statistics of persistent events an exactly soluble model it was recently realized that the persistence exponent appearing in the dynamics of nonequilibrium systems is a special member of a continuously varying family of exponents describing generalized persistence properties we propose and solve a simple stochastic spin model where time intervals between spin flips are independent and distributed according to a l evy law both the limit distribution of the mean magnetization and the generalized persistence exponents are obtained exactly we discuss the relevance of this model for phase ordering spin glasses and random walks

self diffusion and visited surface in the droplet condensation problem breath figures abstract we study experimentally and theoretically new aspects of condensation growth and coalescence of droplets on a substrate we address in particular the dynamics of a marked droplet which undergoes coalescences with neighbouring droplets we find that the number of coalescences of the droplet grows as log t t is time and that the traveled distance increases as r t the average radius of the droplets at time t the fraction of the surface which was never covered by any droplet an important quantity for applications such as drug spreading or surface decontamination decays as t showing that completion occurs only slowly heuristic arguments accurate numerical simulations on simplified models which neglect polydispersity and an exact solution reported elsewhere a bray b derrida and c godreche europhys lett 27 1994 175 strongly support these findings and show that this power law decay is a generic feature common to many different situations finally the contour of the ensemble of dry sites appears fractal with dimension d 1 22 an experimental result not reproduced by the simplified models

large deviations and nontrivial exponents in coarsening systems we investigate the statistics of the mean magnetization of its large deviations and persistent large deviations in simple coarsening systems in particular we consider more specifically the case of the diffusion equation of the ising chain at zero temperature and of the two dimensional voter model for the diffusion equation at large times the mean magnetization has a limit law which is studied analytically using the independent interval approximation the probability of persistent large deviations defined as the probability that the mean magnetization was for all previous times greater than some level x decays algebraically at large times with an exponent continuously varying with x when x 1 is the usual persistence exponent similar behaviour is found for the glauber ising chain at zero temperature for the two dimensional voter model large deviations of the mean magnetization are algebraic while the probability of persistent large deviations seem to behave as the usual persistence probability

diffusive persistence and the sign time distribution we present a new method for extracting the persistence exponent theta for the diffusion equation based on the distribution p of sign times with the aid of a numerically verified ansatz for p we derive an exact formula for theta in arbitrary spatial dimension d our results are in excellent agreement with previous numerical studies furthermore our results indicate a qualitative change in p above d 36 signalling the existence of a sharp change in the ergodic properties of the diffusion field

persistence exponents for fluctuating interfaces numerical and analytic results for the exponent ensuremath theta describing the decay of the first return probability of an interface to its initial height are obtained for a large class of linear langevin equations the models are parametrized by the dynamic roughness exponent ensuremath beta with 0l ensuremath beta l1 for ensuremath beta frac 1 2 the time evolution is markovian using simulations of solid on solid models of the discretized continuum equations as well as of the associated zero dimensional stationary gaussian process we address two problems the return of an initially flat interface and the return to an initial state with fully developed steady state roughness the two problems are shown to be governed by different exponents for the steady state case we point out the equivalence to fractional brownian motion which has a return exponent ensuremath theta s 1 ensuremath ensuremath beta the exponent ensuremath theta 0 for the flat initial condition appears to be nontrivial we prove that ensuremath theta 0 ensuremath rightarrow ensuremath infty for ensuremath beta ensuremath rightarrow 0 ensuremath theta 0 g ensuremath theta s for ensuremath beta l frac 1 2 and ensuremath theta 0 l ensuremath theta s for ensuremath beta g frac 1 2 and calculate ensuremath theta 0 s perturbatively to first order in an expansion around the markovian case ensuremath beta frac 1 2 using the exact result ensuremath theta s 1 ensuremath ensuremath beta accurate upper and lower bounds on ensuremath theta 0 can be derived which show in particular that ensuremath theta 0 g 1 ensuremath ensuremath beta 2 ensuremath beta for small ensuremath beta

