; Schmierer, Daniel
2010-11-01
This paper examines the correlated random coefficient model. It extends the analysis of Swamy (1971), who pioneered the uncorrelated random coefficient model in economics. We develop the properties of the correlated random coefficient model and derive a new representation of the variance of the instrumental variable estimator for that model. We develop tests of the validity of the correlated random coefficient model against the null hypothesis of the uncorrelated random coefficient model.
Segmentation of RGB-D indoor scenes by stacking random forests and conditional random fields
Thøgersen, Mikkel; Guerrero, Sergio Escalera; Gonzàlez, Jordi;
2016-01-01
on stacked classifiers; the benefits are two fold: on one hand, the system scales well to consider different types of complex features and, on the other hand, the use of stacked classifiers makes the performance of the proposed technique more accurate. The proposed method consists of a random forest using...... a stacked random forest which gives the final predictions. The model is tested on the renown NYU-v2 dataset and the recently available SUNRGBD dataset. The approach shows that simple multimodal features with the power of using multi-class multi-scale stacked sequential learners (MMSSL) can achieve slight...
Applications of random field theory to functional connectivity.
Worsley, K J; Cao, J; Paus, T; Petrides, M; Evans, A C
1998-01-01
Functional connectivity between two voxels or regions of voxels can be measured by the correlation between voxel measurements from either PET CBF or BOLD fMRI images in 3D. We propose to look at the entire 6D matrix of correlations between all voxels and search for 6D local maxima. The main result is a new theoretical formula based on random field theory for the p-value of these local maxima, which distinguishes true correlations from background noise. This can be applied to crosscorrelations between two different sets of images--such as activations under two different tasks, as well as autocorrelations within the same set of images.
Extremes in random fields a theory and its applications
Yakir, Benjamin
2013-01-01
Presents a useful new technique for analyzing the extreme-value behaviour of random fields Modern science typically involves the analysis of increasingly complex data. The extreme values that emerge in the statistical analysis of complex data are often of particular interest. This book focuses on the analytical approximations of the statistical significance of extreme values. Several relatively complex applications of the technique to problems that emerge in practical situations are presented. All the examples are difficult to analyze using classical methods, and as a result, the author pr
Markov random fields for static foreground classification in surveillance systems
Fitzsimons, Jack K.; Lu, Thomas T.
2014-09-01
We present a novel technique for classifying static foreground in automated airport surveillance systems between abandoned and removed objects by representing the image as a Markov Random Field. The proposed algorithm computes and compares the net probability of the region of interest before and after the event occurs, hence finding which fits more naturally with their respective backgrounds. Having tested on a dataset from the PETS 2006, PETS 2007, AVSS20074, CVSG, VISOR, CANDELA and WCAM datasets, the algorithm has shown capable of matching the results of the state-of-the-art, is highly parallel and has a degree of robustness to noise and illumination changes.
Boundary States of the Potts Model on Random Planar Maps
Atkin, Max; Wheater, John
2015-01-01
We revisit the 3-states Potts model on random planar triangulations as a Hermitian matrix model. As a novelty, we obtain an algebraic curve which encodes the partition function on the disc with both fixed and mixed spin boundary conditions. We investigate the critical behaviour of this model and find scaling exponents consistent with previous literature. We argue that the conformal field theory that describes the double scaling limit is Liouville quantum gravity coupled to the $(A_4,D_4)$ minimal model with extended $\\mathcal{W}_3$-symmetry.
Improving lognormal models for cosmological fields
Xavier, Henrique S; Joachimi, Benjamin
2016-01-01
It is common practice in cosmology to model large-scale structure observables as lognormal random fields, and this approach has been successfully applied in the past to the matter density and weak lensing convergence fields separately. We argue that this approach has fundamental limitations which prevent its use for jointly modelling these two fields since the lognormal distribution's shape can prevent certain correlations to be attainable. Given the need of ongoing and future large-scale structure surveys for fast joint simulations of clustering and weak lensing, we propose two ways of overcoming these limitations. The first approach slightly distorts the power spectra of the fields using one of two algorithms that minimises either the absolute or the fractional distortions. The second one is by obtaining more accurate convergence marginal distributions, for which we provide a fitting function, by integrating the lognormal density along the line of sight. The latter approach also provides a way to determine ...
Testing the Correlated Random Coefficient Model*
Heckman, James J.; Schmierer, Daniel; Urzua, Sergio
2010-01-01
The recent literature on instrumental variables (IV) features models in which agents sort into treatment status on the basis of gains from treatment as well as on baseline-pretreatment levels. Components of the gains known to the agents and acted on by them may not be known by the observing economist. Such models are called correlated random coe cient models. Sorting on unobserved components of gains complicates the interpretation of what IV estimates. This paper examines testable implications of the hypothesis that agents do not sort into treatment based on gains. In it, we develop new tests to gauge the empirical relevance of the correlated random coe cient model to examine whether the additional complications associated with it are required. We examine the power of the proposed tests. We derive a new representation of the variance of the instrumental variable estimator for the correlated random coefficient model. We apply the methods in this paper to the prototypical empirical problem of estimating the return to schooling and nd evidence of sorting into schooling based on unobserved components of gains. PMID:21057649
Delayed Random Walks: Modeling Human Posture Control
Ohira, Toru
1998-03-01
We consider a phenomenological description of a noisy trajectory which appears on a stabiliogram platform during human postural sway. We hypothesize that this trajectory arises due to a mixture of uncontrollable noise and a corrective delayed feedback to an upright position. Based on this hypothesis, we model the process with a biased random walk whose transition probability depends on its position at a fixed time delay in the past, which we call a delayed random walk. We first introduce a very simple model (T. Ohira and J. G. Milton, Phys.Rev.E. 52), 3277, (1995), which can nevertheless capture the rough qualitative features of the two--point mean square displacement of experimental data with reasonable estimation of delay time. Then, we discuss two approaches toward better capturing and understanding of the experimental data. The first approach is an extension of the model to include a spatial displacement threshold from the upright position below which no or only weak corrective feedback motion takes place. This can be incorporated into an extended delayed random walk model. Numerical simulations show that this extended model can better capture the three scaling region which appears in the two--point mean square displacement. The other approach studied the autocorrelation function of the experimental data, which shows oscillatory behavior. We recently investigated a delayed random walk model whose autocorrelation function has analytically tractable oscillatory behavior (T. Ohira, Phys.Rev.E. 55), R1255, (1997). We discuss how this analytical understanding and its application to delay estimation (T. Ohira and R. Sawatari, Phys.Rev.E. 55), R2077, (1997) could possibly be used to further understand the postural sway data.
Optimization by Estimation of Distribution with DEUM Framework Based on Markov Random Fields
Siddhartha Shakya; John McCall
2007-01-01
This paper presents a Markov random field (MRP) approach to estimating and sampling the probability distribution in populations of solutions. The approach is used to define a class of algorithms under the general heading distribution estimation using Markov random fields (DEUM). DEUM is a subclass of estimation of distribution algorithms (EDAs) where interaction between solution variables is represented as an undirected graph and the joint probability of a solution is factorized as a Gibbs distribution derived from the structure of the graph. The focus of this paper will be on describing the three main characteristics of DEUM framework, which distinguishes it from the traditional EDA. They are: 1) use of MRF models, 2) fitness modeling approach to estimating the parameter of the model and 3) Monte Carlo approach to sampling from the model.
Experimental realization of random-field Ising ferromagnetism in a molecular magnet
Sarachik, Myriam P.
2011-03-01
The longitudinal magnetic susceptibility of single crystals of the molecular magnet Mn 12 -acetate obeys a Curie-Weiss law, indicating a transition to a ferromagnetic phase at ~ 0.9 K [1,2]. With increasing magnetic field applied transverse to the easy axis, a marked change is observed in the temperature dependence of the susceptibility, with a considerably more rapid suppression of the Curie-Weiss temperature than predicted by mean-field theory for an ordered single crystal. Our results can instead be fit by a Hamiltonian for a random-field Ising ferromagnet in a transverse magnetic field, where the randomness derives from the intrinsic distribution of locally tilted magnetic easy axes known to exist in Mn 12 -acetate crystals. Mn 12 -ac and other single molecule magnets may thus serve as clean model systems for the study of random field ferromagnetism where the random fields are controllable and considerably larger than typical hyperfine fields. This discovery promises to enable widespread and convenient experimental study of magnetism in a random field in a broad class of new materials. Work performed by and in collaboration with: Bo Wen, and Lin Bo, Physics Dept. City College of New York, CUNY (funded by NSF-DMR-0451605), P. Subedi and A. D. Kent, Physics Dept., NYU, (funded by NSF-DMR-0506946 and ARO-W911NF-08-1-0364) Y. Yeshurun, Physics Dept., Bar Ilan U, (funded by Deutsche Forschungsgemeinschaft), A. J. Millis, Physics Dept. Columbia U. (funded by DMR DMR-0705847), C. Lampropoulos and G. Christou, Chemistry Dept., U. of Florida (funded by NSF -CHE-0910472). Funding provided by NSF award DMR-0451605.
Random surfaces, solvable lattice models and discrete quantum gravity in two dimensions
Kostov, I.K. (CEA Centre d' Etudes Nucleaires de Saclay, 91 - Gif-sur-Yvette (France). Service de Physique Theorique)
1989-07-01
We give a review of the analytical results concerning dynamically triangulated surfaces and statistical models on a planar random lattice. The critical behaviour of these models is described by conformal field theories coupled to 2d quantum gravity. (orig.).
Maximizing Entropy of Pickard Random Fields for 2x2 Binary Constraints
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....
Prediction of the spatial occurrence of fire induced spalling in concrete slabs using random fields
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.
Antiferromagnetic Potts model on the Erdos-Renyi random graph
Contucci, Pierluig; Giardina', Cristian; Starr, Shannon
2011-01-01
We study the antiferromagnetic Potts model on the Erdos-Renyi random graph. By identifying a suitable interpolation structure and proving an extended variational principle we show that the replica symmetric solution is an upper bound for the limiting pressure which can be recovered in the framework of Derrida-Ruelle probability cascades. A comparison theorem with a mixed model made of a mean field Potts-antiferromagnet plus a Potts-Sherrington-Kirkpatrick model allows to show that the replica symmetric solution is exact at high temperatures.
Kinetic models with randomly perturbed binary collisions
Bassetti, Federico; Toscani, Giuseppe
2010-01-01
We introduce a class of Kac-like kinetic equations on the real line, with general random collisional rules, which include as particular cases models for wealth redistribution in an agent-based market or models for granular gases with a background heat bath. Conditions on these collisional rules which guarantee both the existence and uniqueness of equilibrium profiles and their main properties are found. We show that the characterization of these stationary solutions is of independent interest, since the same profiles are shown to be solutions of different evolution problems, both in the econophysics context and in the kinetic theory of rarefied gases.
Exact mean field concept to compute defect energetics in random alloys on rigid lattices
Bonny, G.; Castin, N.; Pascuet, M. I.; Çelik, Y.
2017-07-01
In modern materials science modeling, the evolution of the energetics of random alloys with composition are desirable input parameters for several meso-scale and continuum scale models. When using atomistic methods to parameterize the above mentioned concentration dependent function, a mean field theory can significantly reduce the computational burden associated to obtaining the desired statistics in a random alloy. In this work, a mean field concept is developed to obtain the energetics of point-defect clusters in perfect random alloys. It is demonstrated that for a rigid lattice the concept is mathematically exact. In addition to the accuracy of the presented method, it is also computationally efficient as a small box can be used and perfect statistics are obtained in a single run. The method is illustrated by computing the formation and binding energy of solute and vacancy pairs in FeCr and FeW binaries. Also, the dissociation energy of small vacancy clusters was computed in FeCr and FeCr-2%W alloys, which are considered model alloys for Eurofer steels. As a result, it was concluded that the dissociation energy is not expected to vary by more than 0.1 eV in the 0-10% Cr and 0-2% W composition range. The present mean field concept can be directly applied to parameterize meso-scale models, such as cluster dynamics and object kinetic Monte Carlo models.
Particle filters for random set models
Ristic, Branko
2013-01-01
“Particle Filters for Random Set Models” presents coverage of state estimation of stochastic dynamic systems from noisy measurements, specifically sequential Bayesian estimation and nonlinear or stochastic filtering. The class of solutions presented in this book is based on the Monte Carlo statistical method. The resulting algorithms, known as particle filters, in the last decade have become one of the essential tools for stochastic filtering, with applications ranging from navigation and autonomous vehicles to bio-informatics and finance. While particle filters have been around for more than a decade, the recent theoretical developments of sequential Bayesian estimation in the framework of random set theory have provided new opportunities which are not widely known and are covered in this book. These recent developments have dramatically widened the scope of applications, from single to multiple appearing/disappearing objects, from precise to imprecise measurements and measurement models. This book...
Random graph models for dynamic networks
Zhang, Xiao; Newman, M E J
2016-01-01
We propose generalizations of a number of standard network models, including the classic random graph, the configuration model, and the stochastic block model, to the case of time-varying networks. We assume that the presence and absence of edges are governed by continuous-time Markov processes with rate parameters that can depend on properties of the nodes. In addition to computing equilibrium properties of these models, we demonstrate their use in data analysis and statistical inference, giving efficient algorithms for fitting them to observed network data. This allows us, for instance, to estimate the time constants of network evolution or infer community structure from temporal network data using cues embedded both in the probabilities over time that node pairs are connected by edges and in the characteristic dynamics of edge appearance and disappearance. We illustrate our methods with a selection of applications, both to computer-generated test networks and real-world examples.
A CONDITIONAL RANDOM FIELDS APPROACH TO BIOMEDICAL NAMED ENTITY RECOGNITION
无
2007-01-01
Named entity recognition is a fundamental task in biomedical data mining. In this letter, a named entity recognition system based on CRFs (Conditional Random Fields) for biomedical texts is presented. The system makes extensive use of a diverse set of features, including local features, full text features and external resource features. All features incorporated in this system are described in detail,and the impacts of different feature sets on the performance of the system are evaluated. In order to improve the performance of system, post-processing modules are exploited to deal with the abbreviation phenomena, cascaded named entity and boundary errors identification. Evaluation on this system proved that the feature selection has important impact on the system performance, and the post-processing explored has an important contribution on system performance to achieve better results.
Speckle Optical Tweezers: Micromanipulation with Random Light Fields
Volpe, Giorgio; Callegari, Agnese; Volpe, Giovanni; Gigan, Sylvain
2014-01-01
Current optical manipulation techniques rely on carefully engineered setups and samples. Although similar conditions are routinely met in research laboratories, it is still a challenge to manipulate microparticles when the environment is not well controlled and known a priori, since optical imperfections and scattering limit the applicability of this technique to real-life situations, such as in biomedical or microfluidic applications. Nonetheless, scattering of coherent light by disordered structures gives rise to speckles, random diffraction patterns with well-defined statistical properties. Here, we experimentally demonstrate how speckle fields can become a versatile tool to efficiently perform fundamental optical manipulation tasks such as trapping, guiding and sorting. We anticipate that the simplicity of these "speckle optical tweezers" will greatly broaden the perspectives of optical manipulation for real-life applications.
Strong mixing properties of max-infinitely divisible random fields
Dombry, Clément
2012-01-01
Let $\\eta=(\\eta(t))_{t\\in T}$ be a sample continuous max-infinitely random field on a locally compact metric space $T$. For a closed subset $S\\in T$, we note $\\eta_{S}$ the restriction of $\\eta$ to $S$. We consider $\\beta(S_1,S_2)$ the absolute regularity coefficient between $\\eta_{S_1}$ and $\\eta_{S_2}$, where $S_1,S_2$ are two disjoint closed subsets of $T$. Our main result is a simple upper bound for $\\beta(S_1,S_2)$ involving the exponent measure $\\mu$ of $\\eta$: we prove that $\\beta(S_1,S_2)\\leq 2\\int \\bbP[\\eta\
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...
On Polynomial Lieb-Robinson Bounds for the XY Chain in a Decaying Random Field
Gebert, Martin; Lemm, Marius
2016-08-01
We consider the isotropic XY quantum spin chain in a random external field in the z direction, with single site distributions given by i.i.d. random variables times the critical decaying envelope j^{-1/2}. Our motivation is the study of many-body localization. We investigate transport properties in terms of polynomial Lieb-Robinson (PLR) bounds. We prove a zero-velocity PLR bound for large disorder strength λ and for small λ we show a partial converse, which suggests the existence of a transition to non-trivial transport in the model.
Random pinning glass transition: hallmarks, mean-field theory and renormalization group analysis.
Cammarota, Chiara; Biroli, Giulio
2013-03-28
We present a detailed analysis of glass transitions induced by pinning particles at random from an equilibrium configuration. We first develop a mean-field analysis based on the study of p-spin spherical disordered models and then obtain the three-dimensional critical behavior by the Migdal-Kadanoff real space renormalization group method. We unveil the important physical differences with the case in which particles are pinned from a random (or very high temperature) configuration. We contrast the pinning particles approach to the ones based on biasing dynamical trajectories with respect to their activity and on coupling to equilibrium configurations. Finally, we discuss numerical and experimental tests.
Interfacing materials models with fire field models
Nicolette, V.F.; Tieszen, S.R.; Moya, J.L.
1995-12-01
For flame spread over solid materials, there has traditionally been a large technology gap between fundamental combustion research and the somewhat simplistic approaches used for practical, real-world applications. Recent advances in computational hardware and computational fluid dynamics (CFD)-based software have led to the development of fire field models. These models, when used in conjunction with material burning models, have the potential to bridge the gap between research and application by implementing physics-based engineering models in a transient, multi-dimensional tool. This paper discusses the coupling that is necessary between fire field models and burning material models for the simulation of solid material fires. Fire field models are capable of providing detailed information about the local fire environment. This information serves as an input to the solid material combustion submodel, which subsequently calculates the impact of the fire environment on the material. The response of the solid material (in terms of thermal response, decomposition, charring, and off-gassing) is then fed back into the field model as a source of mass, momentum and energy. The critical parameters which must be passed between the field model and the material burning model have been identified. Many computational issues must be addressed when developing such an interface. Some examples include the ability to track multiple fuels and species, local ignition criteria, and the need to use local grid refinement over the burning material of interest.
Numerical analysis for random temperature fields of embankment in cold regions
LIU ZhiQiang; LAI YuanMing; ZHANG MingYi; ZHANG XueFu
2007-01-01
The stochastic finite element equations for random temperature are obtained using the first-order perturbation technique taking into account the random thermal properties and boundary condition,based on heat transfer variational principle.The local average method for 2-D is used to discretize random fields.Then,the random temperature fields of embankment in cold regions are investigated on condition that the thermal properties and boundary condition are taken as random fields,respectively,by using the program,which is written by the methods.The expected value of temperature field and the standard deviation of the temperature field of embankment in cold regions are obtained and analyzed.
Numerical analysis for random temperature fields of embankment in cold regions
2007-01-01
The stochastic finite element equations for random temperature are obtained using the first-order per-turbation technique taking into account the random thermal properties and boundary condition, based on heat transfer variational principle. The local average method for 2-D is used to discretize random fields. Then, the random temperature fields of embankment in cold regions are investigated on condi-tion that the thermal properties and boundary condition are taken as random fields, respectively, by using the program, which is written by the methods. The expected value of temperature field and the standard deviation of the temperature field of embankment in cold regions are obtained and analyzed.
Estimation in Dirichlet random effects models
Kyung, Minjung; Casella, George; 10.1214/09-AOS731
2010-01-01
We develop a new Gibbs sampler for a linear mixed model with a Dirichlet process random effect term, which is easily extended to a generalized linear mixed model with a probit link function. Our Gibbs sampler exploits the properties of the multinomial and Dirichlet distributions, and is shown to be an improvement, in terms of operator norm and efficiency, over other commonly used MCMC algorithms. We also investigate methods for the estimation of the precision parameter of the Dirichlet process, finding that maximum likelihood may not be desirable, but a posterior mode is a reasonable approach. Examples are given to show how these models perform on real data. Our results complement both the theoretical basis of the Dirichlet process nonparametric prior and the computational work that has been done to date.
Gravity field modelling and gravimetry
Krynski Jan
2015-12-01
Full Text Available The summary of research activities concerning gravity field modelling and gravimetric works performed in Poland in the period of 2011-2014 is presented. It contains the results of research on geoid modelling in Poland and other countries, evaluation of global geopotential models, determination of temporal variations of the gravity field with the use of data from satellite gravity space missions, absolute gravity surveys for the maintenance and modernization of the gravity control in Poland and overseas, metrological aspects in gravimetry, maintenance of gravimetric calibration baselines, and investigations of the nontidal gravity changes. The bibliography of the related works is given in references.
Stochastic-field cavitation model
Dumond, J., E-mail: julien.dumond@areva.com [AREVA Nuclear Professional School, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen (Germany); AREVA GmbH, Erlangen, Paul-Gossen-Strasse 100, D-91052 Erlangen (Germany); Magagnato, F. [Institute of Fluid Mechanics, Karlsruhe Institute of Technology, Kaiserstrasse 12, D-76131 Karlsruhe (Germany); Class, A. [AREVA Nuclear Professional School, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen (Germany); Institute for Nuclear and Energy Technologies, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen (Germany)
2013-07-15
Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian “particles” or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.
Stochastic-field cavitation model
Dumond, J.; Magagnato, F.; Class, A.
2013-07-01
Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian "particles" or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.
Khaneja, Mamta; Ghosh, Santanu; Gautam, Seema; Kumar, Prashant; Rawat, J S; Chaudhury, P K; Vankar, V D; Kumar, Vikram
2015-05-01
High field emission (FE) current density from carbon nanotube (CNT) arrays grown on lithographically patterned silicon substrates is reported. A typical patterned field emitter array consists of bundles of nanotubes separated by a fixed gap and spread over the entire emission area. Emission performance from such an array having randomly oriented nanotube growth within each bundle is reported for different bundle sizes and separations. One typical sample with aligned CNTs within the bundle is also examined for comparison. It is seen that the current density from an array having random nanotube growth within the bundles is appreciably higher as compared to its aligned counterpart. The influence of structure on FE current densities as revealed by Raman spectroscopy is also seen. It is also observed that current density depends on edge length and increases with the same for all samples under study. Highest current density of -100 mA cm(-2) at an applied field of 5 V/μm is achieved from the random growth patterned sample with a bundle size of 2 μm and spacing of 4 μm between the bundles.
A dissipative random velocity field for fully developed fluid turbulence
Pereira, Rodrigo M; Chevillard, Laurent
2015-01-01
We investigate the statistical properties, based on numerical simulations and analytical calculations, of a recently proposed stochastic model for the velocity field of an incompressible, homogeneous, isotropic and fully developed turbulent flow. A key step in the construction of this model is the introduction of some aspects of the vorticity stretching mechanism that governs the dynamics of fluid particles along their trajectory. An additional further phenomenological step aimed at including the long range correlated nature of turbulence makes this model depending on a single free parameter $\\gamma$ that can be estimated from experimental measurements. We confirm the realism of the model regarding the geometry of the velocity gradient tensor, the power-law behaviour of the moments of velocity increments (i.e. the structure functions), including the intermittent corrections, and the existence of energy transfers across scales. We quantify the dependence of these basic properties of turbulent flows on the free...
