symmetries and algebras of the integrable dispersive long wave equations in 2 1 dimensional spaces similarly to the kadomtsev petviashvili kp equation a set of generalized symmetries with arbitrary functions of t is given by a simple constructable formula for the integrable dispersive long wave equations in 2 1 space dimensions these symmetries constitute an infinite dimensional lie algebra which is a generalization to the known winfinity algebra

a further extended tanh function method and new soliton like solutions to the integrable broer kaup bk equations in 2 1 dimensional spaces based on an extended tanh function method a further extended tanh function method is suggested to obtain multiple exact solutions for nonlinear partial differential equations which including soliton like solutions solitary waves and trigonometric function solutions the validity and reliability of the method is tested by its application to the integrable broer kaup equations in 2 1 dimensional spaces more new explicit exact solutions are found

symmetries of the kadomtsev petviashvili equation generalized symmetries with arbitrary functions of time t for the well known 2 1 dimensional integrable model kadomtsev petviashvili kp equation are found by means of the extended mastersymmetry approach then an explicit and simple constructive formula for the symmetries of the kp equation is derived directly from the symmetry definition equation without using complicated recursion operators all the known symmetries appear as special cases of those obtained in this paper the general infinite dimensional lie algebra constituted by these symmetries is also given

conformal invariance and integrable models usually an integrable nonlinear partial differential equation can be transformed to its conformal invariant form schwartz form using the conformal invariance of the integrable models we can obtain many interesting results in this paper we will focus mainly in obtaining new symmetries and new integrable models starting from the conformal invariance of an integrable model one can obtain infinitely many non local symmetries many types of 1 1 and 2 1 dimensional new sine gordon or sinh gordon extensions are obtained from the conformal flow equations of the koerteweg de vries type equations many other kinds of integrable models can be obtained from the conformal constraints of the known integrable models

optimized estimation of moments for nonstationary signals the behavior of nonstationary moment estimators that are based on linear time invariant filtering is analyzed the performance of such estimators is evaluated in terms of their time averaged variance and time averaged squared bias optimal estimators that minimize a convex combination of bias and variance are derived the superiority of such optimally weighted filtering over the conventional exponentially windowed moment estimation technique is demonstrated by means of a simple example the same example also serves to illustrate the difficulties encountered when the construction of optimal estimators relies on uncertain prior information as well as to demonstrate the feasibility of overcoming such difficulties by using appropriately designed robust optimal estimators we also include a brief discussion of the relevance of the proposed moment estimation technique to identification of linear time variant systems and to estimation of time variant spectra

symmetry reduction for nonlinear relativistically invariant equations symmetry reduction is studied for the relativistically invariant scalar partial differential equation h u u 2 u 0 in n 1 dimensional minkowski space m n 1 the introduction of k symmetry variables 1 k as invariants of a subgroup g of the poincare group p n 1 having generic orbits of codimension k n in m n 1 reduces the equation to a pde in k variables all codimension 1 symmetry variables in m n 1 n arbitrary reducing the equation studied to an ode are found as well as all codimension 2 and 3 variables for the low dimensional cases n 2 3 the type of equation studied includes many cases of physical interest in particular nonlinear klein gordon equations such as the sine gordon equation and hamilton jacobi equations

a comparison between two measures of convergence in recursive window based spectrum estimation it is shown that approximations of the infinite impulse response iir of a single pole filter by a rectangular finite impulse response fir through either the effective window length approach or the least squares inverse filtering approach yield the same results both the least squares inverse filter method and the effective window length can be used as measures of convergence in recursive window based spectrum estimators an algebraic proof is given to show that both measures take the same value for the commonly used single pole exponential window

infinitely many lax pairs and symmetry constraints of the kp equation starting from a known lax pair one can get some infinitely many coupled lax pairs infinitely many nonlocal symmetries and infinitely many new integrable models in some different ways in this paper taking the well known kadomtsev petviashvili kp equation as a special example we show that infinitely many nonhomogeneous linear lax pairs can be obtained by using infinitely many symmetries differentiating the spectral functions with respect to the inner parameters using a known lax pair and the darboux transformations dt infinitely many nonhomogeneous nonlinear lax pairs can also be obtained by means of the infinitely many lax pairs dt and the conformal invariance of the schwartz form of the kp equation infinitely many new nonlocal symmetries can be obtained naturally infinitely many integrable models in 1 1 dimensions 2 1 dimensions 3 1 dimensions and even in higher dimensions can be obtained by virtue of symmetry constraints of the kp equation related to the infinitely many lax pairs

