cox s regression model for counting processes a large sample study the cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life time distribution of an individual in this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process this permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring patterns and time dependent covariates furthermore this formulation gives rise to proofs with very simple structure using martingale techniques for the asymptotic properties of the estimators from such a model finally an example of a statistical analysis is included

fully automatic clustering system in this paper the fully automatic clustering system facs is presented it is a technique for clustering and vector quantization whose objective is the automatic calculation of the codebook of the right dimension the desired error or target being fixed at each iteration facs tries to improve the setting of the existing codewords and if necessary some elements are removed from or added to the codebook in order to save on the number of computations per iteration greedy techniques are adopted it has been demonstrated from a heuristic point of view that the number of the codewords determined by facs is very low and that the algorithm quickly converges toward the final solution

optimal adaptive k means algorithm with dynamic adjustment of learning rate adaptive k means clustering algorithms have been used in several artificial neural network architectures such as radial basis function networks or feature map classifiers for a competitive partitioning of the input domain this paper presents an enhancement of the traditional k means algorithm it approximates an optimal clustering solution with an efficient adaptive learning rate which renders it usable even in situations where the statistics of the problem task varies slowly with time this modification is based on the optimality criterion for the k means partition stating that all the regions in an optimal k means partition have the same variations if the number of regions in the partition is large and the underlying distribution for generating input patterns is smooth the goal of equalizing these variations is introduced in the competitive function that assigns each new pattern vector to the appropriate region to evaluate the optimal k means algorithm the authors first compare it to other k means variants on several simple tutorial examples then the authors evaluate it on a practical application vector quantization of image data

an index theory for asymptotic motions under singular potentials abstract we develop an index theory for parabolic and collision solutions to the classical n body problem and we prove sufficient conditions for the finiteness of the spectral index valid in a large class of trajectories ending with a total collapse or expanding with vanishing limiting velocities both problems suffer from a lack of compactness and can be brought in a similar form of a lagrangian system on the half time line by a regularising change of coordinates which preserve the lagrangian structure we then introduce a maslov type index which is suitable to capture the asymptotic nature of these trajectories as half clinic orbits by taking into account the underlying hamiltonian structure we define the appropriate notion of geometric index for this class of solutions and we develop the relative index theory

k means type algorithms a generalized convergence theorem and characterization of local optimality the k means algorithm is a commonly used technique in cluster analysis in this paper several questions about the algorithm are addressed the clustering problem is first cast as a nonconvex mathematical program then a rigorous proof of the finite convergence of the k means type algorithm is given for any metric it is shown that under certain conditions the algorithm may fail to converge to a local minimum and that it converges under differentiability conditions to a kuhn tucker point finally a method for obtaining a local minimum solution is given

on the c8 3 regularisation of simultaneous binary collisions in the collinear 4 body problem abstract a conjecture on the nature of the simultaneous binary collision is explored in the collinear 4 body problem it is known that any attempt to remove the singularity via block regularisation will result in a regularised flow that is no more than c 8 3 differentiable with respect to initial conditions through a blow up of the singularity this loss of differentiability is investigated and a new proof of the c 8 3 regularity is provided in the process it is revealed that the collision manifold consists of two manifolds of normally hyperbolic saddle singularities which are connected by a manifold of heteroclinics by utilising recent work on transitions near such objects and their normal forms an asymptotic series of the transition past the singularity is explicitly computed it becomes remarkably apparent that the finite differentiability at 8 3 is due to the inability to construct a set of integrals local to the simultaneous binary collision the finite differentiability is shown to be independent of the value of the masses

analysis of multi type recurrent events in longitudinal studies application to a skin cancer prevention trial we consider the statistical modeling and analysis of replicated multi type point process data with covariates such data arise when heterogeneous subjects experience repeated events or failures which may be of several distinct types the underlying processes are modeled as nonhomogeneous mixed poisson processes with random subject and fixed covariate effects the method of maximum likelihood is used to obtain estimates and standard errors of the failure rate parameters and regression coefficients score tests and likelihood ratio statistics are used for covariate selection a graphical test of goodness of fit of the selected model is based on generalized residuals measures for determining the influence of an individual observation on the estimated regression coefficients and on the score test statistic are developed an application is described to a large ongoing randomized controlled clinical trial for the efficacy of nutritional supplements of selenium for the prevention of two types of skin cancer