Predictors of Consent in a Randomized Field Study in Child Welfare.
McDonald, Tom; Bhattarai, Jackie; Akin, Becci
2017-01-01
Randomized controlled trials (RCTs) are often viewed as the "gold standard" for proving the efficacy and effectiveness of new interventions. However, some are skeptical of the generalizability of the findings that RCTs produce. The characteristics of those willing to participate in research studies have the potential to affect the generalizability of its findings. This study examined factors that could influence consent among families recruited to participate in a randomized field trial in a real-world child welfare setting. This study tested the Parent Management Training Oregon Model for children in foster care with serious emotional disturbance. It employed a post-randomization consent design, whereby the entire sample of eligible participants, not just those who are willing to consent to randomization, are included in the sample. Initial eligibility assessment data and data from the federally mandated reporting system for public child welfare agencies provided the pool of potential predictors of consent. Bivariate and multivariate analyses were conducted to identify statistically significant predictors of consent. Being a dual reunification family was the most significant factor in predicting consent. Unmarried individuals, younger, female parents, cases where parental incarceration was the reason for removal and cases where the removal reason was not due to their children's behavioral problem(s) were also more likely to participate. As one of the first research studies to examine predictors of consent to a randomized field study in child welfare settings, results presented here can act as a preliminary guide for conducting RCTs in child welfare settings.
A strong law of large numbers for harmonizable isotropic random fields
Randall J. Swift
1997-01-01
Full Text Available The class of harmonizable fields is a natural extension of the class of stationary fields. This paper considers a strong law of large numbers for the spherical average of a harmonizable isotropic random field.
Clustering, randomness, and regularity in cloud fields. 4: Stratocumulus cloud fields
Lee, J.; Chou, J.; Weger, R. C.; Welch, R. M.
1994-01-01
To complete the analysis of the spatial distribution of boundary layer cloudiness, the present study focuses on nine stratocumulus Landsat scenes. The results indicate many similarities between stratocumulus and cumulus spatial distributions. Most notably, at full spatial resolution all scenes exhibit a decidedly clustered distribution. The strength of the clustering signal decreases with increasing cloud size; the clusters themselves consist of a few clouds (less than 10), occupy a small percentage of the cloud field area (less than 5%), contain between 20% and 60% of the cloud field population, and are randomly located within the scene. In contrast, stratocumulus in almost every respect are more strongly clustered than are cumulus cloud fields. For instance, stratocumulus clusters contain more clouds per cluster, occupy a larger percentage of the total area, and have a larger percentage of clouds participating in clusters than the corresponding cumulus examples. To investigate clustering at intermediate spatial scales, the local dimensionality statistic is introduced. Results obtained from this statistic provide the first direct evidence for regularity among large (more than 900 m in diameter) clouds in stratocumulus and cumulus cloud fields, in support of the inhibition hypothesis of Ramirez and Bras (1990). Also, the size compensated point-to-cloud cumulative distribution function statistic is found to be necessary to obtain a consistent description of stratocumulus cloud distributions. A hypothesis regarding the underlying physical mechanisms responsible for cloud clustering is presented. It is suggested that cloud clusters often arise from 4 to 10 triggering events localized within regions less than 2 km in diameter and randomly distributed within the cloud field. As the size of the cloud surpasses the scale of the triggering region, the clustering signal weakens and the larger cloud locations become more random.
Dynamic attack zone of air-to-air missile after being launched in random wind field
Hui Yaoluo; Nan Ying; Chen Shaodong; Ding Quanxin; Wu Shengliang
2015-01-01
A new concept is presented for air-to-air missile which is dynamic attack zone after being launched in random wind field. This new concept can be used to obtain the 4-dimensional (4-D) information regarding the dynamic envelope of an air-to-air missile at any flight time aimed at different flight targets considering influences of random wind, in the situation of flight fighters coop-erated with missiles fighting against each other. Based on an air-to-air missile model, some typical cases of dynamic attack zone after being launched in random wind field were numerically simulated. Compared with the simulation results of traditional dynamic envelope, the properties of dynamic attack zone after being launched are as follows. The 4-D dynamic attack zone after being launched is inside traditional maximum dynamic envelope, but its forane boundary is usually not inside tra-ditional no-escape dynamic envelope;Traditional dynamic attack zone can just be reliably used at launch time, while dynamic envelope after being launched can be reliably and accurately used dur-ing any flight antagonism time. Traditional envelope is a special case of dynamic envelope after being launched when the dynamic envelope is calculated at the launch time;the dynamic envelope after being launched can be influenced by the random wind field.
Continuous Markov Random Fields for Robust Stereo Estimation
Yamaguchi, Koichiro; McAllester, David; Urtasun, Raquel
2012-01-01
In this paper we present a novel slanted-plane MRF model which reasons jointly about occlusion boundaries as well as depth. We formulate the problem as the one of inference in a hybrid MRF composed of both continuous (i.e., slanted 3D planes) and discrete (i.e., occlusion boundaries) random variables. This allows us to define potentials encoding the ownership of the pixels that compose the boundary between segments, as well as potentials encoding which junctions are physically possible. Our approach outperforms the state-of-the-art on Middlebury high resolution imagery as well as in the more challenging KITTI dataset, while being more efficient than existing slanted plane MRF-based methods, taking on average 2 minutes to perform inference on high resolution imagery.
Scaling of coercivity in a 3d random anisotropy model
Proctor, T.C., E-mail: proctortc@gmail.com; Chudnovsky, E.M., E-mail: EUGENE.CHUDNOVSKY@lehman.cuny.edu; Garanin, D.A.
2015-06-15
The random-anisotropy Heisenberg model is numerically studied on lattices containing over ten million spins. The study is focused on hysteresis and metastability due to topological defects, and is relevant to magnetic properties of amorphous and sintered magnets. We are interested in the limit when ferromagnetic correlations extend beyond the size of the grain inside which the magnetic anisotropy axes are correlated. In that limit the coercive field computed numerically roughly scales as the fourth power of the random anisotropy strength and as the sixth power of the grain size. Theoretical arguments are presented that provide an explanation of numerical results. Our findings should be helpful for designing amorphous and nanosintered materials with desired magnetic properties. - Highlights: • We study the random-anisotropy model on lattices containing up to ten million spins. • Irreversible behavior due to topological defects (hedgehogs) is elucidated. • Hysteresis loop area scales as the fourth power of the random anisotropy strength. • In nanosintered magnets the coercivity scales as the six power of the grain size.
A random effects epidemic-type aftershock sequence model.
Lin, Feng-Chang
2011-04-01
We consider an extension of the temporal epidemic-type aftershock sequence (ETAS) model with random effects as a special case of a well-known doubly stochastic self-exciting point process. The new model arises from a deterministic function that is randomly scaled by a nonnegative random variable, which is unobservable but assumed to follow either positive stable or one-parameter gamma distribution with unit mean. Both random effects models are of interest although the one-parameter gamma random effects model is more popular when modeling associated survival times. Our estimation is based on the maximum likelihood approach with marginalized intensity. The methods are shown to perform well in simulation experiments. When applied to an earthquake sequence on the east coast of Taiwan, the extended model with positive stable random effects provides a better model fit, compared to the original ETAS model and the extended model with one-parameter gamma random effects.
Mean-field models for disordered crystals
Cancès, Eric; Lewin, Mathieu
2012-01-01
In this article, we set up a functional setting for mean-field electronic structure models of Hartree-Fock or Kohn-Sham types for disordered crystals. The electrons are quantum particles and the nuclei are classical point-like articles whose positions and charges are random. We prove the existence of a minimizer of the energy per unit volume and the uniqueness of the ground state density of such disordered crystals, for the reduced Hartree-Fock model (rHF). We consider both (short-range) Yukawa and (long-range) Coulomb interactions. In the former case, we prove in addition that the rHF ground state density matrix satisfies a self-consistent equation, and that our model for disordered crystals is the thermodynamic limit of the supercell model.
Kouritzin, Michael A; Newton, Fraser; Wu, Biao
2013-04-01
Herein, we propose generating CAPTCHAs through random field simulation and give a novel, effective and efficient algorithm to do so. Indeed, we demonstrate that sufficient information about word tests for easy human recognition is contained in the site marginal probabilities and the site-to-nearby-site covariances and that these quantities can be embedded directly into certain conditional probabilities, designed for effective simulation. The CAPTCHAs are then partial random realizations of the random CAPTCHA word. We start with an initial random field (e.g., randomly scattered letter pieces) and use Gibbs resampling to re-simulate portions of the field repeatedly using these conditional probabilities until the word becomes human-readable. The residual randomness from the initial random field together with the random implementation of the CAPTCHA word provide significant resistance to attack. This results in a CAPTCHA, which is unrecognizable to modern optical character recognition but is recognized about 95% of the time in a human readability study.
Biomedical image analysis using Markov random fields & efficient linear programing.
Komodakis, Nikos; Besbes, Ahmed; Glocker, Ben; Paragios, Nikos
2009-01-01
Computer-aided diagnosis through biomedical image analysis is increasingly considered in health sciences. This is due to the progress made on the acquisition side, as well as on the processing one. In vivo visualization of human tissues where one can determine both anatomical and functional information is now possible. The use of these images with efficient intelligent mathematical and processing tools allows the interpretation of the tissues state and facilitates the task of the physicians. Segmentation and registration are the two most fundamental tools in bioimaging. The first aims to provide automatic tools for organ delineation from images, while the second focuses on establishing correspondences between observations inter and intra subject and modalities. In this paper, we present some recent results towards a common formulation addressing these problems, called the Markov Random Fields. Such an approach is modular with respect to the application context, can be easily extended to deal with various modalities, provides guarantees on the optimality properties of the obtained solution and is computationally efficient.
Schwinger-Dyson equations in large-N quantum field theories and nonlinear random processes
Buividovich, P V
2010-01-01
We study stochastic methods for solving Schwinger-Dyson equations in large-N quantum field theories. Expectation values of single-trace operators are sampled by stationary probability distributions of so-called nonlinear random processes. The set of all histories of such processes corresponds to the set of all planar diagrams in the perturbative expansion of the theory. We describe stochastic algorithms for summation of planar diagrams in matrix-valued scalar field theory and in the Weingarten model of random planar surfaces on the lattice. For compact field variables, the method does not converge in the physically most interesting weak-coupling limit. In this case one can absorb the divergences into the self-consistent redefinition of expansion parameters. Stochastic solution of the self-consistency conditions can be implemented as a random process with memory. We illustrate this idea on the example of two-dimensional O(N) sigma-model. Extension to non-Abelian lattice gauge theories is discussed.
One- and two-matrix models and random cylindre with two-coloured boundaries
Orantin, Nicolas
2004-01-01
In this training course report, I briefly present the one- and two-matrix models as tools for the study of conformal field theories with boundaries. In a first part, after a short historical presentation of random matrices, I present the matrix models' formalism, their diagramatic interpretation, their link with random surfaces and conformal field theories and the "loop equations" method for the 2-matrix model. In a second part, I use this method for the calculation of the generating function of random cylindres whose boundaries are two-coloured, which was not know before.
Khrennikov, Andrei
2017-02-01
The scientific methodology based on two descriptive levels, ontic (reality as it is) and epistemic (observational), is briefly presented. Following Schrödinger, we point to the possible gap between these two descriptions. Our main aim is to show that, although ontic entities may be unaccessible for observations, they can be useful for clarification of the physical nature of operational epistemic entities. We illustrate this thesis by the concrete example: starting with the concrete ontic model preceding quantum mechanics (the latter is treated as an epistemic model), namely, prequantum classical statistical field theory (PCSFT), we propose the natural physical interpretation for the basic quantum mechanical entity-the quantum state ("wave function"). The correspondence PCSFT ↦ QM is not straightforward, it couples the covariance operators of classical (prequantum) random fields with the quantum density operators. We use this correspondence to clarify the physical meaning of the pure quantum state and the superposition principle-by using the formalism of classical field correlations.
Characteristic Polynomials of Complex Random Matrix Models
Akemann, G
2003-01-01
We calculate the expectation value of an arbitrary product of characteristic polynomials of complex random matrices and their hermitian conjugates. Using the technique of orthogonal polynomials in the complex plane our result can be written in terms of a determinant containing these polynomials and their kernel. It generalizes the known expression for hermitian matrices and it also provides a generalization of the Christoffel formula to the complex plane. The derivation we present holds for complex matrix models with a general weight function at finite-N, where N is the size of the matrix. We give some explicit examples at finite-N for specific weight functions. The characteristic polynomials in the large-N limit at weak and strong non-hermiticity follow easily and they are universal in the weak limit. We also comment on the issue of the BMN large-N limit.
Critical Interfaces in the Random-Bond Potts Model
Jacobsen, Jesper L.; Le Doussal, Pierre; Picco, Marco; Santachiara, Raoul; Wiese, Kay Jörg
2009-02-01
We study geometrical properties of interfaces in the random-temperature q-states Potts model as an example of a conformal field theory weakly perturbed by quenched disorder. Using conformal perturbation theory in q-2 we compute the fractal dimension of Fortuin-Kasteleyn (FK) domain walls. We also compute it numerically both via the Wolff cluster algorithm for q=3 and via transfer-matrix evaluations. We also obtain numerical results for the fractal dimension of spin clusters interfaces for q=3. These are found numerically consistent with the duality κspinκFK=16 as expressed in putative SLE parameters.
CONVERGENCE RATES IN THE STRONG LAWS OF ASYMPTOTICALLY NEGATIVELY ASSOCIATED RANDOM FIELDS
ZhangLixin; WangXiuyun
1999-01-01
In this paper, a notion of negative side p-mixing (p -mixing) which can be regardedas asymptotic negative association is defined, and some Rosenthal type inequalities for p -mix-ing random fields are established. The complete convergence and almost sure summability onthe convergence rates with respect to the strong law of large numbers are also discussed for p--mixing random fields. The results obtained extend those for negatively associated sequences andp" -mixing random fields.
Representation and prediction for locally harmonizable isotropic random fields
Randall J. Swift
1995-01-01
Full Text Available The class of harmonizable fields is a natural extension of the class of stationary fields. This paper considers fields whose increments are harmonizable and isotropic. Spectral representations are obtained for locally harmonizable isotropic fields. A linear least squares prediction for locally harmonizable isotropic fields is considered.
Improved modeling techniques for turbomachinery flow fields
Lakshminarayana, B. [Pennsylvania State Univ., University Park, PA (United States); Fagan, J.R. Jr. [Allison Engine Company, Indianapolis, IN (United States)
1995-10-01
This program has the objective of developing an improved methodology for modeling turbomachinery flow fields, including the prediction of losses and efficiency. Specifically, the program addresses the treatment of the mixing stress tensor terms attributed to deterministic flow field mechanisms required in steady-state Computational Fluid Dynamic (CFD) models for turbo-machinery flow fields. These mixing stress tensors arise due to spatial and temporal fluctuations (in an absolute frame of reference) caused by rotor-stator interaction due to various blade rows and by blade-to-blade variation of flow properties. These tasks include the acquisition of previously unavailable experimental data in a high-speed turbomachinery environment, the use of advanced techniques to analyze the data, and the development of a methodology to treat the deterministic component of the mixing stress tensor. Penn State will lead the effort to make direct measurements of the momentum and thermal mixing stress tensors in high-speed multistage compressor flow field in the turbomachinery laboratory at Penn State. They will also process the data by both conventional and conditional spectrum analysis to derive momentum and thermal mixing stress tensors due to blade-to-blade periodic and aperiodic components, revolution periodic and aperiodic components arising from various blade rows and non-deterministic (which includes random components) correlations. The modeling results from this program will be publicly available and generally applicable to steady-state Navier-Stokes solvers used for turbomachinery component (compressor or turbine) flow field predictions. These models will lead to improved methodology, including loss and efficiency prediction, for the design of high-efficiency turbomachinery and drastically reduce the time required for the design and development cycle of turbomachinery.
Xiaofeng Sun
2017-08-01
Full Text Available As an intermediate step between raw remote sensing data and digital maps, remote sensing data classification has been a challenging and long-standing problem in the remote sensing research community. In this work, an automated and effective supervised classification framework is presented for classifying high-resolution remote sensing data. Specifically, the presented method proceeds in three main stages: feature extraction, classification, and classified result refinement. In the feature extraction stage, both multispectral images and 3D geometry data are used, which utilizes the complementary information from multisource data. In the classification stage, to tackle the problems associated with too many training samples and take full advantage of the information in the large-scale dataset, a random forest (RF ensemble learning strategy is proposed by combining several RF classifiers together. Finally, an improved fully connected conditional random field (FCCRF graph model is employed to derive the contextual information to refine the classification results. Experiments on the ISPRS Semantic Labeling Contest dataset show that the presented 3-stage method achieves 86.9% overall accuracy, which is a new state-of-the-art non-CNN (convolutional neural networks-based classification method.
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%.
Semikoz, V B
1994-01-01
We consider active-sterile neutrino conversions in the early universe hot plasma in the presence of a random magnetic field generated at the electroweak phase transition. Within a random field domain the magnetization asymmetry of the lepton antilepton plasma produced by a uniform constant magnetic field is huge in contrast to their small density asymmetry, leading to a drastic change in the active-sterile conversion rates. Assuming that the random field provides the seed for the galactic field one can estimate the restrictions from primordial nucleosynthesis. Requiring that the extra sterile \
Yang, Yongchao; Sun, Peng; Nagarajaiah, Satish; Bachilo, Sergei M.; Weisman, R. Bruce
2017-07-01
Structural damage is typically a local phenomenon that initiates and propagates within a limited area. As such high spatial resolution measurement and monitoring is often needed for accurate damage detection. This requires either significantly increased costs from denser sensor deployment in the case of global simultaneous/parallel measurements, or increased measurement time and labor in the case of global sequential measurements. This study explores the feasibility of an alternative approach to this problem: a computational solution in which a limited set of randomly positioned, low-resolution global strain measurements are used to reconstruct the full-field, high-spatial-resolution, two-dimensional (2D) strain field and rapidly detect local damage. The proposed approach exploits the implicit low-rank and sparse data structure of the 2D strain field: it is highly correlated without many edges and hence has a low-rank structure, unless damage-manifesting itself as sparse local irregularity-is present and alters such a low-rank structure slightly. Therefore, reconstruction of the full-field, high-spatial-resolution strain field from a limited set of randomly positioned low-resolution global measurements is modeled as a low-rank matrix completion framework and damage detection as a sparse decomposition formulation, enabled by emerging convex optimization techniques. Numerical simulations on a plate structure are conducted for validation. The results are discussed and a practical iterative global/local procedure is recommended. This new computational approach should enable the efficient detection of local damage using limited sets of strain measurements.
Exact simulation of Brown-Resnick random fields at a finite number of locations
Dieker, Ton; Mikosch, Thomas Valentin
2015-01-01
We propose an exact simulation method for Brown-Resnick random fields, building on new representations for these stationary max-stable fields. The main idea is to apply suitable changes of measure.......We propose an exact simulation method for Brown-Resnick random fields, building on new representations for these stationary max-stable fields. The main idea is to apply suitable changes of measure....
Fractional generalized Lévy random fields as white noise functionals
HUANG Zhiyuan; LI Peiyan
2007-01-01
In this paper, we construct the fractional generalized Lévy random fields (FGLRF) as tempered white noise functionals. We find that this white noise approach is very effective in investigating the properties of these fields. Under some conditions, the fractional Lévy fields in the usual sense are obtained. In addition, we also present a method to construct the anisotropic fractional generalized Lévy random fields (AFGLRF).
Magnetic Field Line Random Walk in Isotropic Turbulence with Varying Mean Field
Sonsrettee, W.; Subedi, P.; Ruffolo, D.; Matthaeus, W. H.; Snodin, A. P.; Wongpan, P.; Chuychai, P.; Rowlands, G.; Vyas, S.
2016-08-01
In astrophysical plasmas, the magnetic field line random walk (FLRW) plays an important role in guiding particle transport. The FLRW behavior is scaled by the Kubo number R=(b/{B}0)({{\\ell }}\\parallel /{{\\ell }}\\perp ) for rms magnetic fluctuation b, large-scale mean field {{\\boldsymbol{B}}}0, and coherence scales parallel ({{\\ell }}\\parallel ) and perpendicular ({{\\ell }}\\perp ) to {{\\boldsymbol{B}}}0. Here we use a nonperturbative analytic framework based on Corrsin’s hypothesis, together with direct computer simulations, to examine the R-scaling of the FLRW for varying B 0 with finite b and isotropic fluctuations with {{\\ell }}\\parallel /{{\\ell }}\\perp =1, instead of the well-studied route of varying {{\\ell }}\\parallel /{{\\ell }}\\perp for b \\ll {B}0. The FLRW for isotropic magnetic fluctuations is also of astrophysical interest regarding transport processes in the interstellar medium. With a mean field, fluctuations may have variance anisotropy, so we consider limiting cases of isotropic variance and transverse variance (with b z = 0). We obtain analytic theories, and closed-form solutions for extreme cases. Padé approximants are provided to interpolate all versions of theory and simulations to any B 0. We demonstrate that, for isotropic turbulence, Corrsin-based theories generally work well, and with increasing R there is a transition from quasilinear to Bohm diffusion. This holds even with b z = 0, when different routes to R\\to ∞ are mathematically equivalent; in contrast with previous studies, we find that a Corrsin-based theory with random ballistic decorrelation works well even up to R = 400, where the effects of trapping are barely perceptible in simulation results.
Scene-Layout Compatible Conditional Random Field for Classifying Terrestrial Laser Point Clouds
Luo, C.; Sohn, G.
2014-08-01
Terrestrial Laser Scanning (TLS) rapidly becomes a primary surveying tool due to its fast acquisition of highly dense threedimensional point clouds. For fully utilizing its benefits, developing a robust method to classify many objects of interests from huge amounts of laser point clouds is urgently required. Conditional Random Field (CRF) is a well-known discriminative classifier, which integrates local appearance of the observation (laser point) with spatial interactions among its neighbouring points in classification process. Typical CRFs employ generic label consistency using short-range dependency only, which often causes locality problem. In this paper, we present a multi-range and asymmetric Conditional Random Field (CRF) (maCRF), which adopts a priori information of scene-layout compatibility addressing long-range dependency. The proposed CRF constructs two graphical models, one for enhancing a local labelling smoothness within short-range (srCRF) and the other for favouring a global and asymmetric regularity of spatial arrangement between different object classes within long-range (lrCRF). This maCRF classifier assumes two graphical models (srCRF and lrCRF) are independent of each other. Final labelling decision was accomplished by probabilistically combining prediction results obtained from two CRF models. We validated maCRF's performance with TLS point clouds acquired from RIEGL LMS-Z390i scanner using cross validation. Experiment results demonstrate that synergetic classification improvement can be achievable by incorporating two CRF models.