persistence in nonequilibrium surface growth persistence probabilities of the interface height in 1 1 and 2 1 dimensional atomistic solid on solid stochastic models of surface growth are studied using kinetic monte carlo simulations with emphasis on models that belong to the molecular beam epitaxy mbe universality class both the initial transient and the long time steady state regimes are investigated we show that for growth models in the mbe universality class the nonlinearity of the underlying dynamical equation is clearly reflected in the difference between the measured values of the positive and negative persistence exponents in both transient and steady state regimes for the mbe universality class the positive and negative persistence exponents in the steady state are found to be 0 66 0 02 and 0 78 0 02 respectively in 1 1 dimensions and 0 76 0 02 and 0 85 0 02 respectively in 2 1 dimensions the noise reduction technique is applied on some of the 1 1 dimensional models in order to obtain accurate values of the persistence exponents we show analytically that a relation between the steady state persistence exponent and the dynamic growth exponent found earlier to be valid for linear models should be satisfied by the smaller of the two steady state persistence exponents in the nonlinear models our numerical results for the persistence exponents are consistent with this prediction we also find that the steady state persistence exponents can be obtained from simulations over times that are much shorter than that required for the interface to reach the steady state the dependence of the persistence probability on the system size and the sampling time is shown to be described by a simple scaling form

semiflexible polymer in the half plane and statistics of the integral of a brownian curve a continuum model of a polymer with non zero bending energy fluctuating without overhangs in the half plane is considered the exact partition function is obtained from the marshall watson solution of the klein kramers equation for brownian motion in the half space the partition function contains information on probabilities associated with the integral of a brownian curve and reproduces sinai s t 5 4 result for the asymptotic first passage time density the t 5 2 dependence of a different passage probability implies a first order polymer adsorption transition for short range pinning potentials

a validity measure for fuzzy clustering the authors present a fuzzy validity criterion based on a validity function which identifies compact and separate fuzzy c partitions without assumptions as to the number of substructures inherent in the data this function depends on the data set geometric distance measure distance between cluster centroids and more importantly on the fuzzy partition generated by any fuzzy algorithm used the function is mathematically justified via its relationship to a well defined hard clustering validity function the separation index for which the condition of uniqueness has already been established the performance of this validity function compares favorably to that of several others the application of this validity function to color image segmentation in a computer color vision system for recognition of ic wafer defects which are otherwise impossible to detect using gray scale image processing is discussed

silhouettes a graphical aid to the interpretation and validation of cluster analysis a new graphical display is proposed for partitioning techniques each cluster is represented by a so called silhouette which is based on the comparison of its tightness and separation this silhouette shows which objects lie well within their cluster and which ones are merely somewhere in between clusters the entire clustering is displayed by combining the silhouettes into a single plot allowing an appreciation of the relative quality of the clusters and an overview of the data configuration the average silhouette width provides an evaluation of clustering validity and might be used to select an appropriate number of clusters

experimental measurement of the persistence exponent of the planar ising model using a twisted nematic liquid crystal system exhibiting planar ising model dynamics we have measured the scaling exponent ensuremath theta which characterizes the time evolution p t ensuremath sim t ensuremath ensuremath theta of the probability p t that the local order parameter has not switched its state by the time t for 0 4 sec 200 sec following the phase quench the system exhibits scaling behavior and measured over this interval ensuremath theta 0 19 ifmmode pm else textpm fi 0 03 in good agreement with theoretical analysis and numerical simulations

sign time distributions for interface growth we apply the recently introduced distribution of sign times dst to nonequilibrium interface growth dynamics we are able to treat within a unified picture the persistence properties of a large class of relaxational and noisy linear growth processes and prove the existence of a nontrivial scaling relation a critical dimension is found relating to the persistence properties of these systems we also illustrate by means of numerical simulations the different types of dst to be expected in both linear and nonlinear growth mechanisms