semiparametric estimation of random effects using the cox model based on the em algorithm consider a survival experiment where individuals within a certain subset of the population share a common unobservable random frailty such a frailty could be an unobservable genetic or early environmental effect if individuals were in sibling groups or an environmental effect if individuals were grouped by households suppose that if the frailty omega is known the cox proportional hazards model for the observable covariates is valid with the consequence of the random effect being a multiplicative factor on the hazard rate assuming tht the random frailties follow a gamma distribution estimates of the fixed and random effects are obtained by using an em algorithm based on a profile likelihood construction the method developed is applied to the framingham heart study to examine the risks of smoking and cholesterol levels adjusting for potential random effects

homoclinic orbits and oscillation for the planar three body problem sitnikov proved the existence of oscillation and capture for a special motion of the restricted three body problem m 0 141 alekseev made a systematic study of this situation 11 he also proved the same result for all nonzero masses see section 5 below for a discussion of this case a good exposition of this example following lectures of conley is contained in 9 using the stable manifold result for a degenerately hyperbolic closed orbit of mcgehee 81 easton and mcgehee proposed a planar three body example with negative energy which could possibly exhibit similar oscillation and capture 3 while sitnikov s example has two degrees of freedom this planar example after all the integrals and symmetries are removed has three degrees of freedom they studied a model example which completely decouples when the third body is near infinity and proved oscillation and capture exist for this model example their work left the following three steps undone 1 show the parabolic orbits form a submanifold for the real equations 2 show the a parabolic orbits and w parabolic orbits are transverse in a strong sense see the definition of a hyperbolic homoclinic orbit defined below and 3 show that symbolic dynamics can be used to show oscillation and capture exist using only the fact that the binary asymptotically decouples and not that it completely decouples when the third body is near infinity for negative energy h as the third particle goes to infinity parabolically the asymptotic motion of q r2 rl is that of a two body problem with energy h after regularization the set of all two body motions with energy h 0 is the hopf flow on the three sphere s3 let ivs s3 resp wu s be the set of w parabolic orbits resp w parabolic orbits easton has now shown that ws s3 and wl s3 are lipschitz manifolds 2 this paper proves they are real analytic manifolds and cm at infinity at s

least squares quantization in pcm it has long been realized that in pulse code modulation pcm with a given ensemble of signals to handle the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall it has been shown by panter and dite that in the limit as the number of quanta becomes infinite the asymptotic fractional density of quanta per unit voltage should vary as the one third power of the probability density per unit voltage of signal amplitudes in this paper the corresponding result for any finite number of quanta is derived that is necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy the optimization criterion used is that the average quantization noise power be a minimum it is shown that the result obtained here goes over into the panter and dite result as the number of quanta become large the optimum quautization schemes for 2 b quanta b 1 2 cdots 7 are given numerically for gaussian and for laplacian distribution of signal amplitudes

a successive approximation vector quantizer for wavelet transform image coding a coding method for wavelet coefficients of images using vector quantization called successive approximation vector quantization sa w vq is proposed in this method each vector is coded by a series of vectors of decreasing magnitudes until a certain distortion level is reached the successive approximation using vectors is analyzed and conditions for convergence are derived it is shown that lattice codebooks are an efficient tool for meeting these conditions without the need for very large codebooks regular lattices offer the extra advantage of fast encoding algorithms in sa w vq distortion equalization of the wavelet coefficients can be achieved together with high compression ratio and precise bit rate control the performance of sa w vq for still image coding is compared against some of the most successful image coding systems reported in the literature the comparison shows that sa w vq performs remarkably well at several bit rates and in various test images

inferences on the association parameter in copula models for bivariate survival data we investigate two stage parametric and two stage semi parametric estimation procedures for the association parameter in copula models for bivariate survival data where censoring in either or both components is allowed we derive asymptotic properties of the estimators and compare their performance by simulations both parametric and semi parametric estimators of the association parameter are efficient at independence and the parameter estimates in the margins have high efficiency and are robust to misspecification of dependency structures in addition we propose a consistent variance estimator for the semi parametric estimator of the association parameter we apply the proposed methods to an aids data set for illustration

