fractional diffusion waiting time distributions and cattaneo type equations we discuss a generalized diffusion equation resulting from an additive two state process in combination with an asymptotically fractal asymptotic power law waiting time distribution the obtained equation is an extension to previously discussed fractional diffusion equations our description leads to a mean squared displacement which describes enhanced subballistic transport for long times the short time behavior however is of a ballistic nature this separation into two domains results from the introduction of a time scale through the asymptotically fractal waiting time distribution this is also mirrored by the observation that for small times our generalized diffusion equation reduces to the standard cattaneo equation the asymptotic probability density is of compressed gaussian type and thus differs from the l evy tail generally found for these kinds of processes

random walk in chemical space of cantor dust as a paradigm of superdiffusion we point out that the chemical space of a totally disconnected cantor dust k n ensuremath subset e n is a compact metric space c n with the spectral dimension d s d ensuremath ell ngd where d and d ensuremath ell n are the fractal and chemical dimensions of k n respectively hence we can define a random walk in the chemical space as a markovian gaussian process the mapping of a random walk in c n into k n ensuremath subset e n defines the quenched l evy flight on the cantor dust with a single step duration independent of the step length the equations describing the superdiffusion and diffusion reaction front propagation ruled by the local quenched l evy flight on k n ensuremath subset e n are derived the use of these equations to model superdiffusive phenomena observed in some physical systems in which propagators decay faster than algebraically is discussed

detecting a major gene in an f2 population the aim of this paper is to study the behavior of the likelihood ratio test for the detection of a major gene in an f2 population the model is a mixture of three normal distributions where the proportions are known the information matrix is not positive definite and therefore classical results cannot be used an example concerning beans is given

exponential decay for binary time varying covariates in cox models cox models are commonly used in the analysis of time to event data one advantage of cox models is the ability to include time varying covariates often a binary covariate that codes for the occurrence of an event that affects an individual subject a common assumption in this case is that the effect of the event on the outcome of interest is constant and permanent for each subject in this paper we propose a modification to the cox model to allow the influence of an event to exponentially decay over time methods for generating data using the inverse cumulative density function for the proposed model are developed likelihood ratio tests and aic are investigated as methods for comparing the proposed model to the commonly used permanent exposure model a simulation study is performed and 3 different data sets are presented as examples

survival probability and order statistics of diffusion on disordered media we investigate the first passage time t j n to a given chemical or euclidean distance of the first j of a set of n ensuremath gg 1 independent random walkers all initially placed on a site of a disordered medium to solve this order statistics problem we assume that for short times the survival probability the probability that a single random walker is not absorbed by a hyperspherical surface during some time interval decays for disordered media in the same way as for euclidean and some class of deterministic fractal lattices this conjecture is checked by simulation on the incipient percolation aggregate embedded in two dimensions arbitrary moments of t j n are expressed in terms of an asymptotic series in powers of 1 mathrm ln n which is formally identical to those found for euclidean and some class of deterministic fractal lattices the agreement of the asymptotic expressions with simulation results for the two dimensional percolation aggregate is good when the boundary is defined in terms of the chemical distance the agreement worsens slightly when the euclidean distance is used

extreme value distributions and renormalization group in the classical theorems of extreme value theory the limits of suitably rescaled maxima of sequences of independent identically distributed random variables are studied the vast majority of the literature on the subject deals with affine normalization we argue that more general normalizations are natural from a mathematical and physical point of view and work them out the problem is approached using the language of renormalization group transformations in the space of probability densities the limit distributions are fixed points of the transformation and the study of its differential around them allows a local analysis of the domains of attraction and the computation of finite size corrections

