Texture Classification and Retrieval Using the Random Neural Network Model

We extend the application of the random neural network to texture classification and retrieval. A neuron in the network corresponds to an image pixel and the neurons are connected according to neighboring relationship between pixels. A texture is represented with the weights of the network and the random neural network is used as an associative memory. In order to assess the performance of the method, texture mosaic images are generated from the popular Brodatz album. We also present a real life application in which a specified texture type is retrieved within a large remote sensing image. Results show that error is comparable to that of previous studies on texture classification which make use of other approaches.This is an extended version of the article presented in 2004 IEEE Southwest Symposium on Image Analysis and Interpretation.     

The analytic model of a subnormal operator

The analytic model of a pure subnormal opertor and its conjugate subnormal operator is obtained. A mosaic is introduced for subnormal operator. Some results in spectral analysis of subnormal operators are obtained by means of the analytic model and the mosaic. The form of pure subnormal operators with rank two self-commutator is determined.This work is partially supported by a NSF grant no DMS-8502359.     

Universal Coefficient Theorems and a Paper of DINH THE LUC

The consequences of an ergodic assumption for mosaic processes of random convex polygons are explored in detail. Under certain regularity conditions on the “smallness” and “largeness” of polygons it is shown that the geometric characteristics of the so-called “typical” polygons do in fact exist. New formulae concerning these characteristics are given. The polygon process formed by a Poisson line process is considered as an example of the general theory and, as a result, certain properties of this example which were previously given heuristically, are proved. Edge effects are treated rigorously.     

Vertex Numbers of Weighted Faces in Poisson Hyperplane Mosaics

In the random mosaic generated by a stationary Poisson hyperplane process in ℝ ^d , we consider the typical k-face weighted by the j-dimensional volume of the j-skeleton (0≤j≤k≤d). We prove sharp lower and upper bounds for the expected number of its vertices.     

Extending Mosaic Displays: Marginal,Conditional, and Partial Views of Categorical Data

Abstract

This article first illustrates the use of mosaic displays for the analysis of multiway contingency tables. We then introduce several extensions of mosaic displays designed to integrate graphical methods for categorical data with those used for quantitative data. The scatterplot matrix shows all pairwise (bivariate marginal) views of a set of variables in a coherent display. One analog for categorical data is a matrix of mosaic displays showing some aspect of the bivariate relation between all pairs of variables. The simplest case shows the bivariate marginal relation for each pair of variables. Another case shows the conditional relation between each pair, with all other variables partialled out. For quantitative data this represents (a) a visualization of the conditional independence relations studied by graphical models, and (b) a generalization of partial residual plots. The conditioning plot, or coplot shows a collection of partial views of several quantitative variables, conditioned by the values of one or more other variables. A direct analog of the coplot for categorical data is an array of mosaic plots of the dependence among two or more variables, stratified by the values of one or more given variables. Each such panel then shows the partial associations among the foreground variables; the collection of such plots shows how these associations change as the given variables vary.     

Effects of awareness program for controlling mosaic disease in Jatropha curcas plantations

The shrinkage of fossil fuel resources motivates many countries to search alternative energy sources. Jatropha curcas is a small drought‐resistant shrub from whose seeds a high grade fuel biodiesel can be produced. It is cultivated in many tropical countries including India. However, the plant is affected by the mosaic virus (Begomovirus) through infected white‐flies (Bemisia tabaci) which causes mosaic disease. Disease control is an important factor to obtain healthy crop but in agricultural practice, farming awareness is equally important. Here, we propose a mathematical model for media campaigns for raising awareness among people to protect this plant in small plots and control disease. In order to archive high crop yield, we consider the awareness campaign to be arranged in impulsive way to make people aware from infected white‐flies to protect Jatropha plants from mosaic virus. The study reveals that the spread of mosaic disease can be contained or even eradicated by the awareness campaigns. To attain an effective eradication, awareness campaign should be implemented at sufficiently short time intervals. Copyright © 2016 John Wiley & Sons, Ltd.     