covariate adjustment of event histories estimated from markov chains the additive approach summary markov chain models are frequently used for studying event histories that include transitions between several states an empirical transition matrix for nonhomogeneous markov chains has previously been developed including a detailed statistical theory based on counting processes and martingales in this article we show how to estimate transition probabilities dependent on covariates this technique may e g be used for making estimates of individual prognosis in epidemiological or clinical studies the covariates are included through nonparametric additive models on the transition intensities of the markov chain the additive model allows for estimation of covariate dependent transition intensities and again a detailed theory exists based on counting processes the martingale setting now allows for a very natural combination of the empirical transition matrix and the additive model resulting in estimates that can be expressed as stochastic integrals and hence their properties are easily evaluated two medical examples will be given in the first example we study how the lung cancer mortality of uranium miners depends on smoking and radon exposure in the second example we study how the probability of being in response depends on patient group and prophylactic treatment for leukemia patients who have had a bone marrow transplantation a program in r and s plus that can carry out the analyses described here has been developed and is freely available on the internet

a copula based mixed poisson model for bivariate recurrent events under event dependent censoring in many chronic disease processes subjects are at risk of two or more types of events we describe a bivariate mixed poisson model in which a copula function is used to model the association between two gamma distributed random effects the resulting model is a bivariate negative binomial process in which each type of event arises from a negative binomial process methods for parameter estimation are described for parametric and semiparametric models based on an em algorithm we also consider the issue of event dependent censoring based on one type of event which arises when one event is sufficiently serious that its occurence may influence the decision of whether to withdraw a patient from a study the asymptotic biases of estimators of rate and mean functions from naive marginal analyses are discussed as well as associated treatment effects because the joint model is fit based on a likelihood consistent estimates are obtained simulation studies are carried out to evaluate the empirical performance of the proposed estimators with independent and event dependent censoring and applications to a trial of breast cancer patients with skeletal metastases and a study of patients with chronic obstructive pulmonary disease illustrate the approach

fuzzy algorithms for learning vector quantization this paper presents the development of fuzzy algorithms for learning vector quantization falvq these algorithms are derived by minimizing the weighted sum of the squared euclidean distances between an input vector which represents a feature vector and the weight vectors of a competitive learning vector quantization lvq network which represent the prototypes this formulation leads to competitive algorithms which allow each input vector to attract all prototypes the strength of attraction between each input and the prototypes is determined by a set of membership functions which can be selected on the basis of specific criteria a gradient descent based learning rule is derived for a general class of admissible membership functions which satisfy certain properties the falvq 1 falvq 2 and falvq 3 families of algorithms are developed by selecting admissible membership functions with different properties the proposed algorithms are tested and evaluated using the iris data set the efficiency of the proposed algorithms is also illustrated by their use in codebook design required for image compression based on vector quantization

empirically defined regions of influence for clustering analyses we present a simple but effective clustering algorithm for non hierarchical k dimensional data which is also useful for pattern recognition applications the method uses a visually empirical region of influence veri that we have discovered our approach enables us to use human cluster judgments as the cluster criteria and to extend these criteria in a natural way to k dimensional data the veri algorithm requires no user input e g the number of clusters in the final result or user adjustments beyond providing the data itself the algorithm computes clusterings based on the local k dimensional neighbors of each point and thus handles arbitrary numbers of clusters and arbitrary global cluster shapes we demonstrate that the method works well for a variety of 2d cluster configurations which popular methods cannot treat despite requiring the number of clusters as input and illustrate that the performance is maintained for k dimensional problems the application of the method to pattern recognition problems is outlined and efficient implementations of the veri algorithm are presented

gaussian mixture density modeling decomposition and applications we present a new approach to the modeling and decomposition of gaussian mixtures by using robust statistical methods the mixture distribution is viewed as a contaminated gaussian density using this model and the model fitting mf estimator we propose a recursive algorithm called the gaussian mixture density decomposition gmdd algorithm for successively identifying each gaussian component in the mixture the proposed decomposition scheme has advantages that are desirable but lacking in most existing techniques in the gmdd algorithm the number of components does not need to be specified a priori the proportion of noisy data in the mixture can be large the parameter estimation of each component is virtually initial independent and the variability in the shape and size of the component densities in the mixture is taken into account gaussian mixture density modeling and decomposition has been widely applied in a variety of disciplines that require signal or waveform characterization for classification and recognition we apply the proposed gmdd algorithm to the identification and extraction of clusters and the estimation of unknown probability densities probability density estimation by identifying a decomposition using the gmdd algorithm that is a superposition of normal distributions is successfully applied to automated cell classification computer experiments using both real data and simulated data demonstrate the validity and power of the gmdd algorithm for various models and different noise assumptions