extreme value statistics in records with long term persistence many natural records exhibit long term correlations characterized by a power law decay of the autocorrelation function c s ensuremath sim s ensuremath ensuremath gamma with time lag s and correlation exponent 0l ensuremath gamma l1 we study how the presence of such correlations affects the statistics of the extreme events i e the maximum values of the signal within time segments of the fixed duration r we find numerically that i the integrated distribution function of the maxima converges to a gumbel distribution for large r similar to uncorrelated signals ii the deviations for finite r depend on the initial distribution of the records and on their correlation properties iii the maxima series exhibit long term correlations similar to those of the original data and most notably iv the maxima distribution as well as the mean maxima significantly depend on the history in particular on the previous maximum the last item implies that conditional mean maxima and conditional maxima distributions with the value of the previous maximum as condition should be considered for an improved extreme event prediction we provide indications that this dependence of the mean maxima on the previous maximum occurs also in observational long term correlated records

clouds fibres and echoes a new approach to studying random walks on fractals up to now the general approach of constructing evolution differential equations to describe random walks on fractals has not succeeded is this because the true probability density function is inherently fractal when plotted in the appropriate similarity variable we find a cloud which is not too smooth further investigation shows that this cloud has a structure that might be overlooked if one is looking for the usual single valued probability density function the cloud is composed of an infinite family of smooth fibres each of which describes the behaviour of the walk on an infinite echo point class the fibres are individually smooth and so are naturally amenable to analysis with differential equations

limit laws for random matrices and free products in earlier articles we studied a kind of probability theory in the framework of operator algebras with the tensor product replaced by the free product we prove here that free random variables naturally arise as limits of random matrices and that wigner s semicircle law is a consequence of the central limit theorem for free random variables in this way we obtain a non commutative limit distribution of a general gaussian random matrix as an operator in a certain operator algebra wigner s law being given by the trace of the spectral measure of the selfadjoint component of this operator

continuous time random walks and the fractional diffusion equation the average probability density p r t of random walks on fractals is revisited within the continuous time random walks formalism corrections to the accepted asymptotic stretched gaussian decay of p r t of the form ralpha are discussed it is shown that p r t obeys a diffusion equation with a fractional time derivative asymptotically and predictions about the value of alpha are presented

free point processes and free extreme values we continue here the study of free extreme values begun in ben arous and voiculescu ann probab 34 2037 2059 2006 we study the convergence of the free point processes associated with free extreme values to a free poisson random measure voiculescu in lecture notes in mathematics springer heidelberg pp 279 349 1998 barndorff nielsen and thorbjornsen in probab theory relat fields 131 197 228 2005 we relate this convergence to the free extremal laws introduced in ben arous and voiculescu ann probab 34 2037 2059 2006 and give the limit laws for free order statistics

stable laws and domains of attraction in free probability theory in this paper we determine the distributional behavior of sums of free in the sense of voiculescu identically distributed inflnitesimal random variables the theory is shown to parallel the classical theory of independent random variables though the limit laws are usually quite difierent our work subsumes all previously known instances of weak convergence of sums of free identically distributed random variables in particular we determine the domains of attraction of stable distributions in the free theory these freely stable distributions are studied in detail in the appendix where their unimodality and duality properties are demonstrated

tests of homogeneity for generalized linear models abstract we propose two tests for testing homogeneity among clustered data adjusting for the effects of covariates the first is a score test for a generalized linear model with random effect in which the distribution of the response variable given the random effect is entirely defined in contrast to the likelihood ratio test however the score test does not require estimation of the parameters of a mixed effects model nor specification of the mixing distribution the second test is proposed in the framework of the generalized estimating equation gee approach in deriving this test we need only the specification of the marginal expectation and variance of the response variable and the fourth moment for the overdispersion term whereas for deriving the score test for mixed effects models the entire conditional distribution must be specified we demonstrate that the two tests are identical when the covariance matrix assumed in the gee approach is that of the random effects model in both approaches

free random levy matrices using the theory of free random variables and the coulomb gas analogy we construct stable random matrix ensembles that are random matrix generalizations of the classical one dimensional stable levy distributions we show that the resolvents for the corresponding matrices obey transcendental equations in the large size limit we solve these equations in a number of cases and show that the eigenvalue distributions exhibit levy tails for the analytically known levy measures we explicitly construct the density of states using the method of orthogonal polynomials we show that the levy tail distributions are characterized by a different novel form of microscopic universality

