a generalized histogram clustering scheme for multidimensional image data abstract a clustering procedure called hicap histogram cluster analysis procedure was developed to perform an unsupervised classification of multidimensional image data the clustering approach used in hicap is based upon an algorithm described by narendra and goldberg to classify four dimensional landsat multispectral scanner data hicap incorporates two major modifications to the scheme by narendra and goldberg the first modification is that hicap is generalized to process up to 32 bit data with an arbitrary number of dimensions the second modification is that hicap uses more efficient algorithms to implement the clustering approach described by narendra and goldberg 1 this means that the hicap classification requires less computation although it is otherwise identical to the original classification the computational savings afforded by hicap increases with the number of dimensions in the data

relevance of soft modes for order parameter fluctuations in the two dimensional xy model we analyse the spin wave approximation for the two dimensional xy model directly in reciprocal space in this limit the model is diagonal and the normal modes are statistically independent despite this simplicity non trivial critical properties are observed and exploited we confirm that the observed asymmetry for the probability density function for order parameter fluctuations comes from the divergence of the mode amplitudes across the brillouin zone we show that the asymmetry is a many body effect despite the importance played by the zone centre the precise form of the function is dependent on the details of the microscopic generating function for the modes we discuss the relevance of this to more complex or non equilibrium systems where similar distributions are observed

nonlinear systems of the burgers type equations lie and q conditional symmetries ansatze and solutions abstract a class of nonlinear diffusion convection systems containing two burgers type equations is considered a complete description of lie symmetries is obtained for these systems new results of finding q conditional symmetries are also presented moreover a variety of lie and non lie ansatze and exact solutions of a diffusion convection system invariant under the generalized galilei algebra are constructed

difference schemes for solving the generalized nonlinear schrodinger equation this paper studies finite difference schemes for solving the generalized nonlinear schrodinger gnls equationiut uxx q u 2 u f x t u a new linearlized crank nicolson type scheme is presented by applying an extrapolation technique to the real coefficient of the nonlinear term in the gnls equation several schemes including crank nicolson type schemes hopscotch type schemes split step fourier scheme and pseudospectral scheme are adopted for solving three model problems of gnls equation which arise from many physical problems withq s s2 q s ln 1 s andq s 4s 1 s respectively the numerical results demonstrate that the linearized crank nicolson scheme is efficient and robust

the global attractor of a dissipative nonlinear evolution system we study the global smooth solution and the global attractor for a dissipative nonlinear evolution system given by strongly coupled parabolic equations

on convergence and stability of the explicit difference method for solution of nonlinear schrodinger equations the first boundary value problem for a nonlinear schrodinger equation is investigated the conditional convergence and stability on the initial data of the explicit three level difference scheme of dufort frankel type in c and w 2 1 norms are proved grid analogues of energy conservation laws and grid multiplicative inequalities are used

symmetry classes of variable coefficient nonlinear schrodinger equations a variable coefficient nonlinear schrodinger vcnls equation involving three arbitrary complex functions of space time in 1 1 dimensions is analysed from the point of view of its symmetries all equations of the type studied having non trivial lie point symmetry groups g are identified the symmetry group is shown to be at most five dimensional and only when the equation is equivalent to the nls equation itself or to a rather special complex ginzburg landau equation lie point transformations are used to obtain solutions of specific vcnls equations that should be of interest in nonlinear optics or other branches of physics

conditional symmetry of a porous medium equation abstract we obtain an exhaustive description of conditional symmetries admitted by a nonlinear porous medium equation in one spatial dimension it is proved that solving the determining equations for the conditional symmetries either yields classical lie symmetries or is equivalent to solving the porous medium equation itself the second possibility is shown to be typical for an arbitrary evolution type partial differential equation in one spatial variable we show that this very property is responsible for the well known phenomenon when using non classical symmetries yield exact solutions which prove to be invariant ones