a highly robust estimator through partially likelihood function modeling and its application in computer vision the authors present a highly robust estimator known as the model fitting mf estimator for general regression they explain that high robustness becomes possible through partially but completely modeling the unknown log likelihood function the partial modeling takes place by taking the bayesian statistical decision rule and a number of important heuristics into consideration while maximizing the log likelihood function applications include the automatic selection of multiple thresholds single rigid motion estimation or multiple rigid motion segmentation and estimation from two perspective views it is believed that the proposed mf estimator will aid in solving many robust estimation problems that demand an estimator that is either highly robust or capable of handling contaminated gaussian mixture models

vector quantization of image subbands a survey subband and wavelet decompositions are powerful tools in image coding because of their decorrelating effects on image pixels the concentration of energy in a few coefficients their multirate multiresolution framework and their frequency splitting which allows for efficient coding matched to the statistics of each frequency band and to the characteristics of the human visual system vector quantization vq provides a means of converting the decomposed signal into bits in a manner that takes advantage of remaining inter and intraband correlation as well as of the more flexible partitions of higher dimensional vector spaces since 1988 a growing body of research has examined the use of vq for subband wavelet transform coefficients we present a survey of these methods

unsupervised texture segmentation using gabor filters abstract this paper presents a texture segmentation algorithm inspired by the multi channel filtering theory for visual information processing in the early stages of human visual system the channels are characterized by a bank of gabor filters that nearly uniformly covers the spatial frequency domain and a systematic filter selection scheme is proposed which is based on reconstruction of the input image from the filtered images texture features are obtained by subjecting each selected filtered image to a nonlinear transformation and computing a measure of energy in a window around each pixel a square error clustering algorithm is then used to integrate the feature images and produce a segmentation a simple procedure to incorporate spatial information in the clustering process is proposed a relative index is used to estimate the true number of texture categories

variable rate vector quantization for speech image and video compression the performance of a vector quantizer can be improved by using a variable rate code three variable rate vector quantization systems are applied to speech image and video sources and compared to standard vector quantization and noiseless variable rate coding approaches the systems range from a simple and flexible tree based vector quantizer to a high performance but complex jointly optimized vector quantizer and noiseless code the systems provide significant performance improvements for subband speech coding predictive image coding and motion compensated video but provide only marginal improvements for vector quantization of linear predictive coefficients in speech and direct vector quantization of images criteria are suggested for determining when variable rate vector quantization may provide significant performance improvement over standard approaches

the robust inference for the cox proportional hazards model abstract we derive the asymptotic distribution of the maximum partial likelihood estimator for the vector of regression coefficients under a possibly misspecified cox proportional hazards model as in the parametric setting this estimator converges to a well defined constant vector in addition the random vector n 1 2 is asymptotically normal with mean 0 and with a covariance matrix that can be consistently estimated the newly proposed robust covariance matrix estimator is similar to the so called sandwich variance estimators that have been extensively studied for parametric cases for many misspecified cox models the asymptotic limit or part of it can be interpreted meaningfully in those circumstances valid statistical inferences about the corresponding covariate effects can be drawn based on the aforementioned asymptotic theory of and the related results for the score statistics extensive studies demonstrate that the proposed robust tests and interval estimation procedures

semiparametric modelling and estimation of covariate adjusted dependence between bivariate recurrent events a time dependent measure termed the rate ratio was proposed to assess the local dependence between two types of recurrent event processes in one sample settings however the one sample work does not consider modeling the dependence by covariates such as subject characteristics and treatments received the focus of this paper is to understand how and in what magnitude the covariates influence the dependence strength for bivariate recurrent events we propose the covariate adjusted rate ratio a measure of covariate adjusted dependence we propose a semiparametric regression model for jointly modeling the frequency and dependence of bivariate recurrent events the first level is a proportional rates model for the marginal rates and the second level is a proportional rate ratio model for the dependence structure we develop a pseudo partial likelihood to estimate the parameters in the proportional rate ratio model we establish the asymptotic properties of the estimators and evaluate the finite sample performance via simulation studies we illustrate the proposed models and methods using a soft tissue sarcoma study that examines the effects of initial treatments on the marginal frequencies of local distant sarcoma recurrence and the dependence structure between the two types of cancer recurrence