applications of extreme value statistics in physics we present a descriptive review of physical problems dealing with extreme values in several fields of physics we consider different physical situations involving random variables that are correlated or not and study the statistics of extremal variables which is relevant for situations where height fluctuations catastrophic events such as material failure or power outrage occur we describe the general theory and relate the cumulative limit distributions that can be accessible in experiments to microscopic models in many cases however the random variables are correlated in interface problems for example and the characteristics of the interaction are revealed in the asymptotic behavior of the limit distribution

mixed inar 1 poisson regression models analyzing heterogeneity and serial dependencies in longitudinal count data this paper presents finite mixture versions of integer valued autoregressive inar poisson regression models for investigating regularity and predictability of purchase behavior over time the approach facilitates the analysis of heterogeneity and serial correlation effects as well as conditional and marginal analyses of the effects of covariates an application to scanner panel data of detergents yields substantive insights into sources of autodependencies in individual category purchases

on the asymptotics of constrained m estimation limit theorems for an m estimate constrained to lie in a closed subset of r d are given under two different sets of regularity conditions a consistent sequence of global optimizers converges under chernoff regularity of the parameter set a n consistent sequence of local optimizers converges under clarke regularity of the parameter set in either case the asymptotic distribution is a projection of a normal random vector on the tangent cone of the parameter set at the true parameter value limit theorems for the optimal value are also obtained agreeing with chernoff s result in the case of maximum likelihood with global optimizers

count data distributions some characterizations with applications in this article we characterize all two parameter count distributions satisfying very general conditions that are partially closed under addition we also find those for which the maximum likelihood estimator of the population mean is the sample mean mixed poisson models satisfying these properties are completely determined among these models are the negative binomial poisson inverse gaussian and other known distributions new count distributions can also be constructed using these characterizations three examples of application are given

multifractal fluctuations in the dynamics of disordered systems we review recent developments in the study of the multifractal properties of dynamical processes in disordered systems in particular we discuss the multifractality of the growth probabilities of dla clusters and of the probability density for random walks on random fractals the results for multifractality in dla are based mainly on numerical studies while the results for random walks on random fractals are based on analytical results we find that although a phase transition in the multifractal spectrum occurs for d 2 dla there seems to be no phase transition for d 3 dla this might be explained by the topological differences between d 2 and d 3 dla clusters for the probability density of random walks on random fractals it is found that multifractality occurs for a finite range of moments q qmin q qmax the approach can be applied to other dynamical processes such as fractons or tracer concentration in stratified media

the similarity group and anomalous diffusion equations a number of distinct differential equations known as generalized diffusion equations have been proposed to describe the phenomenon of anomalous diffusion on fractal objects although all are constructed to correctly reproduce the basic subdiffusive property of this phenomenon using similarity methods it becomes very clear that this is far from sufficient to confirm their validity the similarity group that they all have in common is the natural basis for making comparisons between these otherwise different equations and a practical basis for comparisons between the very different modelling assumptions that their solutions each represent similarity induces a natural space in which to compare these solutions both with one another and with data from numerical experiments on fractals it also reduces the differential equations to extra ordinary ones which are presented here for the first time it becomes clear here from this approach that the proposed equations cannot agree even qualitatively with either each other or the data suggesting that a new approach is needed

fractional diffusion exact representations of spectral functions for all the relevant transformed spaces i e fourier laplace and fourier laplace we present exact solutions of a fractional diffusion equation describing random transport on fractals the potential importance of such spectral representations lies in their applications to interpreting experimental measurements of anomalous diffusion processes in contrast to the well known asymptotic results the exact representations provide a much broader basis for comparison with data

brownian motion on the sierpinski gasket we construct a brownian motion taking values in the sierpinski gasket a fractal subset of 2 and study its properties this is a diffusion process characterized by local isotropy and homogeneity properties we show for example that the process has a continuous symmetric transition density p t x y with respect to an appropriate hausdorff measure and obtain estimates on p t x y