real time and automatic two class clustering by analytical formulas several feature preserving two class clustering methods are investigated in this paper by preserving certain features of the input data some formulas useful in calculating the two class representatives and population percentages are derived the derived formulas are expressed in general forms suitable for any dimensionality higher than two the complexities of the investigated methods are all of order n if the data size is n and hence are much faster than any other clustering method which uses n x n dissimilarity matrix additionally all investigated methods use no initial guesses experimental results are included to make a comparison among the four investigated methods so that only two methods are recommended further comparisons with the k means method and hierarchical clustering methods also are included the proposed feature preserving approach was found to be fast automatic and suitable for any field requiring fast high dimensional two class clustering

lie symmetries of nonlinear multidimensional reaction diffusion systems ii we present a complete description of the classical lie symmetries of a coupled system of partial differential equations comprising a pair of semilinear reaction diffusion equations with constant diffusivities and arbitrary nonlinearities in the reaction terms in any number of spatial dimensions part i cherniha r m and king j r 2000 j phys a math gen 33 267 82 j phys a math gen 33 7839 41 addressed the case of unequal diffusivities here we complete the analysis by treating the case of equal diffusivities in which the symmetry structure is richer still such models arise in the description of numerous physical chemical and biological systems and we also indicate the possible application in such contexts of some of the specific cases arising from the group classification specifically a variety of lie s ansatze and exact solutions of the so called reaction diffusion systems of a type that arises in mathematical biology are constructed

nonlocal ansatze reduction and some exact solutions for the system of the van der waals equations abstract in this paper two types of nonlocal equivalence transformations of the system of convection diffusion equations are found using these transformations we obtained two images of the van der waals system lie symmetries of these images are used to construct nonlocal ansatze and reduce that system owing to this it has become possible to have built classes of exact solutions of the van der waals system lie symmetry of this system is used to construct nonlocal ansatze and reduce its both images

a group classification of the general second order coupled diffusion system we classify second order systems of coupled heat diffusion equations the underlying system contains several unknown functions the forms of which are specified via the method of group classification in particular the canonical forms of the low dimensional lie algebras and the lie algebras of higher dimension provide a means to specify the functional forms of these arbitrary functions

symmetry reductions and exact solutions of a class of nonlinear heat equations abstract classical and nonclassical symmetries of the nonlinear heat equation ut uxx f u are considered the method of differential grobner bases is used both to find the conditions on f u under which symmetries other than the trivial spatial and temporal translational symmetries exist and to solve the determining equations for the infinitesimals a catalogue of symmetry reductions is given including some new reductions for the linear heat equation and a catalogue of exact solutions of the nonlinear heat equation for cubic f u in terms of the roots of f u 0

group classification of systems of non linear reaction diffusion equations with general diffusion matrix i generalized ginzburg landau equations abstract a group classification of the generalized complex ginzburg landau equations is presented an approach to group classification of systems of reaction diffusion equations with general diffusion matrix is formulated

classification of coupled systems with two component nonlinear diffusion equations by the invariant subspace method the invariant subspace method is developed to perform classification of systems with two component nonlinear diffusion equations which was carried out with respect to the invariant subspaces defined by linear ordinary differential equations as a result the corresponding exact solutions generated by invariant subspaces to the resulting systems are obtained in most cases two components of these exact solutions belong to different scalar subspaces behaviour to several exact solutions of the systems is described

lie symmetries and form preserving transformations of reaction diffusion convection equations abstract new lie symmetry classification of the known class of reaction diffusion convection equations is presented the classification method is based on combining the standard group classification method and the form preserving transformation approach