fuzzy artmap a neural network architecture for incremental supervised learning of analog multidimensional maps a neural network architecture is introduced for incremental supervised learning of recognition categories and multidimensional maps in response to arbitrary sequences of analog or binary input vectors which may represent fuzzy or crisp sets of features the architecture called fuzzy artmap achieves a synthesis of fuzzy logic and adaptive resonance theory art neural networks by exploiting a close formal similarity between the computations of fuzzy subsethood and art category choice resonance and learning four classes of simulation illustrated fuzzy artmap performance in relation to benchmark backpropagation and generic algorithm systems these simulations include finding points inside versus outside a circle learning to tell two spirals apart incremental approximation of a piecewise continuous function and a letter recognition database the fuzzy artmap system is also compared with salzberg s nge systems and with simpson s fmmc system

parabolic orbits in the planar three body problem it is not known whether there exist oscillatory and capture orbits in the planar 3 body problem sitnikov 6 proved such orbits exist for the restricted 3 body problem alekseev i extended this work and related it to the existence of homoclinic orbits mcgehee and easton 3 studied a model problem closely related to the planar 3 body problem and proved the existence of oscillatory and capture orbits near certain orbits biasymptotic to an invariant 3 sphere the goal of this paper is to construct an invariant 3 sphere at infinity in the planar 3 body problem and to prove that the stable and unstable manifolds of this sphere are lipschitz manifolds to complete the study of oscillatory and capture orbits one must investigate the way in which the stable and unstable manifolds of the 3 sphere intersect each other this is a difficult question which is not treated here however using methods of melnikov and using one of the masses as a perturbation parameter such an investigation might be possible the stable manifold theorem which is proven here is not standard since the invariant 3 sphere is not hyperbolic geometric methods of mcgehee 4 are extended and applied to obtain the theorem a special case of the system of equations that we study has the form j x dy lx e x y l f 4 dy l x e x y l 0 1 4

n body spatial parabolic orbits asymptotic to collinear central configurations an orbit for the newtonian n body problem is called parabolic when all the mutual distances between particles approach infinity while the velocities tend to zero as time t goes to infinity the asymptotic growth rate for these mutual distances turns out to be constant multiples of t raised to the 2 3 power or to the power 2 p 1 for the inverse p central force law 1 p 3 111 indeed when the position vectors are scaled by dividing by t213 or by the square root of the moment of inertia then the scaled position vectors tend to the set of central configurations a central configuration is formed whenever for all the particles a fixed constant multiple of the mass times the position vector is equal to the corresponding force vector it turns out that central configurations can be identified with the critical point set of a certain function then the configurations are classified as being either degenerate or nondegenerate to correspond with the classification of the critical point of this function should the central configuration be nondegenerate as is known to be the case for collinear central configurations the equilateral triangle configuration for the three body problem and the equilateral tetrahedron configuration for the four body problem then the limiting configuration of a given motion must be unique for a discussion of central configurations see 15 chap 5 8 121 this uniqueness follows by combining two facts first the nondegeneracy implies that the orbit of the central configuration by the w 3 action must be isolated in the set of all central configurations the so 3 action on configuration space is rotation about the center of mass of the system secondly there can be no rotation of the limiting configuration in the sense of motion along the so 3 action on configuration space see 71 for the planar three body problem and 13 for the general case the lack of

some simple robust methods for the analysis of recurrent events nelson discussed a method of estimating the cumulative mean function for identically distributed processes of recurrent events we show that a similar approach can be used with more general models including regression the key idea is to use point estimates based on poisson models and to develop robust variance estimates that are valid more generally the methods are illustrated on reliability and warranty data

robust clustering with applications in computer vision a clustering algorithm based on the minimum volume ellipsoid mve robust estimator is proposed the mve estimator identifies the least volume region containing h percent of the data points the clustering algorithm iteratively partitions the space into clusters without prior information about their number at each iteration the mve estimator is applied several times with values of h decreasing from 0 5 a cluster is hypothesized for each ellipsoid the shapes of these clusters are compared with shapes corresponding to a known unimodal distribution by the kolmogorov smirnov test the best fitting cluster is then removed from the space and a new iteration starts constrained random sampling keeps the computation low the clustering algorithm was successfully applied to several computer vision problems formulated in the feature space paradigm multithresholding of gray level images analysis of the hough space and range image segmentation