Mosaic approximations of discrete analogs of Calderón-Zygmund operators

Asymptotic estimates of the form mrA = O(InN · ln ^d ? ^?1), whered is the dimension of the initial space, for mosaic ranks of discrete analog of Calderón-Zygmund operators are obtained for various mosaic covers.     

Attractors of dynamical systems with control: topology of purposeful formation

The definitions of homogeneous and mosaic attractors of codimension one are given. A topological method for their purposeful formation by using the feedback control laws of controlled dynamical systems is suggested.Published in Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 1, pp. 129–132, January, 1995.     

On Finite-Dimensional Distributions of a Random Element Conditioned by the Sum of Random Elements*

A criterion for a random element to be conditioned by a sum of random elements is proved in terms of finitedimensional distributions.     

A bijection between permutations and floorplans, and its applications

A floorplan represents the relative relations between modules on an integrated circuit. Floorplans are commonly classified as slicing, mosaic, or general. Separable and Baxter permutations are classes of permutations that can be defined in terms of forbidden subsequences. It is known that the number of slicing floorplans equals the number of separable permutations and that the number of mosaic floorplans equals the number of Baxter permutations [B. Yao, H. Chen, C.K. Cheng, R.L. Graham, Floorplan representations: complexity and connections, ACM Trans. Design Automation Electron. Systems 8(1) (2003) 55-80]. We present a simple and efficient bijection between Baxter permutations and mosaic floorplans with applications to integrated circuits design. Moreover, this bijection has two additional merits: (1) It also maps between separable permutations and slicing floorplans; and (2) it suggests enumerations of mosaic floorplans according to various structural parameters.     

Reflected pulses from a refractive random medium at grazing incidence

A problem of acoustic pulse reflection by a one-dimensionalrefractive random medium is considered in the case of grazingangle incidence. The material parameters of the medium are assumedto vary with a random microscale and a deterministic macroscale.A system of stochastic equations for random scattering variablesis derived based upon the random modelling of three separatescales of variations. The statistical properties of the reflectedpulses are characterized by an asymptotic diffusion limit theoremof stochastic differential equations with multiple scales. Thetransport equations governing the limiting stochastic distributionsof the random reflection coefficient are obtained in the propagatingregime, which leads to the power spectral densities of the reflectedpressure and particle velocity fields.     

A second-order Monte Carlo method for the solution of the Ito stochastic differential equation

A difference approximation that is second-order accurate in the time step his derived for the general Ito stochastic differential equation. The difference equation has the form of a second-order random walk in which the random terms are non-linear combinations of Gaussian random variables. For a wide class of problems, the transition pdf is joint-normal to second order in h; the technique then reduces to a Gaussian random walk, but its application is not limited to problems having a Gaussian solution. A large number of independent sample paths are generated in a Monte Carlo solution algorithm; any statistical function of the solution (e.g., moments or pdf's) can be estimated by ensemble averaging over these paths     

Three-Dimensional Variational Analysis of Composite Structures Using Bernstein Polynomial Approximations. Report 2

The application of the previously developed 3D varionational analysis approach to the investigation of crack propagation in composite bonded joints is presented. In this application, the propagation of three different types of a 2D planar crack (adhesive, cohesive, and interfacial) is modeled by relaxing the respective continuity conditions for displacements between adjacent bricks in the mosaic structure. The crack propagation process is then characterized by the release rate of the total potential energy between two consecutive states of the mosaic body with different crack lengths. Numerical examples illustrate the 3D analysis of double-lap adhesively bonded joints with unidirectional and cross-ply laminated composite adherends. The numerical results provide an illustration of various characteristics of the crack propagation process. The values of the ultimate failure load predicted by analyzing the initial stage of crack propagation are found to be in a good agreement with experimental data.     