Khrennikov, Andrei
2016-01-01
The scientific methodology based on two descriptive levels, ontic (reality as it is ) and epistemic (observational), is briefly presented. Following Schr\\"odinger, we point to the possible gap between these two descriptions. Our main aim is to show that, although ontic entities may be inaccessible for observations, they can be useful for clarification of the physical nature of operational epistemic entities. We illustrate this thesis by the concrete example: starting with the concrete ontic model preceding quantum mechanics (the latter is treated as an epistemic model), namely, prequantum classical statistical field theory (PCSFT), we propose the natural physical interpretation for the basic quantum mechanical entity - the quantum state ("wave function"). The correspondence PCSFT to QM is not straightforward, it couples the covariance operators of classical (prequantum) random fields with the quantum density operators. We use this correspondence to clarify the physical meaning of the pure quantum state and th...
Self-Organized Criticality in a Random Network Model
Nirei, Makoto
1998-01-01
A new model of self-organized criticality is defined by incorporating a random network model in order to explain endogenous complex fluctuations of economic aggregates. The model can feature many globally interactive systems such as economies or societies.
Automatic Recognition of Chinese Personal Name Using Conditional Random Fields and Knowledge Base
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.
Reduced Wiener Chaos representation of random fields via basis adaptation and projection
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.
Submicron structure random field on granular soil material with retinex algorithm optimization
Liang, Yu; Tao, Chenyuan; Zhou, Bingcheng; Huang, Shuai; Huang, Linchong
2017-06-01
In this paper, a Retinex scale optimized image enhancement algorithm is proposed, which can enhance the micro vision image and eliminate the influence of the uneven illumination. Based on that, a random geometric model of the microstructure of granular materials is established with Monte-Carlo method, the numerical simulation including consolidation process of granular materials is compared with the experimental data. The results have proved that the random field method with Retinex image enhancement algorithm is effective, the image of microstructure of granular materials becomes clear and the contrast ratio is improved, after using Retinex image enhancement algorithm to enhance the CT image. The fidelity of enhanced image is higher than that dealing with other method, which have explained that the algorithm can preserve the microstructure information of the image well. The result of numerical simulation is similar with the one obtained from conventional three axis consolidation test, which proves that the simulation result is reliable.
Distributed Denial of Service Attacks Detection Method Based on Conditional Random Fields
Shi-wen CHEN
2013-04-01
Full Text Available In order to detect distributed denial of service (DDoS attacks accurately and efficiently, a new detection model based on conditional random fields (CRF was proposed. The CRF based model incorporates the signature-based and anomaly-based detection methods to a hybrid system. The selected features include source IP entropy, destination IP entropy, source port entropy, destination port entropy, protocol number and etc. The CRF based model combines these IP flow entropies and other fingerprints into a normalize entropy as the feature vectors to depict the states of the monitoring traffic. The training method of the detection model uses the L-BFGS algorithm. And the model only needs to inspect the IP header fields of each packet, which makes it possible for real-time implementation even on real time network traffic. The CRF based model may have the ability to detect new form of forthcoming attacks, because it is independent from any specific DDoS flooding attack tools. The experiment results show that the CRF based method has higher detection accuracy and sensitivity as well as lower false positive alarms. Experiment with KDD CUP1999, DARPA 2000 and generated attack datasets, the CRF based model outperforms other well-known detection methods such as Naïve Bayes, KNN, SVM and etc. The accuracy goes beyond 95.0% and the false alarm rate is less than 5.0%. Meanwhile, the CRF based model is robust under massive background network traffic.
Competitive growth model involving random deposition and random deposition with surface relaxation
Horowitz, Claudio M.; Monetti, Roberto A.; Albano, Ezequiel V.
2001-06-01
A deposition model that considers a mixture of random deposition with surface relaxation and a pure random deposition is proposed and studied. As the system evolves, random deposition with surface relaxation (pure random deposition) take place with probability p and (1{minus}p), respectively. The discrete (microscopic) approach to the model is studied by means of extensive numerical simulations, while continuous equations are used in order to investigate the mesoscopic properties of the model. A dynamic scaling ansatz for the interface width W(L,t,p) as a function of the lattice side L, the time t and p is formulated and tested. Three exponents, which can be linked to the standard growth exponent of random deposition with surface relaxation by means of a scaling relation, are identified. In the continuous limit, the model can be well described by means of a phenomenological stochastic growth equation with a p-dependent effective surface tension.
Path properties of lp-valued Gaussian random fields
Yong-Kab; CHOI
2007-01-01
)[16]Book S A,Shore T R.On large intervals in the Cs(o)rg(o)-Révész theorem on increments of a Wiener process.Z Wahrsch Verw Gebiete,46:1-11 (1978)[17]Choi Y K,K(o)no N.How big are the increments of a two-parameter Gaussian process? J Theoret Probab,12(1):105-129 (1999)[18]Lin Z Y,Choi Y K.Some limit theorems for fractional Levy Brownian fields.Stoch Proc & Their Appl,82:229-244 (1999)[19]Lin Z Y,Lee S H,Hwang K S et al.Some limit theorems on the increments of lp-valued multi-parameter Gaussian processes.Acta Math Sinica,English Ser,20(6):1019-1028 (2004)[20]Slepian D.The one-sided barrier problem for Gaussian noise.Bell System Tech J,41:463-501 (1962)[21]Choi Y K,Lin Z Y,Sung H S et al.Limit behaviors for the increments of a d-dimensional multi-parameter Gaussian process.J Korean Math Soc,42(6):1265-1278 (2005)[22]Leadbetter M R,Lindgren G,Rootzen H.Extremes and Related Properties of Random Sequences and Processes.New York:Springer-Verlag,1983[23]Li W V,Shao Q M.A normal comparison inequality and its applications.Probab Theory & Rel Fields,122:494-508 (2002)
GENERAL: Mean-field Theory for Some Bus Transport Networks with Random Overlapping Clique Structure
Yang, Xu-Hua; Sun, Bao; Wang, Bo; Sun, You-Xian
2010-04-01
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.
Modeling of Random Delays in Networked Control Systems
Yuan Ge
2013-01-01
Full Text Available In networked control systems (NCSs, the presence of communication networks in control loops causes many imperfections such as random delays, packet losses, multipacket transmission, and packet disordering. In fact, random delays are usually the most important problems and challenges in NCSs because, to some extent, other problems are often caused by random delays. In order to compensate for random delays which may lead to performance degradation and instability of NCSs, it is necessary to establish the mathematical model of random delays before compensation. In this paper, four major delay models are surveyed including constant delay model, mutually independent stochastic delay model, Markov chain model, and hidden Markov model. In each delay model, some promising compensation methods of delays are also addressed.
Estimation of the Nonlinear Random Coefficient Model when Some Random Effects Are Separable
du Toit, Stephen H. C.; Cudeck, Robert
2009-01-01
A method is presented for marginal maximum likelihood estimation of the nonlinear random coefficient model when the response function has some linear parameters. This is done by writing the marginal distribution of the repeated measures as a conditional distribution of the response given the nonlinear random effects. The resulting distribution…
Thierry Géraud
2004-12-01
Full Text Available We present a fast method for road network extraction in satellite images. It can be seen as a transposition of the segmentation scheme Ã¢Â€Âœwatershed transform + region adjacency graph + Markov random fieldsÃ¢Â€Â to the extraction of curvilinear objects. Many road extractors which are composed of two stages can be found in the literature. The first one acts like a filter that can decide from a local analysis, at every image point, if there is a road or not. The second stage aims at obtaining the road network structure. In the method we propose to rely on a Ã¢Â€ÂœpotentialÃ¢Â€Â image, that is, unstructured image data that can be derived from any road extractor filter. In such a potential image, the value assigned to a point is a measure of its likelihood to be located in the middle of a road. A filtering step applied on the potential image relies on the area closing operator followed by the watershed transform to obtain a connected line which encloses the road network. Then a graph describing adjacency relationships between watershed lines is built. Defining Markov random fields upon this graph, associated with an energetic model of road networks, leads to the expression of road network extraction as a global energy minimization problem. This method can easily be adapted to other image processing fields, where the recognition of curvilinear structures is involved.
Certified randomness from a two-level system in a relativistic quantum field
Thinh, Le Phuc; Bancal, Jean-Daniel; Martín-Martínez, Eduardo
2016-08-01
Randomness is an indispensable resource in modern science and information technology. Fortunately, an experimentally simple procedure exists to generate randomness with well-characterized devices: measuring a quantum system in a basis complementary to its preparation. Towards realizing this goal one may consider using atoms or superconducting qubits, promising candidates for quantum information processing. However, their unavoidable interaction with the electromagnetic field affects their dynamics. At large time scales, this can result in decoherence. Smaller time scales in principle avoid this problem, but may not be well analyzed under the usual rotating wave and single mode approximation (RWA and SMA) which break the relativistic nature of quantum field theory. Here, we use a fully relativistic analysis to quantify the information that an adversary with access to the field could get on the result of an atomic measurement. Surprisingly, we find that the adversary's guessing probability is not minimized for atoms initially prepared in the ground state (an intuition derived from the RWA and SMA model).
Random spatial processes and geostatistical models for soil variables
Lark, R. M.
2009-04-01
Geostatistical models of soil variation have been used to considerable effect to facilitate efficient and powerful prediction of soil properties at unsampled sites or over partially sampled regions. Geostatistical models can also be used to investigate the scaling behaviour of soil process models, to design sampling strategies and to account for spatial dependence in the random effects of linear mixed models for spatial variables. However, most geostatistical models (variograms) are selected for reasons of mathematical convenience (in particular, to ensure positive definiteness of the corresponding variables). They assume some underlying spatial mathematical operator which may give a good description of observed variation of the soil, but which may not relate in any clear way to the processes that we know give rise to that observed variation in the real world. In this paper I shall argue that soil scientists should pay closer attention to the underlying operators in geostatistical models, with a view to identifying, where ever possible, operators that reflect our knowledge of processes in the soil. I shall illustrate how this can be done in the case of two problems. The first exemplar problem is the definition of operators to represent statistically processes in which the soil landscape is divided into discrete domains. This may occur at disparate scales from the landscape (outcrops, catchments, fields with different landuse) to the soil core (aggregates, rhizospheres). The operators that underly standard geostatistical models of soil variation typically describe continuous variation, and so do not offer any way to incorporate information on processes which occur in discrete domains. I shall present the Poisson Voronoi Tessellation as an alternative spatial operator, examine its corresponding variogram, and apply these to some real data. The second exemplar problem arises from different operators that are equifinal with respect to the variograms of the
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.
A Note on the Correlated Random Coefficient Model
Kolodziejczyk, Christophe
In this note we derive the bias of the OLS estimator for a correlated random coefficient model with one random coefficient, but which is correlated with a binary variable. We provide set-identification to the parameters of interest of the model. We also show how to reduce the bias of the estimator...
Compact Sets without Converging Sequences in the Random Real Model
D. Fremlin
2007-10-01
Full Text Available It is shown that in the model obtained by adding any number of random reals to a model of CH, there is a compact Hausdorff space of weight w1 which contains no non-trivial converging sequences. It is shown that for certain spaces with noconverging sequences, the addition of random reals will not add any converging sequences.
A random energy model for size dependence : recurrence vs. transience
Külske, Christof
1998-01-01
We investigate the size dependence of disordered spin models having an infinite number of Gibbs measures in the framework of a simplified 'random energy model for size dependence'. We introduce two versions (involving either independent random walks or branching processes), that can be seen as gener
Random non-Hermitian tight-binding models
Marinello, G.; Pato, M. P.
2016-08-01
For a one dimensional system tight binding models are described by sparse tridiagonal matrices which describe interactions between nearest neighbors. In this report, we construct open and closed random tight-binding models based in the tridiagonal matrices of the so-called,β-ensembles of random matrix theory.
Trapping in the random conductance model
Biskup, M; Rozinov, A; Vandenberg-Rodes, A
2012-01-01
We consider random walks on $\\Z^d$ among nearest-neighbor random conductances which are i.i.d., positive, bounded uniformly from above but whose support extends all the way to zero. Our focus is on the detailed properties of the paths of the random walk conditioned to return back to the starting point at time $2n$. We show that in the situations when the heat kernel exhibits subdiffusive decay --- which is known to occur in dimensions $d\\ge4$ --- the walk gets trapped for a time of order $n$ in a small spatial region. This shows that the strategy used earlier to infer subdiffusive lower bounds on the heat kernel in specific examples is in fact dominant. In addition, we settle a conjecture concerning the worst possible subdiffusive decay in four dimensions.
Trapping in the Random Conductance Model
Biskup, M.; Louidor, O.; Rozinov, A.; Vandenberg-Rodes, A.
2013-01-01
We consider random walks on ℤ d among nearest-neighbor random conductances which are i.i.d., positive, bounded uniformly from above but whose support extends all the way to zero. Our focus is on the detailed properties of the paths of the random walk conditioned to return back to the starting point at time 2 n. We show that in the situations when the heat kernel exhibits subdiffusive decay—which is known to occur in dimensions d≥4—the walk gets trapped for a time of order n in a small spatial region. This shows that the strategy used earlier to infer subdiffusive lower bounds on the heat kernel in specific examples is in fact dominant. In addition, we settle a conjecture concerning the worst possible subdiffusive decay in four dimensions.
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).
Remediating Computational Deficits at Third Grade: A Randomized Field Trial
Fuchs, Lynn S.; Powell, Sarah R.; Hamlett, Carol L.; Fuchs, Douglas; Cirino, Paul T.; FLETCHER, JACK M.
2008-01-01
The major purposes of this study were to assess the efficacy of tutoring to remediate 3rd-grade computational deficits and to explore whether remediation is differentially efficacious depending on whether students experience mathematics difficulty alone or concomitantly with reading difficulty. At 2 sites, 127 students were stratified on mathematics difficulty status and randomly assigned to 4 conditions: word recognition (control) tutoring or 1 of 3 computation tutoring conditions: fact retr...
Preventing Youth Violence and Dropout: A Randomized Field Experiment
Sara Heller; Harold A. Pollack; Roseanna Ander; Jens Ludwig
2013-01-01
Improving the long-term life outcomes of disadvantaged youth remains a top policy priority in the United States, although identifying successful interventions for adolescents - particularly males - has proven challenging. This paper reports results from a large randomized controlled trial of an intervention for disadvantaged male youth grades 7-10 from high-crime Chicago neighborhoods. The intervention was delivered by two local non-profits and included regular interactions with a pro-social ...
Papusoi, C. [Spintec, URA 2512 CEA/CNRS, 17 rue des Martyrs, 38054 Grenoble (France)], E-mail: cristian_papusoi@yahoo.com; Conraux, Y.; Prejbeanu, I.L. [Crocus Technology, 5 Robert Schumann, BP 1510, 38025 Grenoble (France); Sousa, R.; Dieny, B. [Spintec, URA 2512 CEA/CNRS, 17 rue des Martyrs, 38054 Grenoble (France)
2009-08-15
The minimum applied field H{sub SW} required to reverse the magnetic moment of the ferromagnetic/antiferromagnetic storage layer of a thermally assisted magnetic random access memory (TA-MRAM) device during the application of a heating electric pulse is investigated as a function of pulse power P{sub HP} and duration {delta}. For the same power of the heating pulse P{sub HP} (or, equivalently, for the same temperature of the storage layer), H{sub SW} increases with decreasing heating time {delta}. This behavior is consistently interpreted by a thermally activated propagating domain-wall switching model, corroborated by a real-time study of switching. The increase of H{sub SW} with decreasing pulse width introduces a constraint for the minimum power consumption of a TA-MRAM where writing combines heating and magnetic field application.
On competitive Lotka–Volterra model in random environments
Zhu, C; Yin, G
2009-01-01
Focusing on competitive Lotka-Volterra model in random environments, this paper uses regime-switching diffusions to model the dynamics of the population sizes of n different species in an ecosystem...
Khrennikov, Andrei
2014-11-01
This paper is a contribution to the project "emergent quantum mechanics" unifying a variety of attempts to treat quantum mechanics (QMs) as emergent from other theories pretending on finer descriptions of quantum phenomena. More concretely it is about an attempt to model detection probabilities predicted by QM for single photon states by using classical random fields interacting with detectors of the threshold type. Continuous field model, prequantum classical statistical field theory (PCSFT), was developed in recent years and its predictions about probabilities and correlations match well with QM. The main problem is to develop the corresponding measurement theory which would describe the transition from continuous fields to discrete events, "clicks of detectors". Some success was achieved and the click-probabilities for quantum observables can be derived from PCSFT by modeling interaction of fields with the threshold type detectors. However, already for the coefficient of second-order coherence g2(0) calculations are too complicated and only an estimation of g2(0) was obtained. In this paper, we present results of numerical simulation based on PCSFT and modeling of interaction with threshold type detectors. The "prequantum random field" interacting with a detector is modeled as the Brownian motion in the space of classical fields (Wiener process in complex Hilbert space). Simulation for g2(0) shows that this coefficient approaches zero with increase of the number of detections.
Aslam, Muhammad Zaheer
2011-01-01
Mobile Adhoc Network is a kind of wireless ad hoc network where nodes are connected wirelessly and the network is self configuring. MANET may work in a standalone manner or may be a part of another network. In this paper we have compared Random Walk Mobility Model and Random Waypoint Mobility Model over two reactive routing protocols Dynamic Source Routing (DSR) and Adhoc On-Demand Distance Vector Routing (AODV) protocol and one Proactive routing protocol Distance Sequenced Distance Vector Routing (DSDV) Our analysis showed that DSR, AODV & DSDV under Random Walk and Random Way Point Mobility models have similar results for similar inputs however as the pause time increases so does the difference in performance rises. They show that their motion, direction, angle of direction, speed is same under both mobility models. We have made their analysis on packet delivery ratio, throughput and routing overhead. We have tested them with different criteria like different number of nodes, speed and different maximum...
Sun, Xu; Yang, Lina; Gao, Lianru; Zhang, Bing; Li, Shanshan; Li, Jun
2015-01-01
Center-oriented hyperspectral image clustering methods have been widely applied to hyperspectral remote sensing image processing; however, the drawbacks are obvious, including the over-simplicity of computing models and underutilized spatial information. In recent years, some studies have been conducted trying to improve this situation. We introduce the artificial bee colony (ABC) and Markov random field (MRF) algorithms to propose an ABC-MRF-cluster model to solve the problems mentioned above. In this model, a typical ABC algorithm framework is adopted in which cluster centers and iteration conditional model algorithm's results are considered as feasible solutions and objective functions separately, and MRF is modified to be capable of dealing with the clustering problem. Finally, four datasets and two indices are used to show that the application of ABC-cluster and ABC-MRF-cluster methods could help to obtain better image accuracy than conventional methods. Specifically, the ABC-cluster method is superior when used for a higher power of spectral discrimination, whereas the ABC-MRF-cluster method can provide better results when used for an adjusted random index. In experiments on simulated images with different signal-to-noise ratios, ABC-cluster and ABC-MRF-cluster showed good stability.
Some random models in traffic science
Hjorth, U.
1996-06-01
We give an overview of stochastic models for the following traffic phenomena. Models for traffic flow including gaps and capacities for lanes, crossings and roundabouts. Models for wanted and achieved speed distributions. Mode selection models including dispersed equilibrium models and traffic accident models. Also some statistical questions are discussed. 60 refs, 1 tab
A Model for Random Student Drug Testing
Nelson, Judith A.; Rose, Nancy L.; Lutz, Danielle
2011-01-01
The purpose of this case study was to examine random student drug testing in one school district relevant to: (a) the perceptions of students participating in competitive extracurricular activities regarding drug use and abuse; (b) the attitudes and perceptions of parents, school staff, and community members regarding student drug involvement; (c)…
Consistent estimators in random censorship semiparametric models
王启华
1996-01-01
For the fixed design regression modelwhen Y, are randomly censored on the right, the estimators of unknown parameter and regression function g from censored observations are defined in the two cases .where the censored distribution is known and unknown, respectively. Moreover, the sufficient conditions under which these estimators are strongly consistent and pth (p>2) mean consistent are also established.
Fisher, D S; Le Doussal, P; Monthus, C
2001-12-01
The nonequilibrium dynamics of classical random Ising spin chains with nonconserved magnetization are studied using an asymptotically exact real space renormalization group (RSRG). We focus on random field Ising model (RFIM) spin chains with and without a uniform applied field, as well as on Ising spin glass chains in an applied field. For the RFIM we consider a universal regime where the random field and the temperature are both much smaller than the exchange coupling. In this regime, the Imry-Ma length that sets the scale of the equilibrium correlations is large and the coarsening of domains from random initial conditions (e.g., a quench from high temperature) occurs over a wide range of length scales. The two types of domain walls that occur diffuse in opposite random potentials, of the form studied by Sinai, and domain walls annihilate when they meet. Using the RSRG we compute many universal asymptotic properties of both the nonequilibrium dynamics and the equilibrium limit. We find that the configurations of the domain walls converge rapidly toward a set of system-specific time-dependent positions that are independent of the initial conditions. Thus the behavior of this nonequilibrium system is pseudodeterministic at long times because of the broad distributions of barriers that occur on the long length scales involved. Specifically, we obtain the time dependence of the energy, the magnetization, and the distribution of domain sizes (found to be statistically independent). The equilibrium limits agree with known exact results. We obtain the exact scaling form of the two-point equal time correlation function and the two-time autocorrelations . We also compute the persistence properties of a single spin, of local magnetization, and of domains. The analogous quantities for the +/-J Ising spin glass in an applied field are obtained from the RFIM via a gauge transformation. In addition to these we compute the two-point two-time correlation function which can in
Time series, correlation matrices and random matrix models
Vinayak [Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, C.P. 62210 Cuernavaca (Mexico); Seligman, Thomas H. [Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, C.P. 62210 Cuernavaca, México and Centro Internacional de Ciencias, C.P. 62210 Cuernavaca (Mexico)
2014-01-08
In this set of five lectures the authors have presented techniques to analyze open classical and quantum systems using correlation matrices. For diverse reasons we shall see that random matrices play an important role to describe a null hypothesis or a minimum information hypothesis for the description of a quantum system or subsystem. In the former case various forms of correlation matrices of time series associated with the classical observables of some system. The fact that such series are necessarily finite, inevitably introduces noise and this finite time influence lead to a random or stochastic component in these time series. By consequence random correlation matrices have a random component, and corresponding ensembles are used. In the latter we use random matrices to describe high temperature environment or uncontrolled perturbations, ensembles of differing chaotic systems etc. The common theme of the lectures is thus the importance of random matrix theory in a wide range of fields in and around physics.