generalized survival in step fluctuations the properties of the generalized survival probability that is the probability of not crossing an arbitrary location r during relaxation have been investigated experimentally via scanning tunneling microscope observations and numerically the results confirm that the generalized survival probability decays exponentially with a time constant tau s r the distance dependence of the time constant is shown to be tau s r tau s0 exp r w t where w2 t is the material dependent mean squared width of the step fluctuations the result reveals the dependence on the physical parameters of the system inherent in the prior prediction of the time constant scaling with r l alpha with l the system size and alpha the roughness exponent the survival behavior is also analyzed using a contrasting concept the generalized inside survival s in t r which involves fluctuations to an arbitrary location r further from the average numerical simulations of the inside survival probability also show an exponential time dependence and the extracted time constant empirically shows r w lambda behavior with lambda varying over 0 6 to 0 8 as the sampling conditions are changed the experimental data show similar behavior and can be well fit with lambda 1 0 for t 300 k and 0 5 lambda 1 for t 460 k over this temperature range the ratio of the fixed sampling time to the underlying physical time constant and thus the true correlation time increases by a factor of approximately 10 3 preliminary analysis indicates that the scaling effect due to the true correlation time is relevant in the parameter space of the experimental observations

third order iterative methods for operators with bounded second derivative abstract we analyse the classical third order methods chebyshev halley super halley to solve a nonlnnear equation f x 0 where f is an operator defined between two banach spaces until now the convergence of these methods is established assuming that the second derivative f satisfies a lipschitz condition in this paper we prove by using recurrence relations the convergence of these and other third order methods just assuming f is bounded we show examples where our conditions are fulfilled and the classical ones fail

genetic algorithm based clustering technique abstract a genetic algorithm based clustering technique called ga clustering is proposed in this article the searching capability of genetic algorithms is exploited in order to search for appropriate cluster centres in the feature space such that a similarity metric of the resulting clusters is optimized the chromosomes which are represented as strings of real numbers encode the centres of a fixed number of clusters the superiority of the ga clustering algorithm over the commonly used k means algorithm is extensively demonstrated for four artificial and three real life data sets

on the algorithmic implementation of multiclass kernel based vector machines in this paper we describe the algorithmic implementation of multiclass kernel based vector machines our starting point is a generalized notion of the margin to multiclass problems using this notion we cast multiclass categorization problems as a constrained optimization problem with a quadratic objective function unlike most of previous approaches which typically decompose a multiclass problem into multiple independent binary classification tasks our notion of margin yields a direct method for training multiclass predictors by using the dual of the optimization problem we are able to incorporate kernels with a compact set of constraints and decompose the dual problem into multiple optimization problems of reduced size we describe an efficient fixed point algorithm for solving the reduced optimization problems and prove its convergence we then discuss technical details that yield significant running time improvements for large datasets finally we describe various experiments with our approach comparing it to previously studied kernel based methods our experiments indicate that for multiclass problems we attain state of the art accuracy

the surface statistics of a granular aggregate the problem of the surface fluctuations in a settled granular material is posed a simple model is given which describes the process by which a particle settles and comes to rest on the existing surface of the packing and from this a set of langevin equations for the fourier modes of the surface are derived these equations imply that the fourier amplitudes behave like the velocities of a set of independent brownian particles we show that this results in logarithmically divergent surface fluctuations if the flux of particles onto the surface is random the divergence being removed by a more accurate description of the settling material for example by having the granules fall through a sieve

a new convergence proof of fuzzy c means in this letter we give a new more direct derivation of the convergence properties of the fuzzy c means fcm algorithm using the equivalence between the original and reduced fcm criterion from the point of view of the reduced criterion the fcm algorithm is simply a steepest descent algorithm with variable steplength we prove that steplength adjustment follows from the majorization principle for steplength by applying the majorization principle we give a straightforward proof of global convergence further convergence properties follow immediately using known results of optimization theory