power and sample size calculation for paired recurrent events data based on robust nonparametric tests the purpose of this paper is to develop a formula for calculating the required sample size for paired recurrent events data the developed formula is based on robust non parametric tests for comparing the marginal mean function of events between paired samples this calculation can accommodate the associations among a sequence of paired recurrent event times with a specification of correlated gamma frailty variables for a proportional intensity model we evaluate the performance of the proposed method with comprehensive simulations including the impacts of paired correlations homogeneous or nonhomogeneous processes marginal hazard rates censoring rate accrual and follow up times as well as the sensitivity analysis for the assumption of the frailty distribution the use of the formula is also demonstrated using a premature infant study from the neonatal intensive care unit of a tertiary center in southern taiwan copyright 2017 john wiley sons ltd

globally minimizing parabolic motions in the newtonian n body problem we consider the n body problem in mathbb r d with the newtonian potential 1 r we prove that for every initial configuration xi and for every minimizing normalized central configuration x0 there exists a collision free parabolic solution starting from xi and asymptotic to x0 this solution is a minimizer in every time interval the proof exploits the variational structure of the problem and it consists in finding a convergent subsequence in a family of minimizing trajectories the hardest part is to show that this solution is parabolic and asymptotic to x0

a gradient procedure for determining clusters of relatively high point density we propose an algorithm for determining clusters of relatively high point density the point density is defined by a parzen estimate of the underlying probability density a gaussian bump is chosen for the parzen window function the algorithm puts points which can be connected by gradient lines to a maximum x 0 of the point density into the same gradient cluster around x 0 for this task a gradient procedure with step control is employed we compare the procedure s convergence properties and computational expenses to those of other procedures for determining gradient clusters notes for choosing optimal standard deviations of the gaussian bump are given

statistical methods for multivariate interval censored recurrent events multi type recurrent event data arise when two or more different kinds of events may occur repeatedly over a period of observation the scientific objectives in such settings are often to describe features of the marginal processes and to study the association between the different types of events interval censored multi type recurrent event data arise when the precise event times are unobserved but intervals are available during which the events are known to have occurred this type of data is common in studies of patients with advanced cancer for example where the events may represent the development of different types of metastatic lesions which are only detectable by conducting bone scans of the entire skeleton in this setting it is of interest to characterize the incidence of the various types of bone lesions to estimate the impact of treatment and other covariate effects on the development of new lesions and to understand the relationship between the processes generating the bone lesions we develop joint models for multi type interval censored recurrent events which accommodate dependencies between different types of events and enable one to examine the covariate effects via regression however since the marginal likelihood resulting from the multivariate random effect model is intractable we describe a gibbs sampling algorithm to facilitate model fitting and inference we use generalized estimating equations for estimation and inference based on marginal models the finite sample properties of the marginal approach are studied via simulation the estimates of both the regression coefficients and the variance covariance parameters are shown to have negligible bias and 95 per cent confidence intervals based on the asymptotic variance formula are shown to have excellent empirical coverage probabilities in all of the settings considered the application of these methods to data from a trial of women with advanced breast cancer provides insight into the clinical course of bone metastases in this population

clustering by competitive agglomeration we present a new clustering algorithm called competitive agglomeration ca which minimizes an objective function that incorporates the advantages of both hierarchical and partitional clustering the ca algorithm produces a sequence of partitions with a decreasing number of clusters the initial partition has an over specified number of clusters and the final one has the optimal number of clusters the update equation in the ca algorithm creates an environment in which clusters compete for feature points and only clusters with large cardinalities survive the algorithm can incorporate different distance measures in the objective function to f find an unknown number of clusters of various shapes

formation of symmetric structures in the dynamics of repelling particles we consider hamiltonian systems corresponding to the motions of a system of n repelling particles evolving in space under the action deriving from a very long range potential energy the asymptotic behavior of the system is analysed for the cases u ln r and only special asymptotic shapes are reached which may present quite interesting symmetries and correspond to the critical points of a gradient system the relationships between the original hamiltonian and the asymptotic gradient system are discussed

on the manifolds of total collapse orbits and of completely parabolic orbits for the n body problem abstract in this paper we show for most choices of masses in the coplanar n body problem and for certain masses in the three dimensional n body problem that the set of initial conditions leading to complete collapse forms a smooth submanifold in phase space where the dimension depends upon properties of the limiting configuration a similar statement holds for completely parabolic motion by a proper scaling these two motions become dual to each other in the sense that one forms the unstable set while the other forms the stable set of a particular set of points in the new phase space most of the paper is devoted to solving the painleve wintner problem which asserts that these types of orbits cannot enter in an infinite spin