Local random potentials of high differentiability to model the Landscape
Battefeld, Thorsten
2015-01-01
We generate random functions locally via a novel generalization of Dyson Brownian motion, such that the functions are in a desired differentiability class, while ensuring that the Hessian is a member of the Gaussian orthogonal ensemble (other ensembles might be chosen if desired). Potentials in such higher differentiability classes are required/desirable to model string theoretical landscapes, for instance to compute cosmological perturbations (e.g., smooth first and second derivatives for the power-spectrum) or to search for minima (e.g., suitable de Sitter vacua for our universe). Since potentials are created locally, numerical studies become feasible even if the dimension of field space is large (D ~ 100). In addition to the theoretical prescription, we provide some numerical examples to highlight properties of such potentials; concrete cosmological applications will be discussed in companion publications.
A simplified analytical random walk model for proton dose calculation
Yao, Weiguang; Merchant, Thomas E.; Farr, Jonathan B.
2016-10-01
We propose an analytical random walk model for proton dose calculation in a laterally homogeneous medium. A formula for the spatial fluence distribution of primary protons is derived. The variance of the spatial distribution is in the form of a distance-squared law of the angular distribution. To improve the accuracy of dose calculation in the Bragg peak region, the energy spectrum of the protons is used. The accuracy is validated against Monte Carlo simulation in water phantoms with either air gaps or a slab of bone inserted. The algorithm accurately reflects the dose dependence on the depth of the bone and can deal with small-field dosimetry. We further applied the algorithm to patients’ cases in the highly heterogeneous head and pelvis sites and used a gamma test to show the reasonable accuracy of the algorithm in these sites. Our algorithm is fast for clinical use.
Outlier Edge Detection Using Random Graph Generation Models and Applications
Zhang, Honglei; Gabbouj, Moncef
2016-01-01
Outliers are samples that are generated by different mechanisms from other normal data samples. Graphs, in particular social network graphs, may contain nodes and edges that are made by scammers, malicious programs or mistakenly by normal users. Detecting outlier nodes and edges is important for data mining and graph analytics. However, previous research in the field has merely focused on detecting outlier nodes. In this article, we study the properties of edges and propose outlier edge detection algorithms using two random graph generation models. We found that the edge-ego-network, which can be defined as the induced graph that contains two end nodes of an edge, their neighboring nodes and the edges that link these nodes, contains critical information to detect outlier edges. We evaluated the proposed algorithms by injecting outlier edges into some real-world graph data. Experiment results show that the proposed algorithms can effectively detect outlier edges. In particular, the algorithm based on the Prefe...
A conditional simulation model of intermittent rain fields
L. G. Lanza
2000-01-01
Full Text Available The synthetic generation of random fields with specified probability distribution, correlation structure and probability of no-rain areas is used as the basis for the formulation of a stochastic space-time rainfall model conditional on rain gauge observations. A new procedure for conditioning while preserving intermittence is developed to provide constraints to Monte Carlo realisations of possible rainfall scenarios. The method addresses the properties of the convolution operator involved in generating random field realisations and is actually independent of the numerical algorithm used for unconditional simulation. It requires only the solution of a linear system of algebraic equations the order of which is given by the number of the conditioning nodes. Applications of the methodology are expected in rainfall field reconstruction from sparse rain gauge data and in rainfall downscaling from the large scale information that may be provided by remote sensing devices or numerical weather prediction models. Keywords: Space-time rainfall; Conditioning; Stochastic models
Analysis of tree stand horizontal structure using random point field methods
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.
Quenched bond randomness in marginal and non-marginal Ising spin models in 2D
Fytas, N. G.; Malakis, A.; Hadjiagapiou, I. A.
2008-11-01
We investigate and contrast, via entropic sampling based on the Wang-Landau algorithm, the effects of quenched bond randomness on the critical behavior of two Ising spin models in 2D. The random bond version of the superantiferromagnetic (SAF) square model with nearest- and next-nearest-neighbor competing interactions and the corresponding version of the simple Ising model are studied, and their general universality aspects are inspected by means of a detailed finite size scaling (FSS) analysis. We find that the random bond SAF model obeys weak universality, hyperscaling, and exhibits a strong saturating behavior of the specific heat due to the competing nature of interactions. On the other hand, for the random Ising model we encounter some difficulties as regards a definite discrimination between the two well-known scenarios of the logarithmic corrections versus the weak universality. However, a careful FSS analysis of our data favors the field theoretically predicted logarithmic corrections.
Random matrix model for disordered conductors
Zafar Ahmed; Sudhir R Jain
2000-03-01
We present a random matrix ensemble where real, positive semi-deﬁnite matrix elements, , are log-normal distributed, $\\exp[-\\log^{2}(x)]$. We show that the level density varies with energy, , as 2/(1 + ) for large , in the unitary family, consistent with the expectation for disordered conductors. The two-level correlation function is studied for the unitary family and found to be largely of the universal form despite the fact that the level density has a non-compact support. The results are based on the method of orthogonal polynomials (the Stieltjes-Wigert polynomials here). An interesting random walk problem associated with the joint probability distribution of the ensuing ensemble is discussed and its connection with level dynamics is brought out. It is further proved that Dyson's Coulomb gas analogy breaks down whenever the conﬁning potential is given by a transcendental function for which there exist orthogonal polynomials.
SkipCor: skip-mention coreference resolution using linear-chain conditional random fields.
Slavko Žitnik
Full Text Available Coreference resolution tries to identify all expressions (called mentions in observed text that refer to the same entity. Beside entity extraction and relation extraction, it represents one of the three complementary tasks in Information Extraction. In this paper we describe a novel coreference resolution system SkipCor that reformulates the problem as a sequence labeling task. None of the existing supervised, unsupervised, pairwise or sequence-based models are similar to our approach, which only uses linear-chain conditional random fields and supports high scalability with fast model training and inference, and a straightforward parallelization. We evaluate the proposed system against the ACE 2004, CoNLL 2012 and SemEval 2010 benchmark datasets. SkipCor clearly outperforms two baseline systems that detect coreferentiality using the same features as SkipCor. The obtained results are at least comparable to the current state-of-the-art in coreference resolution.
Efficient Hierarchical Markov Random Fields for Object Detection on a Mobile Robot
Lea, Colin S
2011-01-01
Object detection and classification using video is necessary for intelligent planning and navigation on a mobile robot. However, current methods can be too slow or not sufficient for distinguishing multiple classes. Techniques that rely on binary (foreground/background) labels incorrectly identify areas with multiple overlapping objects as single segment. We propose two Hierarchical Markov Random Field models in efforts to distinguish connected objects using tiered, binary label sets. Near-realtime performance has been achieved using efficient optimization methods which runs up to 11 frames per second on a dual core 2.2 Ghz processor. Evaluation of both models is done using footage taken from a robot obstacle course at the 2010 Intelligent Ground Vehicle Competition.
Segmentation of angiodysplasia lesions in WCE images using a MAP approach with Markov Random Fields.
Vieira, Pedro M; Goncalves, Bruno; Goncalves, Carla R; Lima, Carlos S
2016-08-01
This paper deals with the segmentation of angiodysplasias in wireless capsule endoscopy images. These lesions are the cause of almost 10% of all gastrointestinal bleeding episodes, and its detection using the available software presents low sensitivity. This work proposes an automatic selection of a ROI using an image segmentation module based on the MAP approach where an accelerated version of the EM algorithm is used to iteratively estimate the model parameters. Spatial context is modeled in the prior probability density function using Markov Random Fields. The color space used was CIELab, specially the a component, which highlighted most these type of lesions. The proposed method is the first regarding this specific type of lesions, but when compared to other state-of-the-art segmentation methods, it almost doubles the results.
Scaling Conditional Random Fields by One-Against-the-Other Decomposition
Hai Zhao; Chunyu Kie
2008-01-01
As a powerful sequence labeling model, conditional random fields (CRFs) have had successful applications in many natural language processing (NLP) tasks. However, the high complexity of CRFs training only allows a very small tag (or label) set, because the training becomes intractable as the tag set enlarges. This paper proposes an improved decomposed training and joint decoding algorithm for CRF learning. Instead of training a single CRF model for all tags, it trains a binary sub-CRF independently for each tag. An optimal tag sequence is then produced by a joint decoding algorithm based on the probabilistic output of all sub-CRFs involved. To test its effectiveness, we apply this approach to tackling Chinese word segmentation (CWS) as a sequence labeling problem. Our evaluation shows that it can reduce the computational cost of this language processing task by 40-50% without any significant performance loss on various large-scale data sets.
Hierarchical Semi-Markov Conditional Random Fields for Recursive Sequential Data
Truyen, Tran The; Bui, Hung H; Venkatesh, Svetha
2010-01-01
Inspired by the hierarchical hidden Markov models (HHMM), we present the hierarchical semi-Markov conditional random field (HSCRF), a generalisation of embedded undirectedMarkov chains tomodel complex hierarchical, nestedMarkov processes. It is parameterised in a discriminative framework and has polynomial time algorithms for learning and inference. Importantly, we consider partiallysupervised learning and propose algorithms for generalised partially-supervised learning and constrained inference. We demonstrate the HSCRF in two applications: (i) recognising human activities of daily living (ADLs) from indoor surveillance cameras, and (ii) noun-phrase chunking. We show that the HSCRF is capable of learning rich hierarchical models with reasonable accuracy in both fully and partially observed data cases.
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.
汤慧旋; 危辉
2009-01-01
提出了一种基于轮廓线统计量的前景分割Markov随机场(Markov random field,MRF)模型.和Grabcut等以往模型不同,本文模型通过在分割标签的编码中加入对轮廓线方向的考虑,将Gestalt知觉组织的原则加入分割约束中去,从而使分割边界更为平滑.作为前景分割和Gestalt知觉组织原则研究的基本框架,本文模型的系统结构分为前景分割、注意力选择和信息整合三个子模块,与相关神经生理研究的结论相一致.最后,分别给出了基于本文模型的自动和半自动前景分割实现,结果好于Grabcut等相关算法的结果.
The Swarm Initial Field Model for the 2014 geomagnetic field
Olsen, Nils; Hulot, Gauthier; Lesur, Vincent;
2015-01-01
Data from the first year of ESA's Swarm constellation mission are used to derive the Swarm Initial Field Model (SIFM), a new model of the Earth's magnetic field and its time variation. In addition to the conventional magnetic field observations provided by each of the three Swarm satellites......, explicit advantage is taken of the constellation aspect by including East-West magnetic intensity gradient information from the lower satellite pair. Along-track differences in magnetic intensity provide further information concerning the North-South gradient. The SIFM static field shows excellent...... agreement (up to at least degree 60) with recent field models derived from CHAMP data, providing an initial validation of the quality of the Swarm magnetic measurements. Use of gradient data improves the determination of both the static field and its secular variation, with the mean misfit for East...
Rare-event Analysis and Computational Methods for Stochastic Systems Driven by Random Fields
2014-12-29
random elliptic differential equations . The equation has been employed to describe physics systems in areas as diverse as material science, fluid...probabilities associated with random fields and the associated random elliptic differential equations . The equation has been employed to describe physics...Received Paper 1.00 3.00 4.00 Gongjun Xu, Guang Lin, Jingchen Liu. Rare-Event Simulation for the Stochastic Korteweg--de Vries Equation , SIAM/ASA
On Closely Coupled Dipoles in a Random Field
Andersen, Jørgen Bach; Vincent, L.
2006-01-01
Reception of partially correlated fields by two closely coupled electrical dipoles is discussed as a function of load impedances and open-circuit correlations. Two local maxima of the power may be achieved for two different load impedances, but in those cases the output correlations are high...
Average Number of Coherent Modes for Pulse Random Fields
Lazaruk, A M; Lazaruk, Alexander M.; Karelin, Nikolay V.
1997-01-01
Some consequences of spatio-temporal symmetry for the deterministic decomposition of complex light fields into factorized components are considered. This enables to reveal interrelations between spatial and temporal coherence properties of wave. An estimation of average number of the decomposition terms is obtained in the case of statistical ensemble of light pulses.
Modulation of electromagnetic fields by a depolarizer of random polarizer array
Ma, Ning; Hanson, Steen Grüner; Wang, Wei
2016-01-01
The statistical properties of the electric fields with random changes of the polarization state in space generated by a depolarizer are investigated on the basis of the coherence matrix. The depolarizer is a polarizer array composed of a multitude of contiguous square cells of polarizers with ran......The statistical properties of the electric fields with random changes of the polarization state in space generated by a depolarizer are investigated on the basis of the coherence matrix. The depolarizer is a polarizer array composed of a multitude of contiguous square cells of polarizers...... with randomly distributed polarization angles, where the incident fields experience a random polarization modulation after passing through the depolarizer. The propagation of the modulated electric fields through any quadratic optical system is examined within the framework of the complex ABCD matrix to show...
Initialization of Markov Random Field Clustering of Large Remote Sensing Images
Tran, T.N.; Wehrens, H.R.M.J.; Hoekman, D.H.; Buydens, L.M.C.
2005-01-01
Markov random field (MRF) clustering, utilizing both spectral and spatial interpixel dependency information, often improves classification accuracy for remote sensing images, such as multichannel polarimetric synthetic aperture radar (SAR) images. However, it is heavily sensitive to initial conditio
Active sterile neutrino conversions in a supernova with random magnetic fields
Pastor, S; Valle, José W F; Pastor, S; Semikoz, V; Valle, Jose W F
1995-01-01
{Large enough random magnetic fields may affect in an important way neutrino conversion rates, even in the case where neutrinos have zero transition magnetic moments. We consider their effect in the case of active to sterile \
Wang, W.; Hanson, Steen Grüner; Miyamoto, Y.;
2005-01-01
We present the first direct experimental evidence of the local properties of optical vortices in a random laser speckle field. We have observed the Berry anisotropy ellipse describing the anisotropic squeezing of phase lines close to vortex cores and quantitatively verified the Dennis angular...... momentum rule for its phase. Some statistics associated with vortices, such as density, anisotropy ellipse eccentricity, and its relation to zero crossings of real and imaginary parts of the random field, are also investigated by experiments....
A domino model for geomagnetic field reversals
Mori, N; Ferriz-Mas, A; Wicht, J; Mouri, H; Nakamichi, A; Morikawa, M
2011-01-01
We solve the equations of motion of a one-dimensional planar Heisenberg (or Vaks-Larkin) model consisting of a system of interacting macro-spins aligned along a ring. Each spin has unit length and is described by its angle with respect to the rotational axis. The orientation of the spins can vary in time due to random forcing and spin-spin interaction. We statistically describe the behaviour of the sum of all spins for different parameters. The term "domino model" in the title refers to the interaction among the spins. We compare the model results with geomagnetic field reversals and find strikingly similar behaviour. The aggregate of all spins keeps the same direction for a long time and, once in a while, begins flipping to change the orientation by almost 180 degrees (mimicking a geomagnetic reversal) or to move back to the original direction (mimicking an excursion). Most of the time the spins are aligned or anti-aligned and deviate only slightly with respect to the rotational axis (mimicking the secular v...
Vink, R L C; Fischer, T; Binder, K
2010-11-01
In systems belonging to the universality class of the random field Ising model, the standard hyperscaling relation between critical exponents does not hold, but is replaced with a modified hyperscaling relation. As a result, standard formulations of finite-size scaling near critical points break down. In this work, the consequences of modified hyperscaling are analyzed in detail. The most striking outcome is that the free-energy cost ΔF of interface formation at the critical point is no longer a universal constant, but instead increases as a power law with system size, ΔF∝L(θ), with θ as the violation of hyperscaling critical exponent and L as the linear extension of the system. This modified behavior facilitates a number of numerical approaches that can be used to locate critical points in random field systems from finite-size simulation data. We test and confirm the approaches on two random field systems in three dimensions, namely, the random field Ising model and the demixing transition in the Widom-Rowlinson fluid with quenched obstacles.
Post-processing scheme for modelling the lithospheric magnetic field
V. Lesur
2013-03-01
Full Text Available We investigated how the noise in satellite magnetic data affects magnetic lithospheric field models derived from these data in the special case where this noise is correlated along satellite orbit tracks. For this we describe the satellite data noise as a perturbation magnetic field scaled independently for each orbit, where the scaling factor is a random variable, normally distributed with zero mean. Under this assumption, we have been able to derive a model for errors in lithospheric models generated by the correlated satellite data noise. Unless the perturbation field is known, estimating the noise in the lithospheric field model is a non-linear inverse problem. We therefore proposed an iterative post-processing technique to estimate both the lithospheric field model and its associated noise model. The technique has been successfully applied to derive a lithospheric field model from CHAMP satellite data up to spherical harmonic degree 120. The model is in agreement with other existing models. The technique can, in principle, be extended to all sorts of potential field data with "along-track" correlated errors.
Mean-field models and exotic nuclei
Bender, M.; Buervenich, T.; Maruhn, J.A.; Greiner, W. [Inst. fuer Theoretische Physik, Univ. Frankfurt (Germany); Rutz, K. [Inst. fuer Theoretische Physik, Univ. Frankfurt (Germany)]|[Gesellschaft fuer Schwerionenforschung mbH, Darmstadt (Germany); Reinhard, P.G. [Inst. fuer Theoretische Physik, Univ. Erlangen (Germany)
1998-06-01
We discuss two widely used nuclear mean-field models, the relativistic mean-field model and the (nonrelativistic) Skyrme-Hartree-Fock model, and their capability to describe exotic nuclei. Test cases are superheavy nuclei and neutron-rich Sn isotopes. New information in this regime helps to fix hitherto loosely determined aspects of the models. (orig.)
Random Field Satisfying a Linear Partial Differential Equation with Random Forcing Term.
1984-01-01
physical approximation 12 may be taken equal to 1. For k = 0, the experimental spectral density function of the random fluctuations of the pressure in deep...fa e , tlpt 2 in R , and the power spectral density function is 1 0 y(v) - 27 2 2’ y I a +v Proof: In that case da = X 0dT and r(tl,t2) =- e , the...power spectral density function of the solution X is V R___ 1 __ 2 I The second order properties are the same for every Poisson, Gaussian, Levy centered
Revisiting Boltzmann learning: parameter estimation in Markov random fields
Hansen, Lars Kai; Andersen, Lars Nonboe; Kjems, Ulrik
1996-01-01
This article presents a generalization of the Boltzmann machine that allows us to use the learning rule for a much wider class of maximum likelihood and maximum a posteriori problems, including both supervised and unsupervised learning. Furthermore, the approach allows us to discuss regularization...... and generalization in the context of Boltzmann machines. We provide an illustrative example concerning parameter estimation in an inhomogeneous Markov field. The regularized adaptation produces a parameter set that closely resembles the “teacher” parameters, hence, will produce segmentations that closely reproduce...
Random walk study of electron motion in helium in crossed electromagnetic fields
Englert, G. W.
1972-01-01
Random walk theory, previously adapted to electron motion in the presence of an electric field, is extended to include a transverse magnetic field. In principle, the random walk approach avoids mathematical complexity and concomitant simplifying assumptions and permits determination of energy distributions and transport coefficients within the accuracy of available collisional cross section data. Application is made to a weakly ionized helium gas. Time of relaxation of electron energy distribution, determined by the random walk, is described by simple expressions based on energy exchange between the electron and an effective electric field. The restrictive effect of the magnetic field on electron motion, which increases the required number of collisions per walk to reach a terminal steady state condition, as well as the effect of the magnetic field on electron transport coefficients and mean energy can be quite adequately described by expressions involving only the Hall parameter.
Arnaut, L R
2006-01-01
Using a TE/TM decomposition for an angular plane-wave spectrum of free random electromagnetic waves and matched boundary conditions, we derive the probability density function for the energy density of the vector electric field in the presence of a semi-infinite isotropic medium. The theoretical analysis is illustrated with calculations and results for good electric conductors and for a lossless dielectric half-space. The influence of the permittivity and conductivity on the intensity, random polarization, statistical distribution and standard deviation of the field is investigated, both for incident plus reflected fields and for refracted fields. External refraction is found to result in compression of the fluctuations of the random field.
Zi, Bin; Zhou, Bin
2016-07-01
For the prediction of dynamic response field of the luffing system of an automobile crane (LSOAAC) with random and interval parameters, a hybrid uncertain model is introduced. In the hybrid uncertain model, the parameters with certain probability distribution are modeled as random variables, whereas, the parameters with lower and upper bounds are modeled as interval variables instead of given precise values. Based on the hybrid uncertain model, the hybrid uncertain dynamic response equilibrium equation, in which different random and interval parameters are simultaneously included in input and output terms, is constructed. Then a modified hybrid uncertain analysis method (MHUAM) is proposed. In the MHUAM, based on random interval perturbation method, the first-order Taylor series expansion and the first-order Neumann series, the dynamic response expression of the LSOAAC is developed. Moreover, the mathematical characteristics of extrema of bounds of dynamic response are determined by random interval moment method and monotonic analysis technique. Compared with the hybrid Monte Carlo method (HMCM) and interval perturbation method (IPM), numerical results show the feasibility and efficiency of the MHUAM for solving the hybrid LSOAAC problems. The effects of different uncertain models and parameters on the LSOAAC response field are also investigated deeply, and numerical results indicate that the impact made by the randomness in the thrust of the luffing cylinder F is larger than that made by the gravity of the weight in suspension Q . In addition, the impact made by the uncertainty in the displacement between the lower end of the lifting arm and the luffing cylinder a is larger than that made by the length of the lifting arm L .
Multi-fidelity Gaussian process regression for prediction of random fields
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.
Weighted Hybrid Decision Tree Model for Random Forest Classifier
Kulkarni, Vrushali Y.; Sinha, Pradeep K.; Petare, Manisha C.
2016-06-01
Random Forest is an ensemble, supervised machine learning algorithm. An ensemble generates many classifiers and combines their results by majority voting. Random forest uses decision tree as base classifier. In decision tree induction, an attribute split/evaluation measure is used to decide the best split at each node of the decision tree. The generalization error of a forest of tree classifiers depends on the strength of the individual trees in the forest and the correlation among them. The work presented in this paper is related to attribute split measures and is a two step process: first theoretical study of the five selected split measures is done and a comparison matrix is generated to understand pros and cons of each measure. These theoretical results are verified by performing empirical analysis. For empirical analysis, random forest is generated using each of the five selected split measures, chosen one at a time. i.e. random forest using information gain, random forest using gain ratio, etc. The next step is, based on this theoretical and empirical analysis, a new approach of hybrid decision tree model for random forest classifier is proposed. In this model, individual decision tree in Random Forest is generated using different split measures. This model is augmented by weighted voting based on the strength of individual tree. The new approach has shown notable increase in the accuracy of random forest.