generalized riccati equation expansion method and its application to the 3 1 dimensional jumbo miwa equation based on the computerized symbolic system maple and a riccati equation a generalized riccati equation expansion method for constructing soliton like solutions of non linear evolution equations nees is presented by a new general ansatz the proposed method is more powerful than most of the existing tanh methods the extended tanh function method the modified extended tanh function method and generalized hyperbolic function method by use of the method we not only can successfully recover the previously known formal solutions but also construct new and more general formal solutions for some nees making use of the method we study the the 3 1 dimensional jumbo miwa equation and obtain rich new families of the exact solutions including the non travelling wave and coefficient functions soliton like solutions singular soliton like solutions periodic form solutions

novel interacting phenomena in 2 1 dimensional akns system abstract by means of an new auxiliary equation method based on mapping method and the second order linear ordinary differential equation some types of variable separation solutions with two arbitrary lower dimensional functions of the 2 1 dimensional ablowitz kaup newell segur system are derived based on the derived variable separation excitation some new special types of non localized solutions such as doubly periodic wave and line periodic wave are constructed by choosing appropriate functions in addition we also investigate the annihilation phenomenon and non elastic interaction graphically

special solutions from the variable separation approach the davey stewartson equation a variable separation procedure for the davey stewartson ds equation is proposed by using a prior ansatz to its bilinear form the reduced equations for two variable separated fields have the same trilinear form although they possess different independent variables the trilinear equation can be changed to a spacetime symmetric form and can be solved by means of a boussinesq type equation system whenever a pair of solutions of the reduced fields are obtained a corresponding solution of the ds equation can be obtained algebraically the single dromion solution and some kinds of positon solutions are obtained explicitly

lie symmetry analysis and some new exact solutions of the wu zhang equation the lie symmetry analysis and the basic similarity reductions are performed for the wu zhang equation a 2 1 dimensional nonlinear dispersive wave equation some new exact solutions generated from the similarity transformation are provided they demonstrate some new three dimensional features of a single solitary wave and two interacting solitary waves

real nonparametric regression using complex wavelets summary wavelet shrinkage is an effective nonparametric regression technique especially when the underlying curve has irregular features such as spikes or discontinuities the basic idea is simple take the discrete wavelet transform dwt of data consisting of a signal corrupted by noise shrink or remove the wavelet coefficients to remove the noise and then invert the dwt to form an estimate of the true underlying curve various authors have proposed increasingly sophisticated methods of doing this using real valued wavelets complex valued wavelets exist but are rarely used we propose two new shrinkage techniques which use complex valued wavelets extensive simulations show that our methods almost always give significantly more accurate estimates when compared with methods based on real valued wavelets further one of our methods is both simpler and dramatically faster than its competitors in an attempt to understand the excellent performance of this latter method we present a new risk bound on its hard thresholded coefficients

nonclassical analysis and painleve property for the kupershmidt equations by means of the nonclassical lie approach and the direct method all the similarity reductions of the kupershmidt equations are found two reduction equations which can also be obtained by the classical lie approach are the painleve type ii and iv respectively the other three reduction equations which cannot be obtained by the classical lie approach are only linear or riccati type

pfaffianization of the two dimensional toda lattice pfaffianization procedure due to hirota and ohta is applied to the two dimensional toda lattice as a result a pfaffianized version of the two dimensional toda lattice is found

non classical symmetry reduction example of the boussinesq equation a symmetry of an equation will leave the set of all solutions invariant a conditional symmetry will leave only a subset of solutions defined by some differential condition invariant the authors show how a specific class of conditional symmetries can be used to reduce a partial differential equation to an ordinary one in particular for the boussinesq equation these conditional symmetries together with the ordinary ones provide all possible reductions to ordinary differential equations a group theoretical explanation of the recently obtained new reductions is provided