Solution of partial differential equations by a modified random walk

A new Monte Carlo technique is applied to solve difference equations of elliptic and parabolic partial differential equations with given boundary values. Fixed random walk is extended to modified random walk, whereby a random walk is made on a maximum square. The average number of steps and the computational time in a modified random walk is much less than in a fixed random walk. Numerical examples support the utility of this method.     

Visualizing Loglinear Models

Abstract

We consider visual methods based on mosaic plots for interpreting and modeling categorical data. Categorical data are most often modeled using loglinear models. For certain loglinear models, mosaic plots have unique shapes that do not depend on the actual data being modeled. These shapes reflect the structure of a model, defined by the presence and absence of particular model coefficients. Displaying the expected values of a loglinear model allows one to incorporate the residuals of the model graphically and to visually judge the adequacy of the loglinear fit. This procedure leads to stepwise interactive graphical modeling of loglinear models. We show that it often results in a deeper understanding of the structure of the data. Linking mosaic plots to other interactive displays offers additional power that allows the investigation of more complex dependence models than provided by static displays.     

Derived random measures

A derived random measure is constructed by integration of a random process with respect to a random measure independent of that process. Basic distributional properties, a continuity theorem, sample path properties, a strong law of large numbers, and a central limit theorem for derived random measures are established. Applications are given to compounding and thinning of point processes and the measure of a random set.     

Numerical solutions of random mean square Fisher-KPP models with advection

This paper deals with the construction of numerical stable solutions of random mean square Fisher-Kolmogorov-Petrosky-Piskunov (Fisher-KPP) models with advection. The construction of the numerical scheme is performed in two stages. Firstly, a semidiscretization technique transforms the original continuous problem into a nonlinear inhomogeneous system of random differential equations. Then, by extending to the random framework, the ideas of the exponential time differencing method, a full vector discretization of the problem addresses to a random vector difference scheme. A sample approach of the random vector difference scheme, the use of properties of Metzler matrices and the logarithmic norm allow the proof of stability of the numerical solutions in the mean square sense. In spite of the computational complexity, the results are illustrated by comparing the results with a test problem where the exact solution is known.     

Generating uniform random vectors over a simplex with implications to the volume of a certain polytope and to multivariate extremes

A uniform random vector over a simplex is generated. An explicit expression for the first moment of its largest spacing is derived. The result is used in a proposed diagnostic tool which examines the validity of random number generators. It is then shown that the first moment of the largest uniform spacing is related to the dependence measure of random vectors following any extreme value distribution. The main result is proved by a geometric proof as well as by a probabilistic one.     

Stationary Conjugation of Flows for Parabolic SPDEs with Multiplicative Noise and Some Applications

Abstract

The purpose of this paper is to transform a nonlinear stochastic partial differential equation of parabolic type with multiplicative noise into a random partial differential equation by using a bijective random process. A stationary conjugation is constructed, which is of interest for asymptotic problems. The conjugation is used here to prove the existence of the stochastic flow, the perfect cocycle property and the existence of the random attractor, all nontrivial properties in the case of multiplicative noise.     

Weak ergodicity and products of random matrices

A representation for a weakly ergodic sequence of (nonstochastic) matrices allows products of nonnegative matrices which eventually become strictly positive to be expressed via products of some associated stochastic matrices and ratios of values of a certain function. This formula used in a random setup leads to a representation for the logarithm of a random matrix product. If the sequence of random matrices is in addition stationary then automatically almost all sequences are weakly ergodic, and the representation is expressed in terms of an one-dimensional stationary process. This permits properties of products of random matrices to be deduced from the latter. Second moment assumptions guarantee that central limit theorems and laws of the iterated logarithm hold for the random matrix products if and only if they hold for the corresponding stationary process. Finally, a central limit theorem for some classes of weakly dependent stationary random matrices is derived doing away with the restriction of boundedness of the ratios of colum entries assumed by previous studies. Extensions beyond stationarity are discussed.