Carrozza, Sylvain
2015-01-01
We define in this paper a class of three indices tensor models, endowed with $O(N)^{\\otimes 3}$ invariance ($N$ being the size of the tensor). This allows to generate, via the usual QFT perturbative expansion, a class of Feynman tensor graphs which is strictly larger than the class of Feynman graphs of both the multi-orientable model (and hence of the colored model) and the $U(N)$ invariant models. We first exhibit the existence of a large $N$ expansion for such a model with general interactions. We then focus on the quartic model and we identify the leading and next-to-leading order (NLO) graphs of the large $N$ expansion. Finally, we prove the existence of a critical regime and we compute the critical exponents, both at leading order and at NLO. This is achieved through the use of various analytic combinatorics techniques.
Carrozza, Sylvain; Tanasa, Adrian
2016-08-01
We define in this paper a class of three-index tensor models, endowed with {O(N)^{⊗ 3}} invariance (N being the size of the tensor). This allows to generate, via the usual QFT perturbative expansion, a class of Feynman tensor graphs which is strictly larger than the class of Feynman graphs of both the multi-orientable model (and hence of the colored model) and the U(N) invariant models. We first exhibit the existence of a large N expansion for such a model with general interactions. We then focus on the quartic model and we identify the leading and next-to-leading order (NLO) graphs of the large N expansion. Finally, we prove the existence of a critical regime and we compute the critical exponents, both at leading order and at NLO. This is achieved through the use of various analytic combinatorics techniques.
Multilevel random effect and marginal models for longitudinal data ...
Multilevel random effect and marginal models for longitudinal data. ... Ethiopian Journal of Science and Technology ... the occurrence of specific adverse events than children injected with licensed vaccine, and if so, to quantify the difference.
A Tractable Complex Network Model based on the Stochastic Mean-field Model of Distance
Aldous, David J.
2003-01-01
Much recent research activity has been devoted to empirical study and theoretical models of complex networks (random graphs) with three qualitative features: power-law degree distribution, local clustering of edges, and small diameter. We point out a new (in this context) platform for such models -- the stochastic mean-field model of distance -- and within this platform study a simple two-parameter proportional attachment model. The model is mathematicallly natural, permits a wide variety of ...
A Gompertzian model with random effects to cervical cancer growth
Mazlan, Mazma Syahidatul Ayuni; Rosli, Norhayati [Faculty of Industrial Sciences and Technology, Universiti Malaysia Pahang, Lebuhraya Tun Razak, 26300 Gambang, Pahang (Malaysia)
2015-05-15
In this paper, a Gompertzian model with random effects is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via maximum likehood estimation. We apply 4-stage Runge-Kutta (SRK4) for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of the cervical cancer growth. Low values of root mean-square error (RMSE) of Gompertzian model with random effect indicate good fits.
Hida, Kazuo
2006-07-01
The multiple reentrant quantum phase transitions in the S=1/2 antiferromagnetic Heisenberg chains with random bond alternation in the magnetic field are investigated by the density matrix renormalization group method combined with interchain mean field approximation. It is assumed that odd numbered bonds are antiferromagnetic with strength J and even numbered bonds can take the values JS and JW (JS > J > JW > 0) randomly with the probabilities p and 1- p, respectively. The pure version ( p=0 and 1) of this model has a spin gap but exhibits a field-induced antiferromagnetism in the presence of interchain coupling if Zeeman energy due to the magnetic field exceeds the spin gap. For 0 < p < 1, antiferromagnetism is induced by randomness at the small field region where the ground state is disordered due to the spin gap in the pure version. At the same time, this model exhibits randomness-induced plateaus at several values of magnetization. The antiferromagnetism is destroyed on the plateaus. As a consequence, we find a series of reentrant quantum phase transitions between transverse antiferromagnetic phases and disordered plateau phases with the increase of magnetic field for a moderate strength of interchain coupling. Above the main plateaus, the magnetization curve consists of a series of small plateaus and jumps between them. It is also found that antiferromagnetism is induced by infinitesimal interchain coupling at the jumps between the small plateaus. We conclude that this antiferromagnetism is supported by the mixing of low-lying excited states by the staggered interchain mean field even though the spin correlation function is short ranged in the ground state of each chain.
Multicritical tensor models and hard dimers on spherical random lattices
Bonzom, Valentin
2012-01-01
Random tensor models which display multicritical behaviors in a remarkably simple fashion are presented. They come with entropy exponents \\gamma = (m-1)/m, similarly to multicritical random branched polymers. Moreover, they are interpreted as models of hard dimers on a set of random lattices for the sphere in dimension three and higher. Dimers with their exclusion rules are generated by the different interactions between tensors, whose coupling constants are dimer activities. As an illustration, we describe one multicritical point, which is interpreted as a transition between the dilute phase and a crystallized phase, though with negative activities.
Bayesian nonparametric centered random effects models with variable selection.
Yang, Mingan
2013-03-01
In a linear mixed effects model, it is common practice to assume that the random effects follow a parametric distribution such as a normal distribution with mean zero. However, in the case of variable selection, substantial violation of the normality assumption can potentially impact the subset selection and result in poor interpretation and even incorrect results. In nonparametric random effects models, the random effects generally have a nonzero mean, which causes an identifiability problem for the fixed effects that are paired with the random effects. In this article, we focus on a Bayesian method for variable selection. We characterize the subject-specific random effects nonparametrically with a Dirichlet process and resolve the bias simultaneously. In particular, we propose flexible modeling of the conditional distribution of the random effects with changes across the predictor space. The approach is implemented using a stochastic search Gibbs sampler to identify subsets of fixed effects and random effects to be included in the model. Simulations are provided to evaluate and compare the performance of our approach to the existing ones. We then apply the new approach to a real data example, cross-country and interlaboratory rodent uterotrophic bioassay.
Ming Xu
2015-01-01
Full Text Available In order to improve offline map matching accuracy of uncertain GPS trajectories, a map matching algorithm based on conditional random fields (CRF and route preference mining is proposed. In this algorithm, road offset distance and the temporal-spatial relationship between the sampling points are used as features of GPS trajectory in a CRF model, which integrates the temporal-spatial context information flexibly. The driver route preference is also used to bolster the temporal-spatial context when a low GPS sampling rate impairs the resolving power of temporal-spatial context in CRF, allowing the map matching accuracy of uncertain GPS trajectories to get improved significantly. The experimental results show that our proposed algorithm is more accurate than existing methods, especially in the case of a low-sampling-rate.
Time-dependent Relativistic Mean-field Theory and Random Phase Approximation
P.Ring; D.Vretenar; A.Wandelt; NguyenVanGiai; MAZhong-yu; CAOLi-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 ah 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 116Sn. It is shown that
Scene estimation from speckled synthetic aperture radar imagery: Markov-random-field approach.
Lankoande, Ousseini; Hayat, Majeed M; Santhanam, Balu
2006-06-01
A novel Markov-random-field model for speckled synthetic aperture radar (SAR) imagery is derived according to the physical, spatial statistical properties of speckle noise in coherent imaging. A convex Gibbs energy function for speckled images is derived and utilized to perform speckle-compensating image estimation. The image estimation is formed by computing the conditional expectation of the noisy image at each pixel given its neighbors, which is further expressed in terms of the derived Gibbs energy function. The efficacy of the proposed technique, in terms of reducing speckle noise while preserving spatial resolution, is studied by using both real and simulated SAR imagery. Using a number of commonly used metrics, the performance of the proposed technique is shown to surpass that of existing speckle-noise-filtering methods such as the Gamma MAP, the modified Lee, and the enhanced Frost.
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).
A Markov-random-field-based filter for speckle reduction in ultrasound imagery
Lankoande, Ousseini; Hayat, Majeed M.; Santhanam, Balu
2009-02-01
The coherent nature of ultrasound imaging inherently produces the notorious signal-dependent speckle noise. Recently, a novel approach based upon embedding the statistical and physical properties of speckle patterns into a Markov-random-field (MRF) framework was developed and demonstrated by the authors in the context of synthetic-aperture radar imaging. The contributions of this work are twofold. First, the MRF approach is extended to include a pseudo maximum-likelihood estimator of a key model parameter, making the approach fully autonomous. Second, the capability of the extended approach, called the modified MRF-based conditional-expectation approach (MRFCEA), in denoising real ultrasound imagery is demonstrated. The proposed MRFCEA approach offers superior performance over existing methods by reducing speckle noise without compromising the spatial resolution. In addition, MRFCEA is autonomous, contrary to existing methods such as the enhanced-Frost or the modified-Lee, which require user's input.
A Remark on the Lifshitz Tail for Schrödinger Operator with Random Magnetic Field
Shu Nakamura
2002-02-01
In this note, we consider the Lifshitz singularity for Schrödinger operator with ergodic random magnetic field. A key estimate is an energy bound for magnetic Schrödinger operators as discussed in Nakamura [8]. Here we remove a technical assumption in [8], namely, the uniform boundedness of the magnetic field.
Scheerlinck, N.; Verboven, P.; Stigter, J.D.; Baerdenmaeker, de J.; Impe, van J.F.; Nicolai, B.A.
2000-01-01
A first-order perturbation algorithm for the computation of mean values and variances of transient temperature and moisture fields during coupled heat and mass transfer problems with random field parameters has been developed and implemented. The algorithm is based on the Galerkin finite-element dis
Rumor spreading models with random denials
Giorno, Virginia; Spina, Serena
2016-11-01
The concept of denial is introduced on rumor spreading processes. The denials occur with a certain rate and they reset to start the initial situation. A population of N individuals is subdivided into ignorants, spreaders and stiflers; at the initial time there is only one spreader and the rest of the population is ignorant. The denials are introduced in the classic DK model and in its generalization, in which a spreader can transmit the rumor at most to k ignorants. The steady state densities are analyzed for these models. Finally, a numerical analysis is performed to study the rule of the involved parameters and to compare the proposed models.
Configuring Random Graph Models with Fixed Degree Sequences
Fosdick, Bailey K; Nishimura, Joel; Ugander, Johan
2016-01-01
Random graph null models have found widespread application in diverse research communities analyzing network datasets. The most popular family of random graph null models, called configuration models, are defined as uniform distributions over a space of graphs with a fixed degree sequence. Commonly, properties of an empirical network are compared to properties of an ensemble of graphs from a configuration model in order to quantify whether empirical network properties are meaningful or whether they are instead a common consequence of the particular degree sequence. In this work we study the subtle but important decisions underlying the specification of a configuration model, and investigate the role these choices play in graph sampling procedures and a suite of applications. We place particular emphasis on the importance of specifying the appropriate graph labeling---stub-labeled or vertex-labeled---under which to consider a null model, a choice that closely connects the study of random graphs to the study of...
Crop Type Mapping from a Sequence of Terrasar-X Images with Dynamic Conditional Random Fields
Kenduiywo, B. K.; Bargiel, D.; Soergel, U.
2016-06-01
Crop phenology is dynamic as it changes with times of the year. Such biophysical processes also look spectrally different to remote sensing satellites. Some crops may depict similar spectral properties if their phenology coincide, but differ later when their phenology diverge. Thus, conventional approaches that select only images from phenological stages where crops are distinguishable for classification, have low discrimination. In contrast, stacking images within a cropping season limits discrimination to a single feature space that can suffer from overlapping classes. Since crop backscatter varies with time, it can aid discrimination. Therefore, our main objective is to develop a crop sequence classification method using multitemporal TerraSAR-X images. We adopt first order markov assumption in undirected temporal graph sequence. This property is exploited to implement Dynamic Conditional Random Fields (DCRFs). Our DCRFs model has a repeated structure of temporally connected Conditional Random Fields (CRFs). Each node in the sequence is connected to its predecessor via conditional probability matrix. The matrix is computed using posterior class probabilities from association potential. This way, there is a mutual temporal exchange of phenological information observed in TerraSAR-X images. When compared to independent epoch classification, the designed DCRF model improved crop discrimination at each epoch in the sequence. However, government, insurers, agricultural market traders and other stakeholders are interested in the quantity of a certain crop in a season. Therefore, we further develop a DCRF ensemble classifier. The ensemble produces an optimal crop map by maximizing over posterior class probabilities selected from the sequence based on maximum F1-score and weighted by correctness. Our ensemble technique is compared to standard approach of stacking all images as bands for classification using Maximum Likelihood Classifier (MLC) and standard CRFs. It
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.
Table Extraction from Web Pages Using Conditional Random Fields to Extract Toponym Related Data
Luthfi Hanifah, Hayyu’; Akbar, Saiful
2017-01-01
Table is one of the ways to visualize information on web pages. The abundant number of web pages that compose the World Wide Web has been the motivation of information extraction and information retrieval research, including the research for table extraction. Besides, there is a need for a system which is designed to specifically handle location-related information. Based on this background, this research is conducted to provide a way to extract location-related data from web tables so that it can be used in the development of Geographic Information Retrieval (GIR) system. The location-related data will be identified by the toponym (location name). In this research, a rule-based approach with gazetteer is used to recognize toponym from web table. Meanwhile, to extract data from a table, a combination of rule-based approach and statistical-based approach is used. On the statistical-based approach, Conditional Random Fields (CRF) model is used to understand the schema of the table. The result of table extraction is presented on JSON format. If a web table contains toponym, a field will be added on the JSON document to store the toponym values. This field can be used to index the table data in accordance to the toponym, which then can be used in the development of GIR system.
Janssen, Hans-Karl; Stenull, Olaf
2004-02-01
We investigate corrections to scaling induced by irrelevant operators in randomly diluted systems near the percolation threshold. The specific systems that we consider are the random resistor network and a class of continuous spin systems, such as the x-y model. We focus on a family of least irrelevant operators and determine the corrections to scaling that originate from this family. Our field theoretic analysis carefully takes into account that irrelevant operators mix under renormalization. It turns out that long standing results on corrections to scaling are respectively incorrect (random resistor networks) or incomplete (continuous spin systems).
Modelling Of Random Vertical Irregularities Of Railway Tracks
Podwórna M.
2015-08-01
Full Text Available The study presents state-of-the-art in analytical and numerical modelling of random vertical irregularities of continuously welded ballasted railway tracks. The common model of railway track irregularity vertical profiles is applied, in the form of a stationary and ergodic Gaussian process in space. Random samples of track irregularity vertical profiles are generated with the Monte-Carlo method. Based on the numerical method developed in the study, the minimum and recommended sampling number required in the random analysis of railway bridges and number of frequency increments (harmonic components in track irregularity vertical profiles simulation are determined. The lower and upper limits of wavelengths are determined based on the literature studies. The approach yields track irregularity random samples close to reality. The track irregularity model developed in the study can be used in the dynamic analysis of railway bridge / track structure / highspeed train systems.
Sums of Ramdom Matrices and the Potts Model on Random Planar Maps
Atkin, Max R; Wheater, John F
2015-01-01
We compute the partition function of the $q$-states Potts model on a random planar lattice with $p\\leq q$ allowed, equally weighted colours on a connected boundary. To this end, we employ its matrix model representation in the planar limit, generalising a result by Voiculescu for the addition of random matrices to a situation beyond free probability theory. We show that the partition functions with $p$ and $q-p$ colours on the boundary are related algebraically. Finally, we investigate the phase diagram of the model when $0\\leq q\\leq 4$ and comment on the conformal field theory description of the critical points.
Money creation in a random matching model
Alexei Deviatov
2004-01-01
I study money creation in versions of the Trejos-Wright (1995) and Shi (1995) models with indivisible money and individual holdings bounded at two units. I work with the same class of policies as in Deviatov and Wallace (2001), who study money creation in that model. However, I consider an alternative notion of implementability–the ex ante pairwise core. I compute a set of numerical examples to determine whether money creation is beneficial. I find beneficial e?ects of money creation if indiv...
冯蕴天; 张宏军; 郝文宁
2016-01-01
Traditional methods of natural language processing input a good deal of handmade features into statistics learning models to process the text.At present,conditional random field model performed well in many natural language processing tasks,but the way of handmaking features and huge number of features made it more difficult to build the model,reduced the speed of model computing,and generated overfitting phenomenon.To solve these problems mentioned above,this paper intro-duced a novel conditional random field model extended by tensor.It designed complicated features automatically,reduced the workloads of handmaking features,used the Tucker decomposition algorithm to speed the model,and could be applied in many natural language processing tasks.Experiments show that the model can perform better in many natural language processing tasks than traditional conditional random field model if using the same elementary features.%传统的自然语言处理方法是将大量手工制定的特征输入到统计学习模型中，以完成文本的加工处理。条件随机场模型在多种自然语言处理任务中都取得了较好的效果，但手工特征制定的方式以及庞大的特征数量增加了模型建立的难度，降低了模型运算的速度，同时易使模型“过拟合”。为了解决上述问题，提出一种张量扩展的条件随机场模型，利用张量变换自动构建出复杂的特征，减少了手工特征制定的工作量，并使用Tucker分解算法加速模型，得到的模型可用于多种自然语言处理任务。实验表明，在提取相同基本特征的前提下，与传统的条件随机场模型相比，模型在多种自然语言处理任务中的性能都有所提高，具有一定的使用价值。
A generalized model via random walks for information filtering
Ren, Zhuo-Ming, E-mail: zhuomingren@gmail.com [Department of Physics, University of Fribourg, Chemin du Musée 3, CH-1700, Fribourg (Switzerland); Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, ChongQing, 400714 (China); Kong, Yixiu [Department of Physics, University of Fribourg, Chemin du Musée 3, CH-1700, Fribourg (Switzerland); Shang, Ming-Sheng, E-mail: msshang@cigit.ac.cn [Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, ChongQing, 400714 (China); Zhang, Yi-Cheng [Department of Physics, University of Fribourg, Chemin du Musée 3, CH-1700, Fribourg (Switzerland)
2016-08-06
There could exist a simple general mechanism lurking beneath collaborative filtering and interdisciplinary physics approaches which have been successfully applied to online E-commerce platforms. Motivated by this idea, we propose a generalized model employing the dynamics of the random walk in the bipartite networks. Taking into account the degree information, the proposed generalized model could deduce the collaborative filtering, interdisciplinary physics approaches and even the enormous expansion of them. Furthermore, we analyze the generalized model with single and hybrid of degree information on the process of random walk in bipartite networks, and propose a possible strategy by using the hybrid degree information for different popular objects to toward promising precision of the recommendation. - Highlights: • We propose a generalized recommendation model employing the random walk dynamics. • The proposed model with single and hybrid of degree information is analyzed. • A strategy with the hybrid degree information improves precision of recommendation.
Liu, Hui-Fang; Yang, Lin; He, Hong-Chen; Zhou, Jun; Liu, Ying; Wang, Chun-Yan; Wu, Yuan-Chao; He, Cheng-Qi
2013-05-01
A randomized, active-controlled clinical trial was conducted to examine the effect of pulsed electromagnetic fields (PEMFs) on women with postmenopausal osteoporosis (PMO) in southwest China. Forty-four participants were randomly assigned to receive alendronate or one course of PEMFs treatment. The primary endpoint was the mean percentage change in bone mineral density of the lumbar spine (BMDL), and secondary endpoints were the mean percentage changes in left proximal femur bone mineral density (BMDF), serum 25OH vitamin D3 (25(OH)D) concentrations, total lower-extremity manual muscle test (LE MMT) score, and Berg Balance Scale (BBS) score. The BMDL, BMDF, total LE MMT score and BBS score were recorded at baseline, 5, 12, and 24 weeks. Serum concentrations of 25(OH)D were measured at baseline and 5 weeks. Using a mixed linear model, there was no significant treatment difference between the two groups in the BMDL, BMDF, total LE MMT score, and BBS score (P ≥ 0.05). For 25(OH)D concentrations, the effects were also comparable between the two groups (P ≥ 0.05) with the Mann-Whitney's U-test. These results suggested that a course of PEMFs treatment with specific parameters was as effective as alendronate in treating PMO within 24 weeks.
A theory of solving TAP equations for Ising models with general invariant random matrices
Opper, Manfred; Çakmak, Burak; Winther, Ole
2016-01-01
We consider the problem of solving TAP mean field equations by iteration for Ising models with coupling matrices that are drawn at random from general invariant ensembles. We develop an analysis of iterative algorithms using a dynamical functional approach that in the thermodynamic limit yields a...... the iteration dependent on a Gaussian distributed field only. The TAP magnetizations are stable fixed points if a de Almeida–Thouless stability criterion is fulfilled. We illustrate our method explicitly for coupling matrices drawn from the random orthogonal ensemble....
Chang, Ju Yong
2016-08-01
We present a new gesture recognition method that is based on the conditional random field (CRF) model using multiple feature matching. Our approach solves the labeling problem, determining gesture categories and their temporal ranges at the same time. A generative probabilistic model is formalized and probability densities are nonparametrically estimated by matching input features with a training dataset. In addition to the conventional skeletal joint-based features, the appearance information near the active hand in an RGB image is exploited to capture the detailed motion of fingers. The estimated likelihood function is then used as the unary term for our CRF model. The smoothness term is also incorporated to enforce the temporal coherence of our solution. Frame-wise recognition results can then be obtained by applying an efficient dynamic programming technique. To estimate the parameters of the proposed CRF model, we incorporate the structured support vector machine (SSVM) framework that can perform efficient structured learning by using large-scale datasets. Experimental results demonstrate that our method provides effective gesture recognition results for challenging real gesture datasets. By scoring 0.8563 in the mean Jaccard index, our method has obtained the state-of-the-art results for the gesture recognition track of the 2014 ChaLearn Looking at People (LAP) Challenge.
Video object tracking in the compressed domain using spatio-temporal Markov random fields.
Khatoonabadi, Sayed Hossein; Bajić, Ivan V
2013-01-01
Despite the recent progress in both pixel-domain and compressed-domain video object tracking, the need for a tracking framework with both reasonable accuracy and reasonable complexity still exists. This paper presents a method for tracking moving objects in H.264/AVC-compressed video sequences using a spatio-temporal Markov random field (ST-MRF) model. An ST-MRF model naturally integrates the spatial and temporal aspects of the object's motion. Built upon such a model, the proposed method works in the compressed domain and uses only the motion vectors (MVs) and block coding modes from the compressed bitstream to perform tracking. First, the MVs are preprocessed through intracoded block motion approximation and global motion compensation. At each frame, the decision of whether a particular block belongs to the object being tracked is made with the help of the ST-MRF model, which is updated from frame to frame in order to follow the changes in the object's motion. The proposed method is tested on a number of standard sequences, and the results demonstrate its advantages over some of the recent state-of-the-art methods.
Beyond-mean-field corrections within the second random-phase approximation
Grasso, M.; Gambacurta, D.; Engel, J.