new variable separation approach application to nonlinear diffusion equations the concept of the derivative dependent functional separable solution ddfss as a generalization to the functional separable solution is proposed as an application it is used to discuss the generalized nonlinear diffusion equations based on the generalized conditional symmetry approach as a consequence a complete list of canonical forms for such equations which admit the ddfss is obtained and some exact solutions to the resulting equations are described

deformations of the riccati equation by using miura type transformations using some different miura type transformations a c integrable ordinary differential equation the riccati equation is deformed to some different s integrable models such as the 1 1 dimensional and 2 1 dimensional sinh gordon equations and mikhailov dodd bullough equations

generalized method and new exact wave solutions for 2 1 dimensional broer kaup kupershmidt system in this paper a new algebra method i e generalized elliptic equation rational expansion method is devised to uniformly construct a series of exact solutions for nonlinear partial differential equations compared with most existing tanh methods the proposed method not only recover some known solutions but also find some new and general solutions the efficiency of the method can be demonstrated on the 2 1 dimensional broer kaup kupershmidt system as a result we obtain many new types of solutions include rational formal solitary wave solutions rational formal triangular periodic wave solutions rational formal jacobi and weierstrass double period solutions and rational wave solutions

an adaptive optimal kernel time frequency representation time frequency representations with fixed windows or kernels figure prominently in many applications but perform well only for limited classes of signals representations with signal dependent kernels can overcome this limitation however while they often perform well most existing schemes are block oriented techniques unsuitable for on line implementation or for tracking signal components with characteristics that change with time the time frequency representation developed in the present paper based on a signal dependent radially gaussian kernel that adapts over time surmounts these difficulties the method employs a short time ambiguity function both for kernel optimization and as an intermediate step in computing constant time slices of the representation careful algorithm design provides reasonably efficient computation and allows on line implementation certain enhancements such as cone kernel constraints and approximate retention of marginals are easily incorporated with little additional computation while somewhat more expensive than fixed kernel representations this new technique often provides much better performance several examples illustrate its behavior on synthetic and real world signals

adaptive tracking of multiple sinusoids whose power levels are widely separated the behavior of the gradient transversal filter lms the gradient lattice gl and the least squares lattice lsl when used to track multiple sinusoidal or narrow band components whose power levels are widely separated is investigated these approaches to the realization of the pth order one step linear predictor of the time series are recursive in time the lags of the instantaneous frequency estimates from their actual underlying values are of particular interest the frequency tracking characteristics of the lms gl and lsl algorithms are illustrated in several situations included are simulations of dual sinusoids undergoing a variety of frequency versus time dynamics and a formant tracking example of real speech

empirical bayes approach to improve wavelet thresholding for image noise reduction wavelet threshold algorithms replace small magnitude wavelet coefficients with zero and keep or shrink the other coefficients this is basically a local procedure because wavelet coefficients characterize the local regularity of a function although a wavelet transform has decorrelating properties structures in images like edges are never decorrelated completely and these structures appear in the wavelet coefficients a classification based on a local criterion like coefficient magnitude is not the perfect method to distinguish important uncorrupted coefficients from coefficients dominated by noise we therefore introduce a geometrical prior model for configurations of important wavelet coefficients and combine this with local characterization of a classical threshold procedure into a bayesian framework the local characterization is incorporated into the conditional model whereas the prior model describes only configurations not coefficient values more precisely local characterization favors co

similarity solutions of the kadomtsev petviashvili equation using the direct method introduced by clarkson and kruskal ck 1989 recently the author obtains the similarity reductions of the kadomtsev petviashvili equation kpe some of them possess the same painleve properties as that of the boussinesq equation be obtained by ck however the similarity solutions of kpe may include some more than three arbitrary functions of time there exist some other types of similarity reductions of the kpe different from the similarity reductions of the be obtained by ck