an efficient technique for superfamily classification of amino acid sequences feature extraction fuzzy clustering and prototype selection in this article we propose an efficient technique for classifying amino acid sequences into different superfamilies the proposed method first extracts 20 features from a set of training sequences the extracted features are such that they take into consideration the probabilities of occurrences of the amino acids in the different positions of the sequences thereafter a genetic fuzzy clustering approach is used to automatically evolve a set of prototypes representing each class the characteristic of this clustering method is that it does not require the a priori information about the number of clusters and is also able to come out of locally optimal configurations finally the nearest neighbor rule is used to classify an unknown sequence into a particular superfamily class based on its proximity to the prototypes evolved using the genetic fuzzy clustering technique this results in a significant improvement in the time required for classifying unknown sequences results for three superfamilies namely globin trypsin and ras demonstrate the effectiveness of the proposed technique with respect to the case where all the training sequences are considered for classification using the same set of features comparison with the well known technique blast also shows that the proposed method provides a significant improvement in terms of the time required for classification while providing comparable classification performance

genetic clustering for automatic evolution of clusters and application to image classification abstract in this article the searching capability of genetic algorithms has been exploited for automatically evolving the number of clusters as well as proper clustering of any data set a new string representation comprising both real numbers and the do not care symbol is used in order to encode a variable number of clusters the davies bouldin index is used as a measure of the validity of the clusters effectiveness of the genetic clustering scheme is demonstrated for both artificial and real life data sets utility of the genetic clustering technique is also demonstrated for a satellite image of a part of the city calcutta the proposed technique is able to distinguish some characteristic landcover types in the image

spatial persistence and survival probabilities for fluctuating interfaces we report the results of numerical investigations of the steady state ss and finite initial conditions fic spatial persistence and survival probabilities for 1 1 dimensional interfaces with dynamics governed by the nonlinear kardar parisi zhang equation and the linear edwards wilkinson ew equation with both white uncorrelated and colored spatially correlated noise we study the effects of a finite sampling distance on the measured spatial persistence probability and show that both ss and fic persistence probabilities exhibit simple scaling behavior as a function of the system size and the sampling distance analytical expressions for the exponents associated with the power law decay of ss and fic spatial persistence probabilities of the ew equation with power law correlated noise are established and numerically verified

mapping spatial persistent large deviations of nonequilibrium surface growth processes onto the temporal persistent large deviations of stochastic random walk processes spatial persistent large deviations probability of surface growth processes governed by the edwards wilkinson dynamics px x s with 1 or s or 1 is mapped isomorphically onto the temporal persistent large deviations probability pt t s associated with the stochastic markovian random walk problem we show using numerical simulations that the infinite family of spatial persistent large deviations exponents thetax s characterizing the power law decay of px x s agrees as predicted on theoretical grounds by phys rev lett 86 3700 2001 with the numerical measurements of thetat s the continuous family of exponents characterizing the long time power law behavior of pt t s we also discuss the simulations of the spatial persistence probability corresponding to a discrete model in the mullins herring universality class where our discrete simulations do not agree well with the theoretical predictions perhaps because of the severe finite size corrections which are known to strongly inhibit the manifestation of the asymptotic continuum behavior in discrete models involving large values of the dynamical exponent and the associated extremely slow convergence to the asymptotic regime

towards improving fuzzy clustering using support vector machine application to gene expression data recent advancement in microarray technology permits monitoring of the expression levels of a large set of genes across a number of time points simultaneously for extracting knowledge from such huge volume of microarray gene expression data computational analysis is required clustering is one of the important data mining tools for analyzing such microarray data to group similar genes into clusters researchers have proposed a number of clustering algorithms in this purpose in this article an attempt has been made in order to improve the performance of fuzzy clustering by combining it with support vector machine svm classifier a recently proposed real coded variable string length genetic algorithm based clustering technique and an iterated version of fuzzy c means clustering have been utilized in this purpose the performance of the proposed clustering scheme has been compared with that of some well known existing clustering algorithms and their svm boosted versions for one simulated and six real life gene expression data sets statistical significance test based on analysis of variance anova followed by posteriori tukey kramer multiple comparison test has been conducted to establish the statistical significance of the superior performance of the proposed clustering scheme moreover biological significance of the clustering solutions have been established