temperature dependent fluctuations in the two dimensional xy model we present a detailed investigation of the probability density function pdf of order parameter fluctuations in the finite two dimensional xy 2dxy model in the low temperature critical phase of this model the pdf approaches a universal non gaussian limit distribution in the limit t 0 our analysis resolves the question of temperature dependence of the pdf in this regime for which conflicting results have been reported we show analytically that a weak temperature dependence results from the inclusion of multiple loop graphs in a previously derived graphical expansion this is confirmed by numerical simulations on two controlled approximations to the 2dxy model the harmonic and harmonic xy models the harmonic model has no kosterlitz thouless berezinskii ktb transition and the pdf becomes progressively less skewed with increasing temperature until it closely approximates a gaussian function above t approximate to 4 pi near to that temperature we find some evidence of a phase transition although our observations appear to exclude a thermodynamic singularity

realizations of real low dimensional lie algebras using a new powerful technique based on the notion of megaideal we construct a complete set of inequivalent realizations of real lie algebras of dimension no greater than four in vector fields on a space of an arbitrary finite number of variables our classification amends and essentially generalizes earlier works on the subject

an investigation of mountain method clustering for large data sets the mountain method of clustering was introduced by yager and filev and refined for practical use by chiu the approach is based on density estimation in feature space with the highest peak extracted as a cluster center and a new density estimation created for extraction of the next cluster center the process is repeated until a stopping condition is met the chiu version of this approach has been implemented in the matlab fuzzy logic tool in this paper we develop an alternate implementation that allows large data sets to be processed effectively methods to set the parameters required by the algorithm are also given magnetic resonance images of the human brain are used as a test domain comparisons with the matlab implementation show that our new approach is considerably more practical in terms of the time required to cluster as well as better at producing partitions of the data that correspond to those expected comparisons are also made to the fuzzy c means clustering algorithm which show that our improved mountain method is a viable competitor producing excellent partitions of large data sets

group classification of systems of non linear reaction diffusion equations with general diffusion matrix ii generalized turing systems abstract group classification of systems of two coupled non linear reaction diffusion equation with a diagonal diffusion matrix is carried out symmetries of diffusion systems with singular diffusion matrix and additional first order derivative terms are described

scanning the critical fluctuations application to the phenomenology of the two dimensional xy model we show how applying field conjugated to the order parameter may act as a very precise probe to explore the probability distribution function of the order parameter using this magnetic field scanning on large scale numerical simulations of the critical two dimensional xy model we are able to discard the conjectured double exponential form of the large magnetization asymptote

preliminary group classification of the nonlinear differential difference equations abstract preliminary group classification of the nonlinear differential difference equations of the form u n f n t u n 1 u n u n 1 is considered by using the classical infinitesimal lie method and the theory of classification of abstract low dimensional lie algebras restrict to lie point symmetries and assume that the lie algebra of the symmetry group is realized by a particular vector field it is proved that there is only one equation admitting three dimensional simple lie algebras what is more all the inequivalent equations admitting semi simple lie algebras are nothing but the one also there exist inequivalent equations admitting low dimensional solvable lie algebras and semi direct sums of semi simple and solvable lie algebras

systems of reaction convection diffusion equations invariant under galilean algebras abstract systems which are invariant under galilean algebras with and without mass operator and their main extensions by operators of scale and projective transformations are selected from a class of systems of reaction convection diffusion equations for two dimensional vector field with one space variable

non linear reaction diffusion systems with variable diffusivities lie symmetries ansatze and exact solutions abstract this work first considers the classical lie symmetry analysis of a class of systems of two quasilinear reaction diffusion equations having variable diffusivities subsequently non lie reductions to systems of first order ordinary differential equations are obtained for a subclass of these systems in particular families of exact solutions of a diffusive lotka volterra type system are constructed

magnetic fluctuations in the classical xy model the origin of an exponential tail in a complex system we study the probability density function for the fluctuations of the magnetic order parameter in the low temperature phase of the mathrm xy model of finite size in two dimensions this system is critical over the whole of the low temperature phase it is shown analytically and without recourse to the scaling hypothesis that in this case the distribution is non gaussian and of universal form independent of both system size and critical exponent ensuremath eta an exact expression for the generating function of the distribution is obtained which is transformed and compared with numerical data from high resolution molecular dynamics and monte carlo simulations the asymptotes of the distribution are calculated and found to be of exponential and double exponential form the calculated distribution is fitted to three standard functions a generalization of gumbel s first asymptote distribution from the theory of extremal statistics a generalized log normal distribution and a ensuremath chi 2 distribution the calculation is extended to general dimension and an exponential tail is found in all dimensions less than 4 despite the fact that critical fluctuations are limited to d 2 these results are discussed in the light of similar behavior observed in models of interface growth and for dissipative systems driven into a nonequilibrium steady state