new similarity reductions of the boussinesq equation some new similarity reductions of the boussinesq equation which arises in several physical applications including shallow water waves and also is of considerable mathematical interest because it is a soliton equation solvable by inverse scattering are presented these new similarity reductions including some new reductions to the first second and fourth painleve equations cannot be obtained using the standard lie group method for finding group invariant solutions of partial differential equations they are determined using a new and direct method that involves no group theoretical techniques

on computing and implementing the running bispectra the paper extends recursion to bispectrum estimation problems and presents the systolic array implementation of the recursive higher order spectrum in which the bispectrum estimate is updated every data sample forward and reverse sequence running fourier transforms are first systolically realized the results are then used to drive a second systolic array whose outputs represent the ft of the data third order moment the proposed systolic arrays have no global communications with a number of processing elements independent of the size of the employed 2d lag window

image denoising using scale mixtures of gaussians in the wavelet domain we describe a method for removing noise from digital images based on a statistical model of the coefficients of an overcomplete multiscale oriented basis neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables a gaussian vector and a hidden positive scalar multiplier the latter modulates the local variance of the coefficients in the neighborhood and is thus able to account for the empirically observed correlation between the coefficient amplitudes under this model the bayesian least squares estimate of each coefficient reduces to a weighted average of the local linear estimates over all possible values of the hidden multiplier variable we demonstrate through simulations with images contaminated by additive white gaussian noise that the performance of this method substantially surpasses that of previously published methods both visually and in terms of mean squared error

computationally lag invariant recursive spectrum estimators this paper is concerned with fourier based nonparametric spectral estimation methods for time varying environments it presents a class of interactive spectrum estimators in which the number of computations required to update the estimate at every data sample is independent of the number of the autocorrelation lags employed to produce this estimate these estimators are termed lag invariant and form an important class due to their computational simplicity because of the lag invariant property resolution enhancement is achieved without additional cost in computations per frequency sample the proposed class of recursive spectral estimators is based on specific selection of the lagged product windows used in the autocorrelation function estimation in this paper the conditions necessary to produce the lag invariance property are delineated

a new korteweg de vries equation based sub equation method and its application to the 2 1 dimensional korteweg de vries equation with the help of the symbolic computation system maple we present korteweg de vries equation based sub equation method being concise and straightforward it is applied to the 2 1 dimensional korteweg de vries equation it is shown that n soliton solution of the 2 1 dimensional korteweg de vries equation can be found by this new method the method can be applied to other nonlinear partial differential equations in mathematical physics

information theoretic analysis of interscale and intrascale dependencies between image wavelet coefficients this paper presents an information theoretic analysis of statistical dependencies between image wavelet coefficients the dependencies are measured using mutual information which has a fundamental relationship to data compression estimation and classification performance mutual information is computed analytically for several statistical image models and depends strongly on the choice of wavelet filters in the absence of an explicit statistical model a method is studied for reliably estimating mutual information from image data the validity of the model based and data driven approaches is assessed on representative real world photographic images our results are consistent with empirical observations that coding schemes exploiting inter and intrascale dependencies alone perform very well whereas taking both into account does not significantly improve coding performance a similar observation applies to other image processing applications

maximum likelihood estimation logic and practice introduction the logic of maximum likelihood a general modeling framework using maximum likelihood methods an introduction to basic estimation techniques further empirical examples additional likelihoods conclusions

symmetry reduction for the kadomtsev petviashvili equation using a loop algebra the kadomtsev petviashvili kp equation ut 3uux 2 1 4 uxxx x 3 uyy 4 0 allows an infinite dimensional lie group of symmetries i e a group transforming solutions amongst each other the lie algebra of this symmetry group depends on three arbitrary functions of time t and is shown to be related to a subalgebra of the loop algebra a 1 4 low dimensional subalgebras of the symmetry algebra are identified specifically all those of dimension n 3 and also a physically important six dimensional lie algebra containing translations dilations galilei transformations and quasirotations new solutions of the kp equation are obtained by symmetry reduction using the one dimensional subalgebras of the symmetry algebra these solutions contain up to three arbitrary functions of t