2016-06-01
A subtraction procedure, introduced to overcome double-counting problems in beyond-mean-field theories, is used in the second random-phase approximation (SRPA). Doublecounting problems arise in the energy-density functional framework in all cases where effective interactions tailored at leading order are used for higher-order calculations, such as those done in the SRPA model. It was recently shown that this subtraction procedure also guarantees that the stability condition related to the Thouless theorem is verified in extended RPA models. We discuss applications of the subtraction procedure, introduced within the SRPA model, to the nucleus 16O. The application of the subtraction procedure leads to: (i) stable results that are weakly cutoff dependent; (ii) a considerable upwards correction of the SRPA spectra (which were systematically shifted downwards by several MeV with respect to RPA spectra, in all previous calculations). With this important implementation of the model, many applications may be foreseen to analyze the genuine impact of 2 particle-2 hole configurations (without any cutoff dependences and anomalous shifts) on the excitation spectra of medium-mass and heavy nuclei.
Wei, Qikang; Chen, Tao; Xu, Ruifeng; He, Yulan; Gui, Lin
2016-01-01
The recognition of disease and chemical named entities in scientific articles is a very important subtask in information extraction in the biomedical domain. Due to the diversity and complexity of disease names, the recognition of named entities of diseases is rather tougher than those of chemical names. Although there are some remarkable chemical named entity recognition systems available online such as ChemSpot and tmChem, the publicly available recognition systems of disease named entities are rare. This article presents a system for disease named entity recognition (DNER) and normalization. First, two separate DNER models are developed. One is based on conditional random fields model with a rule-based post-processing module. The other one is based on the bidirectional recurrent neural networks. Then the named entities recognized by each of the DNER model are fed into a support vector machine classifier for combining results. Finally, each recognized disease named entity is normalized to a medical subject heading disease name by using a vector space model based method. Experimental results show that using 1000 PubMed abstracts for training, our proposed system achieves an F1-measure of 0.8428 at the mention level and 0.7804 at the concept level, respectively, on the testing data of the chemical-disease relation task in BioCreative V. Database URL: http://219.223.252.210:8080/SS/cdr.html PMID:27777244
Tseng, Yuan Heng; Shen, Wen Chao; Lin, Chrong Jung
2012-04-01
The intense development and study of resistive random access memory (RRAM) devices has opened a new era in semiconductor memory manufacturing. Resistive switching and carrier conduction inside RRAM films have become critical issues in recent years. Electron trapping/detrapping behavior is observed and investigated in the proposed contact resistive random access memory (CR-RAM) cell. Through the fitting of the space charge limiting current (SCLC) model, and analysis in terms of the random telegraph noise (RTN) model, the temperature-dependence of resistance levels and the high-temperature data retention behavior of the contact RRAM film are successfully and completely explained. Detail analyses of the electron capture and emission from the traps by forward and reverse read measurements provide further verifications for hopping conduction mechanism and current fluctuation discrepancies.
Quantum field theory competitive models
Tolksdorf, Jürgen; Zeidler, Eberhard
2009-01-01
For more than 70 years, quantum field theory (QFT) can be seen as a driving force in the development of theoretical physics. Equally fascinating is the fruitful impact which QFT had in rather remote areas of mathematics. The present book features some of the different approaches, different physically viewpoints and techniques used to make the notion of quantum field theory more precise. For example, the present book contains a discussion including general considerations, stochastic methods, deformation theory and the holographic AdS/CFT correspondence. It also contains a discussion of more recent developments like the use of category theory and topos theoretic methods to describe QFT. The present volume emerged from the 3rd 'Blaubeuren Workshop: Recent Developments in Quantum Field Theory', held in July 2007 at the Max Planck Institute of Mathematics in the Sciences in Leipzig/Germany. All of the contributions are committed to the idea of this workshop series: 'To bring together outstanding experts working in...
The CHAOS-4 geomagnetic field model
Olsen, Nils; Lühr, H.; Finlay, Chris;
2014-01-01
We present CHAOS-4, a new version in the CHAOS model series, which aims to describe the Earth's magnetic field with high spatial and temporal resolution. Terms up to spherical degree of at least n = 85 for the lithospheric field, and up to n = 16 for the time-varying core field are robustly deter...
The CHAOS-4 Geomagnetic Field Model
Olsen, Nils; Finlay, Chris; Lühr, H.
We present CHAOS-4, a new version in the CHAOS model series, which aims at describing the Earth's magnetic field with high spatial resolution (terms up to spherical degree n=90 for the crustal field, and up to n=16 for the time-varying core field are robustly determined) and high temporal resolut...
Effects of the random field on the magnetic behavior of nanowires with core/shell morphology
Zaim, A., E-mail: ah_zaim@yahoo.fr [Laboratoire Physique des Matériaux et Modélisation des Systèmes (LP2MS), Unité Associée au CNRST-URAC: 08, Faculty of Sciences, University Moulay Ismail, B.P. 11201, Zitoune, Meknes (Morocco); Kerouad, M., E-mail: kerouad@fs-umi.ac.ma [Laboratoire Physique des Matériaux et Modélisation des Systèmes (LP2MS), Unité Associée au CNRST-URAC: 08, Faculty of Sciences, University Moulay Ismail, B.P. 11201, Zitoune, Meknes (Morocco); Boughrara, M. [Laboratoire Physique des Matériaux et Modélisation des Systèmes (LP2MS), Unité Associée au CNRST-URAC: 08, Faculty of Sciences, University Moulay Ismail, B.P. 11201, Zitoune, Meknes (Morocco)
2013-04-15
We have used the effective field theory based on probability distribution method to investigate the hysteresis behavior of the magnetic nanowires with core/shell morphology in a random magnetic field. The hysteresis curves are obtained for different values of the random magnetic field, both ferromagnetic and antiferromagnetic couplings between the shell and the core are considered. A number of characteristic behaviors are find, such as the existence of double or triple hysteresis loops for appropriate values of the system parameters affected by the random magnetic field, temperature, and interfacial coupling. -- Highlights: ► The hysteresis behavior of the Ising nanowires has been studied by EFT. ► The effects of the random field on the hysteresis loops have been examined. ► The hysteresis loops are obtained for different values of the interfacial coupling constant. ► The triple hysteresis loops occur for the larger antiferromagnetic coupling constant. ► The dependence of the coercive field on the temperature is investigated.
Money creation process in a random redistribution model
Chen, Siyan; Wang, Yougui; Li, Keqiang; Wu, Jinshan
2014-01-01
In this paper, the dynamical process of money creation in a random exchange model with debt is investigated. The money creation kinetics are analyzed by both the money-transfer matrix method and the diffusion method. From both approaches, we attain the same conclusion: the source of money creation in the case of random exchange is the agents with neither money nor debt. These analytical results are demonstrated by computer simulations.
Effect of randomization in the Biham-Middleton-Levine traffic flow model
Ding, Zhong-Jun; Jiang, Rui; Huang, Wei; Wang, Bing-Hong
2011-06-01
This paper studies the effect of randomization in the Biham-Middleton-Levine (BML) traffic flow model. It is found that the average velocity exhibits a first-order phase transition from moving phase to jamming phase under periodic boundary conditions. The intermediate stable phase identified in the original deterministic BML model disappears with the introduction of randomization. The average velocity in the moving phase and the critical car density decrease as the randomization probability increases. We have developed a mean-field theory which successfully predicts the average velocity in the moving phase. Under open boundary conditions, there are only two phases and the maximum current phase does not occur. The dependence of the average velocity, the density and the flow rate on the injection probability in the moving phase have also been obtained through the mean-field theory.
Application of Markov random fields to landmine detection in ground penetrating radar data
Torrione, Peter A.; Collins, Leslie
2008-04-01
Recent advances in ground penetrating radar (GPR) design and fabrication have resulted in improved fidelity responses from relatively small, shallow-buried objects like landmines and improvised explosive devices. As the responses measured with GPR improve, more and more advanced processing techniques can be brought to bear on the problem of target identification in GPR data. From an electromagnetic point of view, the problem of target detection in GPR signal processing is reducible to inferring the presence or absence of changes in the electromagnetic properties of soils and thus the presence or absence of buried targets. Problems arise because the algorithms required for the full electromagnetic inversion of GPR signals are extremely computationally expensive, and usually rely on assumptions of electromagnetically constant transmission media; these problems typically make the real-time implementation of purely electromagnetic-inspired algorithms infeasible. On the other hand, purely statistical or signal-processing inspired approaches to target identification in GPR often lack a solid theoretical basis in the underlying physics, which is fundamental to understanding responses in GPR. In this work, we propose a model for responses in time-domain ground penetrating radar that attempts to incorporate the underlying physics of the problem, but avoids several of the issues inherent in assuming constant media with known electrical parameters by imposing a statistical model over the observed parameters of interest in A-scans - namely the signal gains, times of arrival, etc. The spatial requirements of the proposed statistical model suggests the application of Markov random field (MRF) distributions which provide expressive, but computationally simple models of spatial interactions. In this work we will explore the application of physics-based MRF's as generative models for time-domain GPR data, the pre-screening algorithms that this model motivates, and discuss how the
Randomness in highly reflective silver nanoparticles and their localized optical fields
Naruse, Makoto; Yasuda, Hideki; Tate, Naoya; Ohtsu, Motoichi; Naya, Masayuki
2014-01-01
Reflection of near-infrared light is important for preventing heat transfer in energy saving applications. A large-area, mass-producible reflector that contains randomly distributed disk-shaped silver nanoparticles and that exhibits high reflection at near-infrared wavelengths was demonstrated. Although resonant coupling between incident light and the nanostructure of the reflector plays some role, what is more important is the geometrical randomness of the nanoparticles, which serves as the origin of a particle-dependent localization and hierarchical distribution of optical near-fields in the vicinity of the nanostructure. Here we show and clarified the unique optical near-field processes associated with the randomness seen in experimentally fabricated silver nanostructures by adapting a rigorous theory of optical near-fields based on an angular spectrum and detailed electromagnetic calculations.
Return probability and recurrence for the random walk driven by two-dimensional Gaussian free field
Biskup, Marek; Ding, Jian; Goswami, Subhajit
2016-01-01
Given any $\\gamma>0$ and for $\\eta=\\{\\eta_v\\}_{v\\in \\mathbb Z^2}$ denoting a sample of the two-dimensional discrete Gaussian free field on $\\mathbb Z^2$ pinned at the origin, we consider the random walk on $\\mathbb Z^2$ among random conductances where the conductance of edge $(u, v)$ is given by $\\mathrm{e}^{\\gamma(\\eta_u + \\eta_v)}$. We show that, for almost every $\\eta$, this random walk is recurrent and that, with probability tending to 1 as $T\\to \\infty$, the return probability at time $2...
A random effects generalized linear model for reliability compositive evaluation
无
2009-01-01
This paper first proposes a random effects generalized linear model to evaluate the storage life of one kind of high reliable and small sample-sized products by combining multi-sources information of products coming from the same population but stored at different environments. The relevant algorithms are also provided. Simulation results manifest the soundness and effectiveness of the proposed model.
Single-cluster dynamics for the random-cluster model
Deng, Y.; Qian, X.; Blöte, H.W.J.
2009-01-01
We formulate a single-cluster Monte Carlo algorithm for the simulation of the random-cluster model. This algorithm is a generalization of the Wolff single-cluster method for the q-state Potts model to noninteger values q>1. Its results for static quantities are in a satisfactory agreement with those
Least squares estimation in a simple random coefficient autoregressive model
Johansen, Søren; Lange, Theis
2013-01-01
The question we discuss is whether a simple random coefficient autoregressive model with infinite variance can create the long swings, or persistence, which are observed in many macroeconomic variables. The model is defined by yt=stρyt−1+εt,t=1,…,n, where st is an i.i.d. binary variable with p=P(...
Least squares estimation in a simple random coefficient autoregressive model
Johansen, Søren; Lange, Theis
2013-01-01
The question we discuss is whether a simple random coefficient autoregressive model with infinite variance can create the long swings, or persistence, which are observed in many macroeconomic variables. The model is defined by yt=stρyt−1+εt,t=1,…,n, where st is an i.i.d. binary variable with p=P(...
Simulating intrafraction prostate motion with a random walk model
Tobias Pommer, PhD
2017-07-01
Conclusions: Random walk modeling is feasible and recreated the characteristics of the observed prostate motion. Introducing artificial transient motion did not improve the overall agreement, although the first 30 seconds of the traces were better reproduced. The model provides a simple estimate of prostate motion during delivery of radiation therapy.
Single-cluster dynamics for the random-cluster model
Deng, Y.; Qian, X.; Blöte, H.W.J.
2009-01-01
We formulate a single-cluster Monte Carlo algorithm for the simulation of the random-cluster model. This algorithm is a generalization of the Wolff single-cluster method for the q-state Potts model to noninteger values q>1. Its results for static quantities are in a satisfactory agreement with those
A random effects generalized linear model for reliability compositive evaluation
ZHAO Hui; YU Dan
2009-01-01
This paper first proposes a random effects generalized linear model to evaluate the storage life of one kind of high reliable and small sample-sized products by combining multi-sources information of products coming from the same population but stored at different environments.The relevant algorithms are also provided.Simulation results manifest the soundness and effectiveness of the proposed model.
Alien wavelength modeling tool and field trial
Sambo, N.; Sgambelluri, A.; Secondini, M.
2015-01-01
A modeling tool is presented for pre-FEC BER estimation of PM-QPSK alien wavelength signals. A field trial is demonstrated and used as validation of the tool's correctness. A very close correspondence between the performance of the field trial and the one predicted by the modeling tool has been...
Geostatistical methods applied to field model residuals
Maule, Fox; Mosegaard, K.; Olsen, Nils
consists of measurement errors and unmodelled signal), and is typically assumed to be uncorrelated and Gaussian distributed. We have applied geostatistical methods to analyse the residuals of the Oersted(09d/04) field model [http://www.dsri.dk/Oersted/Field_models/IGRF_2005_candidates/], which is based...
Zhang, Yongsheng; Xiong, Hongkai; He, Zhihai; Yu, Songyu
2010-07-01
An important issue in Wyner-Ziv video coding is the reconstruction of Wyner-Ziv frames with decoded bit-planes. So far, there are two major approaches: the Maximum a Posteriori (MAP) reconstruction and the Minimum Mean Square Error (MMSE) reconstruction algorithms. However, these approaches do not exploit smoothness constraints in natural images. In this paper, we model a Wyner-Ziv frame by Markov random fields (MRFs), and produce reconstruction results by finding an MAP estimation of the MRF model. In the MRF model, the energy function consists of two terms: a data term, MSE distortion metric in this paper, measuring the statistical correlation between side-information and the source, and a smoothness term enforcing spatial coherence. In order to better describe the spatial constraints of images, we propose a context-adaptive smoothness term by analyzing the correspondence between the output of Slepian-Wolf decoding and successive frames available at decoders. The significance of the smoothness term varies in accordance with the spatial variation within different regions. To some extent, the proposed approach is an extension to the MAP and MMSE approaches by exploiting the intrinsic smoothness characteristic of natural images. Experimental results demonstrate a considerable performance gain compared with the MAP and MMSE approaches.
Eigenvalue Separation in Some Random Matrix Models
Bassler, Kevin E; Frankel, Norman E
2008-01-01
The eigenvalue density for members of the Gaussian orthogonal and unitary ensembles follows the Wigner semi-circle law. If the Gaussian entries are all shifted by a constant amount c/Sqrt(2N), where N is the size of the matrix, in the large N limit a single eigenvalue will separate from the support of the Wigner semi-circle provided c > 1. In this study, using an asymptotic analysis of the secular equation for the eigenvalue condition, we compare this effect to analogous effects occurring in general variance Wishart matrices and matrices from the shifted mean chiral ensemble. We undertake an analogous comparative study of eigenvalue separation properties when the size of the matrices are fixed and c goes to infinity, and higher rank analogues of this setting. This is done using exact expressions for eigenvalue probability densities in terms of generalized hypergeometric functions, and using the interpretation of the latter as a Green function in the Dyson Brownian motion model. For the shifted mean Gaussian u...
Force Limited Random Vibration Test of TESS Camera Mass Model
Karlicek, Alexandra; Hwang, James Ho-Jin; Rey, Justin J.
2015-01-01
The Transiting Exoplanet Survey Satellite (TESS) is a spaceborne instrument consisting of four wide field-of-view-CCD cameras dedicated to the discovery of exoplanets around the brightest stars. As part of the environmental testing campaign, force limiting was used to simulate a realistic random vibration launch environment. While the force limit vibration test method is a standard approach used at multiple institutions including Jet Propulsion Laboratory (JPL), NASA Goddard Space Flight Center (GSFC), European Space Research and Technology Center (ESTEC), and Japan Aerospace Exploration Agency (JAXA), it is still difficult to find an actual implementation process in the literature. This paper describes the step-by-step process on how the force limit method was developed and applied on the TESS camera mass model. The process description includes the design of special fixtures to mount the test article for properly installing force transducers, development of the force spectral density using the semi-empirical method, estimation of the fuzzy factor (C2) based on the mass ratio between the supporting structure and the test article, subsequent validating of the C2 factor during the vibration test, and calculation of the C.G. accelerations using the Root Mean Square (RMS) reaction force in the spectral domain and the peak reaction force in the time domain.
Dynamics of Crowd Behaviors: From Complex Plane to Quantum Random Fields
Ivancevic, Vladimir G.; Reid, Darryn J.
2015-11-01
The following sections are included: * Complex Plane Dynamics of Crowds and Groups * Introduction * Complex-Valued Dynamics of Crowd and Group Behaviors * Kähler Geometry of Crowd and Group Dynamics * Computer Simulations of Crowds and Croups Dynamics * Braids of Agents' Behaviors in the Complex Plane * Hilbert-Space Control of Crowds and Groups Dynamics * Quantum Random Fields: A Unique Framework for Simulation, Optimization, Control and Learning * Introduction * Adaptive Quantum Oscillator * Optimization and Learning on Banach and Hilbert Spaces * Appendix * Complex-Valued Image Processing * Linear Integral Equations * Riemann-Liouville Fractional Calculus * Rigorous Geometric Quantization * Supervised Machine-Learning Methods * First-Order Logic and Quantum Random Fields
THE DECISION OF THE OPTIMAL PARAMETERS IN MARKOV RANDOM FIELDS OF IMAGES BY GENETIC ALGORITHM
无
2000-01-01
This paper introduces the principle of genetic algorithm and the basic method of solving Markov random field parameters.Focusing on the shortcomings in present methods,a new method based on genetic algorithms is proposed to solve the parameters in the Markov random field.The detailed procedure is discussed.On the basis of the parameters solved by genetic algorithms,some experim ents on classification of aerial images are given.Experimental results show that the proposed method is effective and the classification results are satisfactory.
Excursion sets of infinitely divisible random fields with convolution equivalent Lévy measure
Rønn-Nielsen, Anders; Jensen, Eva B. Vedel
We consider a continuous, infinitely divisible random field in R d , d = 1, 2, 3, given as an integral of a kernel function with respect to a Lévy basis with convolution equivalent Lévy measure. For a large class of such random fields we compute the asymptotic probability that the excursion set a...... at level x contains some rotation of an object with fixed radius as x → ∞. Our main result is that the asymptotic probability is equivalent to the right tail of the underlying Lévy measure...
A Novel Microaneurysms Detection Method Based on Local Applying of Markov Random Field.
Ganjee, Razieh; Azmi, Reza; Moghadam, Mohsen Ebrahimi
2016-03-01
Diabetic Retinopathy (DR) is one of the most common complications of long-term diabetes. It is a progressive disease and by damaging retina, it finally results in blindness of patients. Since Microaneurysms (MAs) appear as a first sign of DR in retina, early detection of this lesion is an essential step in automatic detection of DR. In this paper, a new MAs detection method is presented. The proposed approach consists of two main steps. In the first step, the MA candidates are detected based on local applying of Markov random field model (MRF). In the second step, these candidate regions are categorized to identify the correct MAs using 23 features based on shape, intensity and Gaussian distribution of MAs intensity. The proposed method is evaluated on DIARETDB1 which is a standard and publicly available database in this field. Evaluation of the proposed method on this database resulted in the average sensitivity of 0.82 for a confidence level of 75 as a ground truth. The results show that our method is able to detect the low contrast MAs with the background while its performance is still comparable to other state of the art approaches.
Modelling electricity forward markets by ambit fields
Barndorff-Nielsen, Ole; Fred Espen Benth, Fred Espen; Veraart, Almut
This paper proposes a new modelling framework for electricity forward markets, which is based on ambit fields. The new model can capture many of the stylised facts observed in energy markets. One of the main differences to the traditional models lies in the fact that we do not model the dynamics...
Daniels, Marcus G.; Farmer, J. Doyne; Gillemot, László; Iori, Giulia; Smith, Eric
2003-03-01
We model trading and price formation in a market under the assumption that order arrival and cancellations are Poisson random processes. This model makes testable predictions for the most basic properties of markets, such as the diffusion rate of prices (which is the standard measure of financial risk) and the spread and price impact functions (which are the main determinants of transaction cost). Guided by dimensional analysis, simulation, and mean-field theory, we find scaling relations in terms of order flow rates. We show that even under completely random order flow the need to store supply and demand to facilitate trading induces anomalous diffusion and temporal structure in prices.
Extremes of random fields over arbitrary domains with application to concrete rupture stresses
Ditlevsen, Ove Dalager
2004-01-01
To find the exact probability distribution of the global maximum or minimum of a random field within a bounded domain is a pending problem even for Gaussian fields. Except for very special examples of fields, recourse must be taken to approximate reasoning or asymptotic considerations to be judged....... In this paper, the distribution function is obtained in general for Gaussian fields over arbitrary bounded domains with piecewise continuous and differentiable boundaries, and as in earlier works the distribution function is tested against empirical distribution functions obtained by simulation of sample...
The Effect of Random Voids in the Modified Gurson Model
Fei, Huiyang; Yazzie, Kyle; Chawla, Nikhilesh; Jiang, Hanqing
2012-02-01
The porous plasticity model (usually referred to as the Gurson-Tvergaard-Needleman model or modified Gurson model) has been widely used in the study of microvoid-induced ductile fracture. In this paper, we studied the effects of random voids on the porous plasticity model. Finite-element simulations were conducted to study a copper/tin/copper joint bar under uniaxial tension using the commercial finite-element package ABAQUS. A randomly distributed initial void volume fraction with different types of distribution was introduced, and the effects of this randomness on the crack path and macroscopic stress-strain behavior were studied. It was found that consideration of the random voids is able to capture more detailed and localized deformation features, such as different crack paths and different ultimate tensile strengths, and meanwhile does not change the macroscopic stress-strain behavior. It seems that the random voids are able to qualitatively explain the scattered observations in experiments while keeping the macroscopic measurements consistent.