a tabu search approach to the clustering problem in this paper we consider the problem of clustering m objects into c clusters the objects are represented by points in an n dimensional euclidean space and the objective is to classify these m points into c clusters such that the distance between points within a cluster and its center which is to be found is minimized the problem is a nonconvex program that has many local minima it has been studied by many researchers and the most well known algorithm for solving it is the k means algorithm in this paper we develop a new algorithm for solving this problem based on a tabu search technique preliminary computational experience on the developed algorithm are encouraging and compare favorably with both the k means and the simulated annealing algorithms

a robust competitive clustering algorithm with applications in computer vision this paper addresses three major issues associated with conventional partitional clustering namely sensitivity to initialization difficulty in determining the number of clusters and sensitivity to noise and outliers the proposed robust competitive agglomeration rca algorithm starts with a large number of clusters to reduce the sensitivity to initialization and determines the actual number of clusters by a process of competitive agglomeration noise immunity is achieved by incorporating concepts from robust statistics into the algorithm rca assigns two different sets of weights for each data point the first set of constrained weights represents degrees of sharing and is used to create a competitive environment and to generate a fuzzy partition of the data set the second set corresponds to robust weights and is used to obtain robust estimates of the cluster prototypes by choosing an appropriate distance measure in the objective function rca can be used to find an unknown number of clusters of various shapes in noisy data sets as well as to fit an unknown number of parametric models simultaneously several examples such as clustering mixture decomposition line plane fitting segmentation of range images and estimation of motion parameters of multiple objects are shown

recurrent events analysis in the presence of time dependent covariates and dependent censoring summary recurrent events models have had considerable attention recently the majority of approaches show the consistency of parameter estimates under the assumption that censoring is independent of the recurrent events process of interest conditional on the covariates that are included in the model we provide an overview of available recurrent events analysis methods and present an inverse probability of censoring weighted estimator for the regression parameters in the andersen gill model that is commonly used for recurrent event analysis this estimator remains consistent under informative censoring if the censoring mechanism is estimated consistently and it generally improves on the naive estimator for the andersen gill model in the case of independent censoring we illustrate the bias of ad hoc estimators in the presence of informative censoring with a simulation study and provide a data analysis of recurrent lung exacerbations in cystic fibrosis patients when some patients are lost to follow up

regression methods for poisson process data abstract this article is directed toward situations where individuals can experience repeated events and data on an individual consist of the number and occurrence times of events along with concomitant variables methods of regression analysis are presented based on poisson process and proportional intensity assumptions these include parametric and semi parametric approaches to model fitting model assessment and the treatment of random effects in addition insight is gained as to the central role of poisson and mixed poisson regression analysis of counts in these methods and as to the effects of unobserved heterogeneity on semi parametric analyses the methods in the article are based on the proportional intensity poisson process model for which an individual with given fixed covariate vector x has repeated events occur according to a nonhomogeneous poisson process with intensity function x t 0 t exp x estimation of and the baseline intensity 0 t are considered when 0 t is specifi

on the dependence structure of bivariate recurrent event processes inference and estimation bivariate or multivariate recurrent event processes are often encountered in longitudinal studies in which more than one type of event is of interest there has been much research on regression analysis for such data but little has been done to measure the dependence between recurrent event processes we propose a time dependent measure termed the rate ratio to assess the local dependence between two types of recurrent event processes we model the rate ratio as a parametric function of time and leave unspecified all other aspects of the distribution we develop a composite likelihood procedure for model fitting and parameter estimation we show that the proposed estimator is consistent and asymptotically normal its finite sample performance is evaluated by simulation and illustrated by an application to a soft tissue sarcoma study

finding the observed information matrix when using the em algorithm a procedure is derived for extracting the observed information matrix when the em algorithm is used to find maximum likelihood estimates in incomplete data problems the technique requires computation of a complete data gradient vector or second derivative matrix but not those associated with the incomplete data likelihood in addition a method useful in speeding up the convergence of the em algorithm is developed two examples are presented

stacked central configurations for newtonian n 2p body problems abstract we show the existence of spatial central configurations for the n 2 p body problems in such a configuration n bodies are at the vertices of a regular n gon t 2 p bodies are symmetric with respect to the center of t and located on the straight line which is perpendicular to the regular n gon t and passes through the center of t the masses located on the vertices of the regular n gon are assumed to be equal the masses located on the same line and symmetric with respect to the center of t are equal