improved kinetic renormalisation group approach to diffusion limited aggregation an improved kinetic renormalisation group approach to diffusion limited aggregation is presented this approach is based on the growth process itself and accounts for the dispersity in the growth probabilities it yields the multifractal spectrum d q with better values at smaller q on the 2d square lattice the authors find df 1 694 for the fractal dimensions of the cluster and that of its interface and d 1 1 01 for the information dimension the former agrees with the simulation results df approximately 1 70 and the latter compares very well with the exact value d 1 1

bivariate shrinkage functions for wavelet based denoising exploiting interscale dependency most simple nonlinear thresholding rules for wavelet based denoising assume that the wavelet coefficients are independent however wavelet coefficients of natural images have significant dependencies we only consider the dependencies between the coefficients and their parents in detail for this purpose new non gaussian bivariate distributions are proposed and corresponding nonlinear threshold functions shrinkage functions are derived from the models using bayesian estimation theory the new shrinkage functions do not assume the independence of wavelet coefficients we show three image denoising examples in order to show the performance of these new bivariate shrinkage rules in the second example a simple subband dependent data driven image denoising system is described and compared with effective data driven techniques in the literature namely visushrink sureshrink bayesshrink and hidden markov models in the third example the same idea is applied to the dual tree complex wavelet coefficients

image modeling using interscale phase properties of complex wavelet coefficients this paper describes an approach to image modelling using interscale phase relationships of wavelet coefficients for use in image estimation applications the method is based on the dual tree complex wavelet transform but a phase rotation is applied to the coefficients to create complex derotated coefficients these derotated coefficients are shown to have increased correlation compared to standard wavelet coefficients near edge and ridge features allowing improved signal estimation in these areas the nature of the benefits brought by the derotated coefficients are analyzed and the implications for image estimation algorithm design noted the observations and conclusions provide a basis for design of the de noising algorithm in 1

similarity reductions of the kp equation by a direct method basing on a direct method developed by clarkson and kruskal 1989 the kadomtsev petviashvili kp equation has been reduced to three types of 1 1 dimensional partial differential equations which are equivalent to the three types of the similarity reduction equations obtained by the classical lie approach but with different independent variables more arbitrary functions which have been missed by the classical lie approach have been included in the solutions of the kp equation for instance the third type of reduction obtained by the direct method can be divided into three subcases and the third type of solution of the kp equation obtained by the classical lie approach is only a special case of one subcase of the authors results

a parametric texture model based on joint statistics of complex wavelet coefficients we present a universal statistical model for texture images in the context of an overcomplete complex wavelet transform the model is parameterized by a set of statistics computed on pairs of coefficients corresponding to basis functions at adjacent spatial locations orientations and scales we develop an efficient algorithm for synthesizing random images subject to these constraints by iteratively projecting onto the set of images satisfying each constraint and we use this to test the perceptual validity of the model in particular we demonstrate the necessity of subgroups of the parameter set by showing examples of texture synthesis that fail when those parameters are removed from the set we also demonstrate the power of our model by successfully synthesizing examples drawn from a diverse collection of artificial and natural textures

maximal abelian subalgebras of real and complex symplectic lie algebras we provide guidelines for classifying maximal abelian subalgebras masa s of the symplectic lie algebras sp 2n r and sp 2n c into conjugacy classes under the lie groups sp 2n r and sp 2n c respectively the task of classifying all masa s is reduced to the classification of orthogonally indecomposable oid masa s two types of orthogonally indecomposable masa s of sp 2n c exist 1 indecomposable maximal abelian nilpotent subalgebras mans s 2 decomposable masa s their classification reduces to a classification of mans s of sl n c four types of orthogonally indecomposable masa s of sp 2n r exist 1 absolutely indecomposable masa s mans s 2 relatively indecomposable masa s their classification reduces to a classification of mans s of su p q for p q n 3 decomposable absolutely oid masa s involving mans s of sl n r 4 decomposable relatively oid masa s involving mans s of sl n 2 c for n even low dimensional cases of sp 2n f n 1 2 3 f r or c are treated exhau