Carbon nanotube field emitters on KOVAR substrate modified by random pattern
Park, Seol Ah; Song, Eun-Ho; Kang, Byung Hyun; Ju, Byeong-Kwon, E-mail: bkju@korea.ac.kr [Korea University, Display and Nanosystem Laboratory, College of Engineering (Korea, Republic of)
2015-07-15
We investigated the field emission characteristics of patterned carbon nanotubes (CNTs) on KOVAR substrates with different surface morphologies. The substrate with a micro-sized random pattern was fabricated through chemical wet etching, whereas the substrate with a nano-sized random pattern was formed by surface roughening process of polymer and chemical wet etching. The field emission characteristics of these substrates were the compared with those of non-treated substrates. It was clearly revealed that the field emission characteristics of CNTs were influenced by the surface morphology of the cathode substrate. When the surface of cathode was modified by random pattern, the modified substrate provided a large surface area and a wider print area. Also, the modified surface morphology of the cathode provided strong adhesion between the CNT paste and the cathode. Particularly, the substrate with the nano-sized random pattern showed that the turn-on field value decreases and the field enhancement factor value improves as compared with non-treated substrate.
Anomalous scaling in a non-Gaussian random shell model for passive scalars
2007-01-01
In this paper, we have introduced a shell-model of Kraichnan's passive scalar problem. Different from the original problem, the prescribed random velocity field is non-Gaussian and δ correlated in time, and its introduction is inspired by She and Lév(e)que (Phys. Rev. Lett. 72,336 (1994)). For comparison, we also give the passive scalar advected by the Gaussian random velocity field. The anomalous scaling exponents H(p) of passive scalar advected by these two kinds of random velocities above are determined for structure function with values of p up to 15 by Monte Carlo simulations of the random shell model, with Gear methods used to solve the stochastic differential equations. We find that the H(p) advected by the non-Gaussian random velocity is not more anomalous than that advected by the Gaussian random velocity. Whether the advecting velocity is non-Gaussian or Gaussian, similar scaling exponents of passive scalar are obtained with the same molecular diffusivity.
Effects of random noise in a dynamical model of love
Xu Yong, E-mail: hsux3@nwpu.edu.cn [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China); Gu Rencai; Zhang Huiqing [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China)
2011-07-15
Highlights: > We model the complexity and unpredictability of psychology as Gaussian white noise. > The stochastic system of love is considered including bifurcation and chaos. > We show that noise can both suppress and induce chaos in dynamical models of love. - Abstract: This paper aims to investigate the stochastic model of love and the effects of random noise. We first revisit the deterministic model of love and some basic properties are presented such as: symmetry, dissipation, fixed points (equilibrium), chaotic behaviors and chaotic attractors. Then we construct a stochastic love-triangle model with parametric random excitation due to the complexity and unpredictability of the psychological system, where the randomness is modeled as the standard Gaussian noise. Stochastic dynamics under different three cases of 'Romeo's romantic style', are examined and two kinds of bifurcations versus the noise intensity parameter are observed by the criteria of changes of top Lyapunov exponent and shape of stationary probability density function (PDF) respectively. The phase portraits and time history are carried out to verify the proposed results, and the good agreement can be found. And also the dual roles of the random noise, namely suppressing and inducing chaos are revealed.
INFLUENCE ANALYSIS ON EXPONENTIAL NONLINEAR MODELS WITH RANDOM EFFECTS
宗序平; 赵俊; 王海斌; 韦博成
2003-01-01
This paper presents a unified diagnostic method for exponential nonlinear models with random effects based upon the joint likelihood given by Robinson in 1991.The authors show that the case deletion model is equivalent to mean shift outlier model.From this point of view,several diagnostic measures,such as Cook distance,score statistics are derived.The local influence measure of Cook is also presented.Numerical example illustrates that our method is available.
INFLUENCE ANALYSIS IN NONLINEAR MODELS WITH RANDOM EFFECTS
WeiBocheng; ZhongXuping
2001-01-01
Abstract. In this paper,a unified diagnostic method for the nonlinear models with random ef-fects based upon the joint likelihood given by Robinson in 1991 is presented. It is shown that thecase deletion model is equivalent to the mean shift outlier model. From this point of view ,sever-al diagnostic measures, such as Cook distance, score statistics are derived. The local influencemeasure of Cook is also presented. A numerical example illustrates that the method is avail-able
Discrete Modeling of the Worm Spread with Random Scanning
Uchida, Masato
In this paper, we derive a set of discrete time difference equations that models the spreading process of computer worms such as Code-Red and Slammer, which uses a common strategy called “random scanning” to spread through the Internet. We show that the derived set of discrete time difference equations has an exact relationship with the Kermack and McKendrick susceptible-infectious-removed (SIR) model, which is known as a standard continuous time model for worm spreading.
Spectra of Anderson Type Models with Decaying Randomness
M Krishna; K B Sinha
2001-05-01
In this paper we consider some Anderson type models, with free parts having long range tails with the random perturbations decaying at different rates in different directions and prove that there is a.c. spectrum in the model which is pure. In addition, we show that there is pure point spectrum outside some interval. Our models include potentials decaying in all directions in which case absence of singular continuous spectrum is also shown.
Using Random Forest Models to Predict Organizational Violence
Levine, Burton; Bobashev, Georgly
2012-01-01
We present a methodology to access the proclivity of an organization to commit violence against nongovernment personnel. We fitted a Random Forest model using the Minority at Risk Organizational Behavior (MAROS) dataset. The MAROS data is longitudinal; so, individual observations are not independent. We propose a modification to the standard Random Forest methodology to account for the violation of the independence assumption. We present the results of the model fit, an example of predicting violence for an organization; and finally, we present a summary of the forest in a "meta-tree,"
Confining Bond Rearrangement in the Random Center Vortex Model
Altarawneh, Derar; Engelhardt, Michael
2015-01-01
We present static meson-meson and baryon--anti-baryon potentials in Z(2) and Z(3) random center vortex models for the infrared sector of Yang-Mills theory, i.e., hypercubic lattice models of random vortex world-surfaces. In particular, we calculate Polyakov loop correlators of two static mesons resp. (anti-)baryons in a center vortex background and observe that their expectation values follow the minimal area law and show bond rearrangement behavior. The static meson-meson and baryon--anti-baryon potentials are compared with theoretical predictions and lattice QCD simulations.
Adams, Roy J; Saleheen, Nazir; Thomaz, Edison; Parate, Abhinav; Kumar, Santosh; Marlin, Benjamin M
2016-06-01
The field of mobile health (mHealth) has the potential to yield new insights into health and behavior through the analysis of continuously recorded data from wearable health and activity sensors. In this paper, we present a hierarchical span-based conditional random field model for the key problem of jointly detecting discrete events in such sensor data streams and segmenting these events into high-level activity sessions. Our model includes higher-order cardinality factors and inter-event duration factors to capture domain-specific structure in the label space. We show that our model supports exact MAP inference in quadratic time via dynamic programming, which we leverage to perform learning in the structured support vector machine framework. We apply the model to the problems of smoking and eating detection using four real data sets. Our results show statistically significant improvements in segmentation performance relative to a hierarchical pairwise CRF.
Disorder fingerprint: Intensity distributions in the near field of random media
Naraghi, R. Rezvani; Sukhov, S.; Dogariu, A.
2016-11-01
The structural morphology of complex dielectric media determines their functionalities by driving the statistical properties of the electromagnetic fields. Our controlled experiments and full electromagnetic calculations that go beyond common dipolar approximations demonstrate that the specific characteristics of disorder lead to non-Rayleigh statistics of detected intensity, which can be directly accessed in the near field of random media and can be unambiguously related to the short-range correlations of disorder.
Approximating the XY model on a random graph with a q -state clock model
Lupo, Cosimo; Ricci-Tersenghi, Federico
2017-02-01
Numerical simulations of spin glass models with continuous variables set the problem of a reliable but efficient discretization of such variables. In particular, the main question is how fast physical observables computed in the discretized model converge toward the ones of the continuous model when the number of states of the discretized model increases. We answer this question for the XY model and its discretization, the q -state clock model, in the mean-field setting provided by random graphs. It is found that the convergence of physical observables is exponentially fast in the number q of states of the clock model, so allowing a very reliable approximation of the XY model by using a rather small number of states. Furthermore, such an exponential convergence is found to be independent from the disorder distribution used. Only at T =0 , the convergence is slightly slower (stretched exponential). Thanks to the analytical solution to the q -state clock model, we compute accurate phase diagrams in the temperature versus disorder strength plane. We find that, at zero temperature, spontaneous replica symmetry breaking takes place for any amount of disorder, even an infinitesimal one. We also study the one step of replica symmetry breaking (1RSB) solution in the low-temperature spin glass phase.
Segmentation of cone-beam CT using a hidden Markov random field with informative priors
Moores, M.; Hargrave, C.; Harden, F.; Mengersen, K.
2014-03-01
Cone-beam computed tomography (CBCT) has enormous potential to improve the accuracy of treatment delivery in image-guided radiotherapy (IGRT). To assist radiotherapists in interpreting these images, we use a Bayesian statistical model to label each voxel according to its tissue type. The rich sources of prior information in IGRT are incorporated into a hidden Markov random field model of the 3D image lattice. Tissue densities in the reference CT scan are estimated using inverse regression and then rescaled to approximate the corresponding CBCT intensity values. The treatment planning contours are combined with published studies of physiological variability to produce a spatial prior distribution for changes in the size, shape and position of the tumour volume and organs at risk. The voxel labels are estimated using iterated conditional modes. The accuracy of the method has been evaluated using 27 CBCT scans of an electron density phantom. The mean voxel-wise misclassification rate was 6.2%, with Dice similarity coefficient of 0.73 for liver, muscle, breast and adipose tissue. By incorporating prior information, we are able to successfully segment CBCT images. This could be a viable approach for automated, online image analysis in radiotherapy.
Phase Field Modeling Using PetIGA
Vignal, Philippe A.
2013-06-01
Phase field modeling has become a widely used framework in the computational material science community. Its ability to model different problems by defining appropriate phase field parameters and relating it to a free energy functional makes it highly versatile. Thermodynamically consistent partial differential equations can then be generated by assuming dissipative dynamics, and setting up the problem as one of minimizing this free energy. The equations are nonetheless challenging to solve, and having a highly efficient and parallel framework to solve them is necessary. In this work, a brief review on phase field models is given, followed by a short analysis of the Phase Field Crystal Model solved with Isogeometric Analysis us- ing PetIGA. We end with an introduction to a new modeling concept, where free energy functions are built with a periodic equilibrium structure in mind.
A combinatorial wind field model
Soleimanzadeh, Maryam; Wisniewski, Rafal; Sloth, Christoffer
2010-01-01
of ordinary dierential equations (ODE). Considering some assumptions on the ow model (e.g. steadiness), the sys- tem can be approximated by a linear n dimensional system. Partitioning the state space into cells is performed by dening Lyapunov function sets, such that each cell is the region between two...... neighboring level surfaces of Lyapunov functions. The resulting discrete system facilitates a supervisory approach to the control....
A combinatorial wind field model
Soleimanzadeh, Maryam; Wisniewski, Rafal; Sloth, Christoffer
2010-01-01
of ordinary dierential equations (ODE). Considering some assumptions on the ow model (e.g. steadiness), the sys- tem can be approximated by a linear n dimensional system. Partitioning the state space into cells is performed by dening Lyapunov function sets, such that each cell is the region between two...... neighboring level surfaces of Lyapunov functions. The resulting discrete system facilitates a supervisory approach to the control....
Buffalos milk yield analysis using random regression models
A.S. Schierholt
2010-02-01
Full Text Available Data comprising 1,719 milk yield records from 357 females (predominantly Murrah breed, daughters of 110 sires, with births from 1974 to 2004, obtained from the Programa de Melhoramento Genético de Bubalinos (PROMEBUL and from records of EMBRAPA Amazônia Oriental - EAO herd, located in Belém, Pará, Brazil, were used to compare random regression models for estimating variance components and predicting breeding values of the sires. The data were analyzed by different models using the Legendre’s polynomial functions from second to fourth orders. The random regression models included the effects of herd-year, month of parity date of the control; regression coefficients for age of females (in order to describe the fixed part of the lactation curve and random regression coefficients related to the direct genetic and permanent environment effects. The comparisons among the models were based on the Akaike Infromation Criterion. The random effects regression model using third order Legendre’s polynomials with four classes of the environmental effect were the one that best described the additive genetic variation in milk yield. The heritability estimates varied from 0.08 to 0.40. The genetic correlation between milk yields in younger ages was close to the unit, but in older ages it was low.
Are Discrepancies in RANS Modeled Reynolds Stresses Random?
Xiao, Heng; Wang, Jian-xun; Paterson, Eric G
2016-01-01
In the turbulence modeling community, significant efforts have been made to quantify the uncertainties in the Reynolds-Averaged Navier--Stokes (RANS) models and to improve their predictive capabilities. Of crucial importance in these efforts is the understanding of the discrepancies in the RANS modeled Reynolds stresses. However, to what extent these discrepancies can be predicted or whether they are completely random remains a fundamental open question. In this work we used a machine learning algorithm based on random forest regression to predict the discrepancies. The success of the regression--prediction procedure indicates that, to a large extent, the discrepancies in the modeled Reynolds stresses can be explained by the mean flow feature, and thus they are universal quantities that can be extrapolated from one flow to another, at least among different flows sharing the same characteristics such as separation. This finding has profound implications to the future development of RANS models, opening up new ...
Bi-Spectrum Scattering Model for Dielectric Randomly Rough Surface
刘宁; 李宗谦
2003-01-01
The bistatic scattering model is offen used for remote microwave sensing. The bi-spectrum model (BSM) for conducting surfaces was used to develop a scattering model for dielectric randomly rough surfaces to estimate their bistatic scattering coefficients. The model for dielectric rough surfaces differs from the BSM for a conducting surface by including Fresnell reflection and transmission from dielectric rough surfaces. The bistatic scattering coefficients were defined to satisfy the reciprocal theorem. Values calculated using the BSM for dielectric randomly rough surfaces compare well with those of the integral equation model (IEM) and with experimental data, showing that the BSM accuracy is acceptable and its range of validity is similar to that of IEM while the BSM expression is simpler than that of IEM.
Individual based and mean-field modeling of direct aggregation
Burger, Martin
2013-10-01
We introduce two models of biological aggregation, based on randomly moving particles with individual stochasticity depending on the perceived average population density in their neighborhood. In the firstorder model the location of each individual is subject to a density-dependent random walk, while in the second-order model the density-dependent random walk acts on the velocity variable, together with a density-dependent damping term. The main novelty of our models is that we do not assume any explicit aggregative force acting on the individuals; instead, aggregation is obtained exclusively by reducing the individual stochasticity in response to higher perceived density. We formally derive the corresponding mean-field limits, leading to nonlocal degenerate diffusions. Then, we carry out the mathematical analysis of the first-order model, in particular, we prove the existence of weak solutions and show that it allows for measure-valued steady states. We also perform linear stability analysis and identify conditions for pattern formation. Moreover, we discuss the role of the nonlocality for well-posedness of the first-order model. Finally, we present results of numerical simulations for both the first- and second-order model on the individual-based and continuum levels of description. 2012 Elsevier B.V. All rights reserved.
Critical slowing down exponents in structural glasses: Random orthogonal and related models
Caltagirone, F.; Ferrari, U.; Leuzzi, L.; Parisi, G.; Rizzo, T.
2012-08-01
An important prediction of mode-coupling theory is the relationship between the power-law decay exponents in the β regime and the consequent definition of the so-called exponent parameter λ. In the context of a certain class of mean-field glass models with quenched disorder, the physical meaning of λ has recently been understood, yielding a method to compute it exactly in a static framework. In this paper we exploit this new technique to compute the critical slowing down exponents for such models including, as special cases, the Sherrington-Kirkpatrick model, the p-spin model, and the random orthogonal model.
Using Conditional Random Fields to Extract Contexts and Answers of Questions from Online Forums
Ding, Shilin; Cong, Gao; Lin, Chin-Yew;
2008-01-01
on Conditional Random Fields (CRFs) to detect the contexts and answers of questions from forum threads. We improve the basic framework by Skip-chain CRFs and 2D CRFs to better accommodate the features of forums for better performance. Experimental results show that our techniques are very promising....
Using Conditional Random Fields to Extract Contexts and Answers of Questions from Online Forums
Ding, Shilin; Cong, Gao; Lin, Chin-Yew
2008-01-01
on Conditional Random Fields (CRFs) to detect the contexts and answers of questions from forum threads. We improve the basic framework by Skip-chain CRFs and 2D CRFs to better accommodate the features of forums for better performance. Experimental results show that our techniques are very promising....
Separate Training for Conditional Random Fields Using Co-occurrence Rate Factorization
Zhu, Zhemin; Hiemstra, Djoerd; Apers, Peter M.G.; Wombacher, Andreas
2012-01-01
The standard training method of Conditional Random Fields (CRFs) is very slow for large-scale applications. As an alternative, piecewise training divides the full graph into pieces, trains them independently, and combines the learned weights at test time. In this paper, we present separate training
A Central Limit Theorem for the Volumes of High Excursions of Stationary Associated Random Fields
Vadim Demichev
2015-05-01
Full Text Available We prove that under certain conditions the excursion sets volumes of stationary positively associated random fields converge after rescaling to the normal distribution as the excursion level and the size of the observation window grow. In addition, we provide a number of examples.
Luan, Nana
2011-01-01
Let $X= \\{X(t), t \\in \\R^N\\}$ be a Gaussian random field with values in $\\R^d$ defined by \\[ X(t) = \\big(X_1(t),..., X_d(t)\\big),\\qquad t \\in \\R^N, \\] where $X_1, ..., X_d$ are independent copies of a real-valued, centered, anisotropic Gaussian random field $X_0$ which has stationary increments and the property of strong local nondeterminism. In this paper we determine the exact Hausdorff measure function for the range $X([0, 1]^N)$. We also provide a sufficient condition for a Gaussian random field with stationary increments to be strongly locally nondeterministic. This condition is given in terms of the spectral measures of the Gaussian random fields which may contain either an absolutely continuous or discrete part. This result strengthens and extends significantly the related theorems of Berman (1973, 1988), Pitt (1978) and Xiao (2007, 2009), and will have wider applicability beyond the scope of the present paper.
Random fields of initial out of straightness leading to column buckling
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...
Modulation of electromagnetic fields by a depolarizer of random polarizer array
Ma, Ning; Hanson, Steen Grüner; Wang, Wei
2016-01-01
The statistical properties of the electric fields with random changes of the polarization state in space generated by a depolarizer are investigated on the basis of the coherence matrix. The depolarizer is a polarizer array composed of a multitude of contiguous square cells of polarizers with ran...
High Performance Ambipolar Field-Effect Transistor of Random Network Carbon Nanotubes
Bisri, Satria Zulkarnaen; Gao, Jia; Derenskyi, Vladimir; Gomulya, Widianta; Iezhokin, Igor; Gordiichuk, Pavlo; Herrmann, Andreas; Loi, Maria Antonietta
2012-01-01
Ambipolar field-effect transistors of random network carbon nanotubes are fabricated from an enriched dispersion utilizing a conjugated polymer as the selective purifying medium. The devices exhibit high mobility values for both holes and electrons (3 cm(2)/V.s) with a high on/off ratio (10(6)). The
Is Bonferroni correction more sensitive than Random Field Theory for most fMRI studies?
Tierney, Tim M; Carmichael, David W
2016-01-01
Random Field Theory has been used in the fMRI literature to address the multiple comparisons problem. The method provides an analytical solution for the computation of precise p-values when its assumptions are met. When its assumptions are not met the thresholds generated by Random Field Theory can be more conservative than Bonferroni corrections, which are arguably too stringent for use in fMRI. As this has been well documented theoretically it is surprising that a majority of current studies (~80%) would not meet the assumptions of Random Field Theory and therefore would have reduced sensitivity. Specifically most data is not smooth enough to meet the good lattice assumption. Current studies smooth data on average by twice the voxel size which is rarely sufficient to meet the good lattice assumption. The amount of smoothing required for Random Field Theory to produce accurate p-values increases with image resolution and decreases with degrees of freedom. There is no rule of thumb that is valid for all study...
On Non-Parametric Field Estimation using Randomly Deployed, Noisy, Binary Sensors
Wang, Ye
2007-01-01
We consider the problem of reconstructing a deterministic data field from binary quantized noisy observations of sensors randomly deployed over the field domain. Our focus is on the extremes of lack of control in the sensor deployment, arbitrariness and lack of knowledge of the noise distribution, and low-precision and unreliability in the sensors. These adverse conditions are motivated by possible real-world scenarios where a large collection of low-cost, crudely manufactured sensors are mass-deployed in an environment where little can be assumed about the ambient noise. We propose a simple estimator that reconstructs the entire data field from these unreliable, binary quantized, noisy observations. Under the assumption of a bounded amplitude field, we prove almost sure and mean-square convergence of the estimator to the actual field as the number of sensors tends to infinity. For fields with bounded-variation, Sobolev differentiable, or finite-dimensionality properties, we derive specific mean squared error...
Unified Dark Matter Scalar Field Models
Daniele Bertacca
2010-01-01
of a single scalar field accounts for a unified description of the Dark Matter and Dark Energy sectors, dubbed Unified Dark Matter (UDM models. In this framework, we consider the general Lagrangian of -essence, which allows to find solutions around which the scalar field describes the desired mixture of Dark Matter and Dark Energy. We also discuss static and spherically symmetric solutions of Einstein's equations for a scalar field with noncanonical kinetic term, in connection with galactic halo rotation curves.
Transverse eV ion heating by random electric field fluctuations in the plasmasphere
Artemyev, A. V.; Mourenas, D.; Agapitov, O. V.; Blum, L.
2017-02-01
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˜0.3 eV could potentially explain the observations.
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.
IMPROVING MARKOV RANDOM FIELD BASED SUPER RESOLUTION MAPPING THROUGH FUZZY PARAMETER INTEGRATION
D. R . Welikanna
2012-07-01
Full Text Available The objective of this study was to improve the Markov Random Field (MRF based Super Resolution Mapping (SRM technique to account for the vague land-cover interpretations (class mixture and the intermediate conditions in an urban area. The algorithm has been improved to integrate the fuzzy mean and fuzzy covariance measurements, to a MRF based SRM scheme to optimize the classification results. The technique was tested on a WORLDVIEW-2 data set, acquired over a highway construction area, in Colombo, Sri Lanka. Based on the visual interpretation of the image, three major land-cover types of this area were identified for the study; those were vegetation, soil and exposed grass and impervious surface with low medium and high albedo. The membership values for each pixel were determined from training samples through Spectral Angle Mapper (SAM technique. The compulsory fuzzy mean and the covariance measurements were derived using these membership grades, and subsequently was applied in MRF based SRM technique. The primary reference data was generated using Maximum Likelihood Classification (MLC performed on the same data which was resampled to 1m resolution. The scale factor was set to be (S = 2, to generate SRM of 1m resolution. The smoothening parameter (λ which balances the prior and likelihood energy terms were tested in the range from 0.3 to 0.9. SRM were generated using fuzzy MRF and the conventional MRF models respectively. Results suggest that the fuzzy integrated model has improved the results with an overall accuracy of 85.60% and kappa value of 0.78 between the optimal results and the reference data, while in the conventional case it was 77.81% of overall accuracy with kappa being 0.65. Among the two MRF models, fuzzy parameter integrated model shows the highest agreement with class fractions from the reference image with a smallest average _MAE (MAE, Mean Absolute Error of 0.03.