estimation and choice of neighbors in spatial interaction models of images some aspects of statistical inference for a class of spatial interaction models for finite images are presented primarily the simultaneous autoregressive sar models and conditional markov cm models each of these models is characterized by a set of neighbors a set of coefficients and a noise sequence of specified characteristics we are concerned with two problems the estimation of the unknown parameters in both sar and cm models and the choice of an appropriate model from a class of such competing models assuming gaussian distributed variables we discuss maximum likelihood ml estimation methods in general the ml scheme leads to nonlinear optimization problems to avoid excessive computation an iterative scheme is given for sar models which gives approximate ml estimates in the gaussian case and reasonably good estimates in some non gaussian situations as well likewise for cm models an easily computable consistent estimate is given the asymptotic mean squared error mse of this estimate for a four neighbor cm model is shown tn be substantially less than the mse of the popular coding estimate asymptotically consistent decision rules are given for choosing an appropriate sar or cm model the usefulness of the estimation scheme and the decision rule for the choice of neighbors is illustrated by using synthetic patterns synthetic patterns obeying known sar and cm models are generated and the models corresponding to true and several competing neighbor sets are fitted the estimation scheme yields estimates close to the parameters of the true models and the decision rule for the choice of neighbors picks up the true model from the class of competing models

systems of reaction diffusion equations and their symmetry properties a constructive algorithm is proposed for the investigation of symmetries of partial differential equations the algorithm is used to present classical lie symmetries of systems of two nonlinear reaction diffusion equations

image segmentation by a parallel non parametric histogram based clustering algorithm abstract this paper describes a totally automatic non parametric clustering algorithm and its application to unsupervised image segmentation the clusters are found by mode analysis of the multidimensional histogram of the considered vectors through a non iterative peak climbing approach systematic methods for automatic selection of an appropriate histogram cell size are developed and discussed the algorithm is easily parallelizable and is simulated on a sequent parallel computer image segmentation is performed by clustering features extracted from small local areas of the image segmentation of textured color and gray level images are considered eight dimensional random field model based features three dimensional rgb components and one dimensional gray levels are utilized for these three types of images respectively for texture segmentation an image plane cluster validity procedure based on region growing of the mapped back clusters in the feature space is developed most of the phases are also parallelized resulting in almost linear speed ups quite satisfactory results are obtained in all cases

unsupervised image segmentation using an unlabeled region process abstract the segmentation of a gray scale image of regions of uniform or slowly varying intensity is discussed a gibbsian representation is given for a partition of a lattice with no labels the homogeneity of each segment is measured by the sample variance of observations in a region merging algorithm the posterior probability of the segmentation is gradually increased it is shown how to simulate partitions with the gibbs sampler and how to combine information in simulated segmentations when the segments cannot be grouped into genuine classes the segmentation methods are preferable to classification by iterated conditional modes icm or by the maximizer of posterior marginals mpm

a new class of solutions to a generalized nonlinear schrodinger equation in this paper we compute new classes of symmetry reduction and associated exact solutions of a generalized nonlinear schrodinger equation gnls the generalized terms modelling dispersion and scattering several authors have obtained symmetry reductions of one two and three dimensional nonlinear schrodinger equations in all cases to date reductions have been based on a real new independent variable in this paper we compute reductions in which the new independent variable is complex we seek new reductions from a two dimensional gnls to a pde in two independent variables and also reductions to odes five new classes of reduction are found