non lie symmetry groups of 2 1 dimensional nonlinear systems obtained from a simple direct method a new direct method is developed to find finite symmetry groups of nonlinear mathematical physics systems using the direct method for the well known 2 1 dimensional kadomtsev petviashvili equation and the ablowitz kaup newell segur system both the lie point symmetry groups and the non lie symmetry groups are obtained the lie symmetry groups obtained via traditional lie approaches are only special cases furthermore the expressions of the exact finite transformations of the lie groups are much simpler than those obtained via the standard approaches

spatially adaptive wavelet thresholding with context modeling for image denoising the method of wavelet thresholding for removing noise or denoising has been researched extensively due to its effectiveness and simplicity much of the literature has focused on developing the best uniform threshold or best basis selection however not much has been done to make the threshold values adaptive to the spatially changing statistics of images such adaptivity can improve the wavelet thresholding performance because it allows additional local information of the image such as the identification of smooth or edge regions to be incorporated into the algorithm this work proposes a spatially adaptive wavelet thresholding method based on context modeling a common technique used in image compression to adapt the coder to changing image characteristics each wavelet coefficient is modeled as a random variable of a generalized gaussian distribution with an unknown parameter context modeling is used to estimate the parameter for each coefficient which is then used to adapt the thresholding strategy this spatially adaptive thresholding is extended to the overcomplete wavelet expansion which yields better results than the orthogonal transform experimental results show that spatially adaptive wavelet thresholding yields significantly superior image quality and lower mse than the best uniform thresholding with the original image assumed known

on the infinite dimensional symmetry group of the davey stewartson equations the lie algebra of the group of point transformations leaving the davey stewartson equations dse s invariant is obtained the general element of this algebra depends on four arbitrary functions of time the algebra is shown to have a loop structure a property shared by the symmetry algebras of all known 2 1 dimensional integrable nonlinear equations subalgebras of the symmetry algebra are classified and used to reduce the dse s to various equations involving only two independent variables

new symmetry reductions and exact solutions of the davey stewartson system i reductions to ordinary differential equations in this article symmetry reductions and exact solutions are presented for the 2 1 dimensional davey stewartson ds system which has the completely integrable dsi and dsii systems as special cases these symmetry reductions are obtained using the direct method originally developed by clarkson and kruskal to study symmetry reductions of the boussinesq equation which involves no group theoretic techniques the ds system is reduced directly to ordinary differential equations with no intermediate step using these reductions exact solutions of the ds system including some expressible in terms of the second and fourth painleve equations and elementary functions are obtained

estimating the probability of the presence of a signal of interest in multiresolution single and multiband image denoising we develop three novel wavelet domain denoising methods for subband adaptive spatially adaptive and multivalued image denoising the core of our approach is the estimation of the probability that a given coefficient contains a significant noise free component which we call signal of interest in this respect we analyze cases where the probability of signal presence is 1 fixed per subband 2 conditioned on a local spatial context and 3 conditioned on information from multiple image bands all the probabilities are estimated assuming a generalized laplacian prior for noise free subband data and additive white gaussian noise the results demonstrate that the new subband adaptive shrinkage function outperforms bayesian thresholding approaches in terms of mean squared error the spatially adaptive version of the proposed method yields better results than the existing spatially adaptive ones of similar and higher complexity the performance on color and on multispectral images is superior with respect to recent multiband wavelet thresholding

adapting to unknown smoothness via wavelet shrinkage abstract we attempt to recover a function of unknown smoothness from noisy sampled data we introduce a procedure sureshrink that suppresses noise by thresholding the empirical wavelet coefficients the thresholding is adaptive a threshold level is assigned to each dyadic resolution level by the principle of minimizing the stein unbiased estimate of risk sure for threshold estimates the computational effort of the overall procedure is order n log n as a function of the sample size n sureshrink is smoothness adaptive if the unknown function contains jumps then the reconstruction essentially does also if the unknown function has a smooth piece then the reconstruction is essentially as smooth as the mother wavelet will allow the procedure is in a sense optimally smoothness adaptive it is near minimax simultaneously over a whole interval of the besov scale the size of this interval depends on the choice of mother wavelet we know from a previous paper by the authors that traditional smoot