Modeling of random wave transformation with strong wave-induced coastal currents
Zheng Jinhai; H. Mase; Li Tongfei
2008-01-01
The propagation and transformation of multi-directional and uni-directional random waves over a coast with complicated bathymetric and geometric features are studied experimentally and numerically. Laboratory investigation indicates that wave energy convergence and divergence cause strong coastal currents to develop and inversely modify the wave fields. A coastal spectral wave model, based on the wave action balance equation with diffraction effect (WABED), is used to simulate the transformation of random waves over the complicated bathymetry. The diffraction effect in the wave model is derived from a parabolic approximation of wave theory, and the mean energy dissipation rate per unit horizontal area due to wave breaking is parameterized by the bore-based formulation with a breaker index of 0.73. The numerically simulated wave field without considering coastal currents is different from that of experiments, whereas model results considering currents clearly reproduce the intensification of wave height in front of concave shorelines.
Comparison of Present SST Gravity Field Models
LUO Jia; SHI Chuang; ZOU Xiancai; WANG Haihong
2006-01-01
Taking the main land of Europe as the region to be studied, the potential of the new satellite gravity technique: satellite-to-satellite tracking (SST) and improving the accuracy of regional gravity field model with the SST models are investigated. The drawbacks of these models are discussed. With GPM98C as the reference, the gravity anomaly residuals of several other models, the latest SST global gravity field models (EIGEN series and GGM series), were computed and compared. The results of the comparison show that in the selected region, some systematic errors with periodical properties exist in the EIGEN and GGM's S series models in the high degree and order. Some information that was not shown in the classic gravity models is detected in the low and middle degree and order of EIGEN and GGM's S series models. At last, the effective maximum degrees and orders of SST models are suggested.
First principles modeling of magnetic random access memory devices (invited)
Butler, W.H.; Zhang, X.; Schulthess, T.C.; Nicholson, D.M.; Oparin, A.B. [Metals and Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 (United States); MacLaren, J.M. [Department of Physics, Tulane University, New Orleans, Louisiana 70018 (United States)
1999-04-01
Giant magnetoresistance (GMR) and spin-dependent tunneling may be used to make magnetic random access memory devices. We have applied first-principles based electronic structure techniques to understand these effects and in the case of GMR to model the transport properties of the devices. {copyright} {ital 1999 American Institute of Physics.}
Performance of Random Effects Model Estimators under Complex Sampling Designs
Jia, Yue; Stokes, Lynne; Harris, Ian; Wang, Yan
2011-01-01
In this article, we consider estimation of parameters of random effects models from samples collected via complex multistage designs. Incorporation of sampling weights is one way to reduce estimation bias due to unequal probabilities of selection. Several weighting methods have been proposed in the literature for estimating the parameters of…
Statistical properties of several models of fractional random point processes
Bendjaballah, C.
2011-08-01
Statistical properties of several models of fractional random point processes have been analyzed from the counting and time interval statistics points of view. Based on the criterion of the reduced variance, it is seen that such processes exhibit nonclassical properties. The conditions for these processes to be treated as conditional Poisson processes are examined. Numerical simulations illustrate part of the theoretical calculations.
A discrete impulsive model for random heating and Brownian motion
Ramshaw, John D.
2010-01-01
The energy of a mechanical system subjected to a random force with zero mean increases irreversibly and diverges with time in the absence of friction or dissipation. This random heating effect is usually encountered in phenomenological theories formulated in terms of stochastic differential equations, the epitome of which is the Langevin equation of Brownian motion. We discuss a simple discrete impulsive model that captures the essence of random heating and Brownian motion. The model may be regarded as a discrete analog of the Langevin equation, although it is developed ab initio. Its analysis requires only simple algebraic manipulations and elementary averaging concepts, but no stochastic differential equations (or even calculus). The irreversibility in the model is shown to be a consequence of a natural causal stochastic condition that is closely analogous to Boltzmann's molecular chaos hypothesis in the kinetic theory of gases. The model provides a simple introduction to several ostensibly more advanced topics, including random heating, molecular chaos, irreversibility, Brownian motion, the Langevin equation, and fluctuation-dissipation theorems.
Asthma Self-Management Model: Randomized Controlled Trial
Olivera, Carolina M. X.; Vianna, Elcio Oliveira; Bonizio, Roni C.; de Menezes, Marcelo B.; Ferraz, Erica; Cetlin, Andrea A.; Valdevite, Laura M.; Almeida, Gustavo A.; Araujo, Ana S.; Simoneti, Christian S.; de Freitas, Amanda; Lizzi, Elisangela A.; Borges, Marcos C.; de Freitas, Osvaldo
2016-01-01
Information for patients provided by the pharmacist is reflected in adhesion to treatment, clinical results and patient quality of life. The objective of this study was to assess an asthma self-management model for rational medicine use. This was a randomized controlled trial with 60 asthmatic patients assigned to attend five modules presented by…
Mathematical Properties Relevant to Geomagnetic Field Modeling
Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils
2010-01-01
properties of those spatial mathematical representations are also discussed, especially in view of providing a formal justification for the fact that geomagnetic field models can indeed be constructed from ground-based and satellite-born observations, provided those reasonably approximate the ideal......Geomagnetic field modeling consists in converting large numbers of magnetic observations into a linear combination of elementary mathematical functions that best describes those observations.The set of numerical coefficients defining this linear combination is then what one refers...... be directly measured. In this chapter, the mathematical foundation of global (as opposed to regional) geomagnetic field modeling is reviewed, and the spatial modeling of the field in spherical coordinates is focussed. Time can be dealt with as an independent variable and is not explicitly considered...
Mathematical Properties Relevant to Geomagnetic Field Modeling
Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils
2014-01-01
properties of those spatial mathematical representations are also discussed, especially in view of providing a formal justification for the fact that geomagnetic field models can indeed be constructed from ground-based and satellite-born observations, provided those reasonably approximate the ideal situation......Geomagnetic field modeling consists in converting large numbers of magnetic observations into a linear combination of elementary mathematical functions that best describes those observations. The set of numerical coefficients defining this linear combination is then what one refers...... be directly measured. In this chapter, the mathematical foundation of global (as opposed to regional) geomagnetic field modeling is reviewed, and the spatial modeling of the field in spherical coordinates is focused. Time can be dealt with as an independent variable and is not explicitly considered...
Quantum random oracle model for quantum digital signature
Shang, Tao; Lei, Qi; Liu, Jianwei
2016-10-01
The goal of this work is to provide a general security analysis tool, namely, the quantum random oracle (QRO), for facilitating the security analysis of quantum cryptographic protocols, especially protocols based on quantum one-way function. QRO is used to model quantum one-way function and different queries to QRO are used to model quantum attacks. A typical application of quantum one-way function is the quantum digital signature, whose progress has been hampered by the slow pace of the experimental realization. Alternatively, we use the QRO model to analyze the provable security of a quantum digital signature scheme and elaborate the analysis procedure. The QRO model differs from the prior quantum-accessible random oracle in that it can output quantum states as public keys and give responses to different queries. This tool can be a test bed for the cryptanalysis of more quantum cryptographic protocols based on the quantum one-way function.
Exact Partition Function for the Random Walk of an Electrostatic Field
Gabriel González
2017-01-01
Full Text Available The partition function for the random walk of an electrostatic field produced by several static parallel infinite charged planes in which the charge distribution could be either ±σ is obtained. We find the electrostatic energy of the system and show that it can be analyzed through generalized Dyck paths. The relation between the electrostatic field and generalized Dyck paths allows us to sum overall possible electrostatic field configurations and is used for obtaining the partition function of the system. We illustrate our results with one example.
Controlling dispersion forces between small particles with artificially created random light fields
Bruegger, Georges; Scheffold, Frank; Saenz, Juan Jose
2015-01-01
Appropriate combinations of laser beams can be used to trap and manipulate small particles with "optical tweezers" as well as to induce significant "optical binding" forces between particles. These interaction forces are usually strongly anisotropic depending on the interference landscape of the external fields. This is in contrast with the familiar isotropic, translationally invariant, van der Waals and, in general, Casimir-Lifshitz interactions between neutral bodies arising from random electromagnetic waves generated by equilibrium quantum and thermal fluctuations. Here we show, both theoretically and experimentally, that dispersion forces between small colloidal particles can also be induced and controlled using artificially created fluctuating light fields. Using optical tweezers as gauge, we present experimental evidence for the predicted isotropic attractive interactions between dielectric microspheres induced by laser-generated, random light fields. These light induced interactions open a path towards...
Field quality control of an earth dam: random versus purposive sampling
Kotzias, P.C.; Stamatopoulos, A.C.
1996-08-01
Two sampling operations, the random and purposive techniques, for field quality control of an earth dam were presented. Each technique was analyzed and their similarities and differences were compared. Each took into consideration the attributes or variables such as strength, temperature, slump, air content, density, and water content. The purposive operation needed much less field sampling and testing than the random operation. The advantages and disadvantages of each technique were described. It was concluded that both techniques could be used individually or jointly on the same project as long as the extent of the application, with all rules and underlying assumptions, were recognized for each case and were strictly adhered to in the field. 19 refs., 4 tabs., 2 figs.
Certified Randomness from a Two-Level System in a Relativistic Quantum Field
Thinh, Le Phuc; Martin-Martinez, Eduardo
2016-01-01
Randomness is an indispensable resource in modern science and information technology. Fortunately, an experimentally simple procedure exists to generate randomness with well-characterized devices: measuring a quantum system in a basis complementary to its preparation. Towards realizing this goal one may consider using atoms or superconducting qubits, promising candidates for quantum information processing. However, their unavoidable interaction with the electromagnetic field affects their dynamics. At large time scales, this can result in decoherence. Smaller time scales in principle avoid this problem, but may not be well analysed under the usual rotating wave and single-mode approximation (RWA and SMA) which break the relativistic nature of quantum field theory. Here, we use a fully relativistic analysis to quantify the information that an adversary with access to the field could get on the result of an atomic measurement. Surprisingly, we find that the adversary's guessing probability is not minimized for ...
Levitation of Extended States in a Random Magnetic Field with a Finite Mean
LIU Wen-Sheng; LEI Xiao-Lin
2004-01-01
We study the localization properties of electrons in a two-dimensional system in a random magnetic field B(r) = Bo + δB(r) with the average Bo and the amplitude of the magnetic field fluctuations δB. The localization length of the system is calculated by using the finite-size scaling method combined with the transfer-matrix technique.Inthe case of weak δB, we find that the random magnetic field system is equivalent to the integer quantum Hall effect system, namely, the energy band splits into a series of disorder broadened Landau bands, at the centers of which states are extended with the localization length exponent v = 2.34 ± 0.02. With increasing δB, the extended states float up in energy, which is similar to the levitation scenario proposed for the integer quantum Hall effect.
Zaim, N.; Zaim, A.; Kerouad, M.
2017-02-01
In this work, the magnetic behavior of the cylindrical nanowire, consisting of a ferromagnetic core of spin-1 atoms surrounded by a ferromagnetic shell of spin-1 atoms is studied in the presence of a random crystal field interaction. Based on Metropolis algorithm, the Monte Carlo simulation has been used to investigate the effects of the concentration of the random crystal field p, the crystal field D and the shell exchange interaction Js on the phase diagrams and the hysteresis behavior of the system. Some characteristic behaviors have been found, such as the first and second-order phase transitions joined by tricritical point for appropriate values of the system parameters, triple and isolated critical points can be also found. Depending on the Hamiltonian parameters, single, double and para hysteresis regions are explicitly determined.
Extended Quark Potential Model From Random Phase Approximation
DENGWei－Zhen; CHENXiao－Lin; 等
2002-01-01
The quark potential model is extended to include the sea quark excitation using the random phase approximation.The effective quark interaction preserves the important QCD properties-chiral symmetry and confinement simultaneously.A primary qualitative analysis shows that the π meson as a well-known typical Goldstone boson and the other mesons made up of valence qq quark pair such as the ρ meson can also be described in this extended quark potential model.
Extended Quark Potential Model from Random Phase Approximation
DENG Wei-Zhen; CHEN Xiao-Lin; LU Da-Hai; YANG Li-Ming
2002-01-01
The quark potential model is extended to include the sea quark excitation using the random phase approx-imation. The effective quark interaction preserves the important QCD properties - chiral symmetry and confinementsimultaneously. A primary qualitative analysis shows that the π meson as a well-known typical Goldstone boson andthe other mesons made up of valence qq quark pair such as the ρ meson can also be described in this extended quarkpotential model.
Investigating Facebook Groups through a Random Graph Model
Dinithi Pallegedara; Lei Pan
2014-01-01
Facebook disseminates messages for billions of users everyday. Though there are log files stored on central servers, law enforcement agencies outside of the U.S. cannot easily acquire server log files from Facebook. This work models Facebook user groups by using a random graph model. Our aim is to facilitate detectives quickly estimating the size of a Facebook group with which a suspect is involved. We estimate this group size according to the number of immediate friends and the number of ext...
A Tractable Complex Network Model Based onthe Stochastic Mean-Field Model of Distance
Aldous, David J.
Much recent research activity has been devoted to empirical study and theoretical models of complex networks (random graphs) possessing three qualitative features: power-law degree distributions, local clustering, and slowly-growing diameter. We point out a new (in this context) platform for such models - the stochastic mean-field model of distances - and within this platform study a simple two-parameter proportional attachment (or copying) model. The model is mathematically natural, permits a wide variety of explicit calculations, has the desired three qualitative features, and fits the complete range of degree scaling exponents and clustering parameters; in these respects it compares favorably with existing models.
The Stochastic Galerkin Method for Darcy Flow Problem with Log-Normal Random Field Coefficients
Michal Beres
2017-01-01
Full Text Available This article presents a study of the Stochastic Galerkin Method (SGM applied to the Darcy flow problem with a log-normally distributed random material field given by a mean value and an autocovariance function. We divide the solution of the problem into two parts. The first one is the decomposition of a random field into a sum of products of a random vector and a function of spatial coordinates; this can be achieved using the Karhunen-Loeve expansion. The second part is the solution of the problem using SGM. SGM is a simple extension of the Galerkin method in which the random variables represent additional problem dimensions. For the discretization of the problem, we use a finite element basis for spatial variables and a polynomial chaos discretization for random variables. The results of SGM can be utilised for the analysis of the problem, such as the examination of the average flow, or as a tool for the Bayesian approach to inverse problems.
Flow field mapping in data rack model
Matěcha J.
2013-04-01
Full Text Available The main objective of this study was to map the flow field inside the data rack model, fitted with three 1U server models. The server model is based on the common four-processor 1U server. The main dimensions of the data rack model geometry are taken fully from the real geometry. Only the model was simplified with respect to the greatest possibility in the experimental measurements. The flow field mapping was carried out both experimentally and numerically. PIV (Particle Image Velocimetry method was used for the experimental flow field mapping, when the flow field has been mapped for defined regions within the 2D/3D data rack model. Ansys CFX and OpenFOAM software were used for the numerical solution. Boundary conditions for numerical model were based on data obtained from experimental measurement of velocity profile at the output of the server mockup. This velocity profile was used as the input boundary condition in the calculation. In order to achieve greater consistency of the numerical model with experimental data, the numerical model was modified with regard to the results of experimental measurements. Results from the experimental and numerical measurements were compared and the areas of disparateness were identified. In further steps the obtained proven numerical model will be utilized for the real geometry of data racks and data.
Random matrices as models for the statistics of quantum mechanics
Casati, Giulio; Guarneri, Italo; Mantica, Giorgio
1986-05-01
Random matrices from the Gaussian unitary ensemble generate in a natural way unitary groups of evolution in finite-dimensional spaces. The statistical properties of this time evolution can be investigated by studying the time autocorrelation functions of dynamical variables. We prove general results on the decay properties of such autocorrelation functions in the limit of infinite-dimensional matrices. We discuss the relevance of random matrices as models for the dynamics of quantum systems that are chaotic in the classical limit. Permanent address: Dipartimento di Fisica, Via Celoria 16, 20133 Milano, Italy.
New 1/N expansions in random tensor models
Bonzom, Valentin
2012-01-01
Although random tensor models were introduced twenty years ago, it is only in 2011 that Gurau proved the existence of a 1/N expansion. Here we show that there actually is more than a single 1/N expansion, depending on the dimension. In the large N limit, these new expansions retain more than the melonic graphs. Still, in most cases, the large N limit is found to be Gaussian, and therefore extends the scope of the universality theorem for large random tensors. Nevertheless, a scaling which leads to non-Gaussian large N limits, in even dimensions, is identified for the first time.
van Nierop, Lotte E; Slottje, Pauline; Kingma, Herman; Kromhout, Hans
2013-07-01
We assessed postural body sway performance after exposure to movement induced time-varying magnetic fields in the static magnetic stray field in front of a 7 Tesla (T) magnetic resonance imaging scanner. Using a double blind randomized crossover design, 30 healthy volunteers performed two balance tasks (i.e., standing with eyes closed and feet in parallel and then in tandem position) after standardized head movements in a sham, low exposure (on average 0.24 T static magnetic stray field and 0.49 T·s(-1) time-varying magnetic field) and high exposure condition (0.37 T and 0.70 T·s(-1)). Personal exposure to static magnetic stray fields and time-varying magnetic fields was measured with a personal dosimeter. Postural body sway was expressed in sway path, area, and velocity. Mixed-effects model regression analysis showed that postural body sway in the parallel task was negatively affected (P static magnetic stray field and time-varying magnetic field exposure. In addition, practical safety implications of these findings, e.g., for surgeons and others working near magnetic resonance imaging scanners need to be investigated.
Generalized linear models with random effects unified analysis via H-likelihood
Lee, Youngjo; Pawitan, Yudi
2006-01-01
Since their introduction in 1972, generalized linear models (GLMs) have proven useful in the generalization of classical normal models. Presenting methods for fitting GLMs with random effects to data, Generalized Linear Models with Random Effects: Unified Analysis via H-likelihood explores a wide range of applications, including combining information over trials (meta-analysis), analysis of frailty models for survival data, genetic epidemiology, and analysis of spatial and temporal models with correlated errors.Written by pioneering authorities in the field, this reference provides an introduction to various theories and examines likelihood inference and GLMs. The authors show how to extend the class of GLMs while retaining as much simplicity as possible. By maximizing and deriving other quantities from h-likelihood, they also demonstrate how to use a single algorithm for all members of the class, resulting in a faster algorithm as compared to existing alternatives. Complementing theory with examples, many of...
Supersymmetric structures in topological field models
Pisar, T
2000-01-01
formalism with the latter proposed method. Besides the calculation of the vector supersymmetry the formalism admits the derivation of another scalar supersymmetry which is present in some particular models. The work is organized as follows. In Chapter 2 we give the technical details, Chapter 3 presents a review of the relevant aspects of topological field theories, in Chapter 4 we introduce a formalism which admits the calculation of the vectorial supersymmetry of the basic fields, and the following Chapter 5 demonstrates its application in the case of a six-dimensional Witten type model. Chapter 6 combines this method with the Batalin-Vilkovisky formalism, also including the BRST doublets and Chapter 7 gives three different applications of the latter procedure. During the eighties topological quantum field theory appears the first time as a new link between topology and quantum field theory. In the actual understanding we distinguish two types of topological field theories, the first one originally introduce...
Arbitrary scalar field and quintessence cosmological models
Harko, Tiberiu; Mak, M K
2014-01-01
The mechanism of the initial inflationary scenario of the universe and of its late-time acceleration can be described by assuming the existence of some gravitationally coupled scalar fields $\\phi $, with the inflaton field generating inflation and the quintessence field being responsible for the late accelerated expansion. Various inflationary and late-time accelerated scenarios are distinguished by the choice of an effective self-interaction potential $V(\\phi)$, which simulates a temporarily non-vanishing cosmological term. In this work, we present a new formalism for the analysis of scalar fields in flat isotropic and homogeneous cosmological models. The basic evolution equation of the models can be reduced to a first order non-linear differential equation. Approximate solutions of this equation can be constructed in the limiting cases of the scalar field kinetic energy and potential energy dominance, respectively, as well as in the intermediate regime. Moreover, we present several new accelerating and dece...
FINITE VARIANCE OF THE NUMBER OF STATIONARY POINTS OF A GAUSSIAN RANDOM FIELD
Estrade, Anne; Fournier, Julie
2015-01-01
Let X be a real-valued stationary Gaussian random field defined on $R^d$ (d ≥ 1), with almost every realization of class $C^2$. This paper is concerned with the random variable giving the number of points in $T$ (a compact set of $R^d$) where the gradient $X'$ takes a fixed value $v\\in R^d$, $N_{X'}(T, v) = \\{t \\in T : X'(t) = v\\}$. More precisely, it deals with the finiteness of the variance of $N_{X'} (T, v)$, under some non-degeneracy hypothesis on $X$. For d = 1, the so-called " Geman con...
Randomized Field Trials and Internal Validity: Not So Fast My Friend.
James H. McMillan
2007-12-01
Full Text Available The purpose of this article is to summarize eight potential threats to internal validity that occur with randomized field trial (RFT studies. Depending on specific contextual factors, RFTs do not necessarily result in strong internal validity. Of particular concern is whether the unit of random assignment is the same as the number of replications of the intervention, threats as a result of local history, and subject effects. The eight threats are described, with suggestions for providing adequate monitoring to know if they rise to the level of likely or plausible threat to internal validity.
Diaz, P. M. A.; Feitosa, R. Q.; Sanches, I. D.; Costa, G. A. O. P.
2016-06-01
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.
Scene Segmentation with Low-Dimensional Semantic Representations and Conditional Random Fields
Triggs Bill
2010-01-01
Full Text Available This paper presents a fast, precise, and highly scalable semantic segmentation algorithm that incorporates several kinds of local appearance features, example-based spatial layout priors, and neighborhood-level and global contextual information. The method works at the level of image patches. In the first stage, codebook-based local appearance features are regularized and reduced in dimension using latent topic models, combined with spatial pyramid matching based spatial layout features, and fed into logistic regression classifiers to produce an initial patch level labeling. In the second stage, these labels are combined with patch-neighborhood and global aggregate features using either a second layer of Logistic Regression or a Conditional Random Field. Finally, the patch-level results are refined to pixel level using MRF or over-segmentation based methods. The CRF is trained using a fast Maximum Margin approach. Comparative experiments on four multi-class segmentation datasets show that each of the above elements improves the results, leading to a scalable algorithm that is both faster and more accurate than existing patch-level approaches.