nonclassical symmetry reductions for the dispersive wave equations in shallow water all six types of the similarity reductions of the dispersive wave equations in shallow water are obtained by the direct method the group explanation of the results is also given it is pointed out that in order to find all the results by nonclassical lie approach two additional condition equations should be satisfied at the same time together with two original equations the logarithmic branch points for time t can be included in two types of the similarity solutions though the model can be cast into the canonical hamiltonian form

noise reduction of cdna microarray images using complex wavelets noise reduction is an essential step of cdna microarray image analysis for obtaining better quality gene expression measurements wavelet based denoising methods have shown significant success in traditional image processing the complex wavelet transform cwt is preferred to the classical discrete wavelet transform for denoising of microarray images due to its improved directional selectivity for better representation of the circular edges of spots and near shift invariance property existing cwt based denoising methods are not efficient for microarray image processing because they fail to take into account the signal as well as noise correlations that exist between red and green channel images in this paper two bivariate estimators are developed for the cwt based denoising of microarray images using the standard maximum a posteriori and linear minimum mean squared error estimation criteria the proposed denoising methods are capable of taking into account both the interchannel signal and noise correlations significance of the proposed denoising methods is assessed by examining the effect of noise reduction on the estimation of the log intensity ratio extensive experimentations are carried out to show that the proposed methods provide better noise reduction of microarray images leading to more accurate estimation of the log intensity ratios as compared to the other cwt based denoising methods

on denoising and compression of dna microarray images we address the problems of noise and huge data sizes in microarray images first we propose a mixture model for describing the statistical and structural properties of microarray images then based on the microarray image model we present methods for denoising and for compressing microarray images the denoising method is based on a variant of the translation invariant wavelet transform the compression method introduces the notion of approximate contexts rather than traditional exact contexts in modeling the symbol probabilities in a microarray image this inexact context modeling approach is important in dealing with the noisy nature of microarray images using the proposed denoising and compression methods we describe a near lossless compression scheme suitable for microarray images results on both denoising and compression are included which show the performance of the proposed methods further experiments using the results of the proposed near lossless compression scheme in gene clustering using cell cycle microarray data for s cerevisiae showed a general improvement in the clustering performance when compared with using the original data this provides an indirect validation of the effectiveness of the proposed denoising method

derivative dependent functional separable solutions for the kdv type equations abstract a complete list of canonical forms for a special kdv type of equations which admit derivative dependent functional separable solutions is obtained by using the generalized conditional symmetry approach some exact solutions to the resulting equations are explicitly obtained

infinitesimal weak symmetries of nonlinear differential equations in two independent variables non classical infinitesimal weak symmetries of pde introduced by olver and rosenau 1987 are analysed in the case of pde in two independent variables it is demonstrated that obtaining such symmetries is equivalent to obtaining the two dimensional modules of non classical partial symmetries the boussinesq and the nonlinear heat equations are treated from the point of view of non classical symmetries

new exact solutions for solving the initial value problem of the kdv kp equation via the lie group method the traveling wave solutions of the two dimensional kdv kp equation are studied via the lie group method the kdv kp equation is a nonlinear partial differential equation in two spatial and one temporal coordinate which describes the evolution of nonlinear long waves of small amplitude with slow dependence on the transverse coordinate the investigation of exact solutions of the kdv kp via the application of lie group and the extended f expansion methods plays the main role in understanding the nonlinear physical phenomena

dynamical survey of a generalized zakharov equation and its exact travelling wave solutions we investigate the dynamical behavior of a generalized zakharov equation for the complex envelope of the high frequency wave and the real low frequency field by analyzing its phase portraits following a dynamical system approach in different parameter regions we depict phase portraits of a travelling wave system through discussing the bifurcation of phase portraits we unwrap explicit miscellaneous travelling waves including localized and periodic ones

building robust wavelet estimators for multicomponent images using stein s principle multichannel imaging systems provide several observations of the same scene which are often corrupted by noise in this paper we are interested in multispectral image denoising in the wavelet domain we adopt a multivariate statistical approach in order to exploit the correlations existing between the different spectral components our main contribution is the application of stein s principle to build a new estimator for arbitrary multichannel images embedded in additive gaussian noise simulation tests carried out on optical satellite images show that the proposed method outperforms conventional wavelet shrinkage techniques

spectral smoothing and recursion based on the nonstationarity of the autocorrelation function averaging and recursion in short time spectral analysis in view of the nature of the nonstationarity of the random process is addressed using the wigner spectrum estimator as a general model this correspondence relates the selection of the time and lag windows to the stationary intervals of the autocorrelation at different lags the lag dependent time averaging for two types of commonly assumed nonstationarities is presented and used to devise the recursive estimates of their time varying spectrum

the fourth painleve equation and associated special polynomials in this article rational solutions and associated polynomials for the fourth painleve equation are studied these rational solutions of the fourth painleve equation are expressible as the logarithmic derivative of special polynomials the okamoto polynomials the structure of the roots of these okamoto polynomials is studied and it is shown that these have a highly regular structure the properties of the okamoto polynomials are compared and contrasted with those of classical orthogonal polynomials further representations are given of the associated rational solutions in the form of determinants through schur functions

equations of arbitrary order invariant under the kadomtsev petviashvili symmetry group by means of a simple new approach a general kadomtsev petviashvili kp family with an arbitrary function of group invariants of arbitrary order is proposed it is proved that the general kp family possesses a common infinite dimensional kac moody virasoro lie point symmetry algebra the known fourth order one can be re obtained as a special example the finite transformation group is presented in a clearer form the kac moody virasoro group invariant solutions and the kac moody group invariant solutions of the kp family are determined by the boussinesq and kdv families respectively

symmetry reductions of a generalized cylindrical nonlinear schrodinger equation in this work symmetry reductions for a generalized cylindrical nonlinear schrodinger equation are presented these are obtained using an extension of the direct method originally developed by clarkson and kruskal 1989 which involves no group theoretic techniques

a new framework for complex wavelet transforms although the discrete wavelet transform dwt is a powerful tool for signal and image processing it has three serious disadvantages shift sensitivity poor directionality and lack of phase information to overcome these disadvantages we introduce two stage mapping based complex wavelet transforms that consist of a mapping onto a complex function space followed by a dwt of the complex mapping unlike other popular transforms that also mitigate dwt shortcomings the decoupled implementation of our transforms has two important advantages first the controllable redundancy of the mapping stage offers a balance between degree of shift sensitivity and transform redundancy this allows us to create a directional non redundant complex wavelet transform with potential benefits for image coding systems to the best of our knowledge no other complex wavelet transform is simultaneously directional and non redundant the second advantage of our approach is the flexibility to use any dwt in the transform implementation as an example we can exploit this flexibility to create the complex double density dwt cddwt a shift insensitive directional complex wavelet transform with a low redundancy of 3 sup m 1 2 sup m 1 in m dimensions to the best of our knowledge no other transform achieves all these properties at a lower redundancy

the design of approximate hilbert transform pairs of wavelet bases several authors have demonstrated that significant improvements can be obtained in wavelet based signal processing by utilizing a pair of wavelet transforms where the wavelets form a hilbert transform pair this paper describes design procedures based on spectral factorization for the design of pairs of dyadic wavelet bases where the two wavelets form an approximate hilbert transform pair both orthogonal and biorthogonal fir solutions are presented as well as iir solutions in each case the solution depends on an allpass filter having a flat delay response the design procedure allows for an arbitrary number of vanishing wavelet moments to be specified a matlab program for the procedure is given and examples are also given to illustrate the results

cdna microarray image processing using fuzzy vector filtering framework this paper presents a novel filtering framework capable of processing cdna microarray images the proposed two component adaptive vector filters integrate well known concepts from the areas of fuzzy set theory nonlinear filtering multidimensional scaling and robust order statistics by appropriately setting the weighting coefficients in a generalized framework the method is capable of removing noise impairments while preserving structural information in cdna microarray images noise removal is performed by tuning a membership function which utilizes distance criteria applied to cdna vectorial inputs at each image location the classical vector representation adopted here for a two channel processing task as well as a new color ratio model representation are used simulation studies reported in this paper indicate that the proposed adaptive fuzzy vector filters are computationally attractive yield excellent performance and are able to preserve structural information while efficiently suppressing noise in cdna microarray data