probability distribution of random walks on self avoiding walks the probability distribution of random walks on one dimensional fractal structures generated by random walks rw chains and self avoiding walks saw chains in d dimensional space is studied analytically in the case where is the fractal dimension of the random walk it is shown that there exists an infinite hierarchy of critical dimensions with for rw chains and for saw chains for each term in the expansion of the scaling part of each transition is characterized by its own logarithmic correction

on the construction of a parameter orthogonal to the mean it is shown that for many parametric families the condition for a parameter to be orthogonal to the mean takes on a particularly simple form as a result it is often possible to obtain analytically an explicit orthogonal parameter thus providing insight into the many situations involving parametric families in which such a parameter is known to exist orthogonal parameterizations are then given for some other models

asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions abstract large sample properties of the likelihood function when the true parameter value may be on the boundary of the parameter space are described specifically the asymptotic distribution of maximum likelihood estimators and likelihood ratio statistics are derived these results generalize the work of moran 1971 chant 1974 and chernoff 1954 some of chant s results are shown to be incorrect the approach used in deriving these results follows from comments made by moran and chant the problem is shown to be asymptotically equivalent to the problem of estimating the restricted mean of a multivariate gaussian distribution from a sample of size 1 in this representation the gaussian random variable corresponds to the limit of the normalized score statistic and the estimate of the mean corresponds to the limit of the normalized maximum likelihood estimator thus the limiting distribution of the maximum likelihood estimator is the same as the distribution of the projection of the gaussian random v

information dimension of stochastic processes on networks relating entropy production to spectral properties we consider discrete stochastic processes modeled by classical master equations on networks the temporal growth of the lack of information about the system is captured by its non equilibrium entropy defined via the transition probabilities between different nodes of the network we derive a relation between the entropy and the spectrum of the master equation s transfer matrix our findings indicate that the temporal growth of the entropy is proportional to the logarithm of time if the spectral density shows scaling in analogy to chaos theory the proportionality factor is called stochastic information dimension and gives a global characterization of the dynamics on the network these general results are corroborated by examples of regular and of fractal networks

free extreme values free probability analogues of the basics of extreme value theory are obtained based on ando s spectral order this includes clas sification of freely max stable laws and their domains of attraction using free extremal convolutions on the distributions these laws coincide with the limit laws in the classical peaks over threshold approach a free extremal projection valued process over a measure space is constructed which is related to the free poisson point process

estimating the parameters of a convolution by maximum likelihood abstract in the present age of computer sophistication computational difficulty is no longer a justification for seeking alternative and inefficient estimation procedures in place of maximum likelihood estimation particularly when there are only two or three parameters to be estimated convolution densities are an example where this has occurred it is shown that in a large class of such densities the maximum likelihood equations can be reduced by one thus for a two parameter family only a single equation need be solved iteratively the required formulas are derived the problem of basing inferences on the resulting maximum likelihood estimates is briefly discussed

open capture recapture models with heterogeneity ii jolly seber model summary estimation of abundance is important in both open and closed population capture recapture analysis but unmodeled heterogeneity of capture probability leads to negative bias in abundance estimates this article defines and develops a suite of open population capture recapture models using finite mixtures to model heterogeneity of capture and survival probabilities model comparisons and parameter estimation use likelihood based methods a real example is analyzed and simulations are used to check the main features of the heterogeneous models especially the quality of estimation of abundance survival recruitment and turnover the two major advances in this article are the provision of realistic abundance estimates that take account of heterogenetiy of capture and an appraisal of the amount of overestimation of survival arising from conditioning on the first capture when heterogeneity of survival is present

the normal distribution is infinitely divisible abstract we prove that the classical normal distribution is infinitely divisible with respect to the free additive convolution we study the voiculescu transform first by giving a survey of its combinatorial implications and then analytically including a proof of free infinite divisibility in fact we prove that a sub family of askey wimp kerov distributions are freely infinitely divisible of which the normal distribution is a special case at the time of this writing this is only the third example known to us of a nontrivial distribution that is infinitely divisible with respect to both classical and free convolution the others being the cauchy distribution and the free 1 2 stable distribution

anisotropic fractional diffusion equation abstract we analyze an anisotropic fractional diffusion equation that extends some known diffusion equations by considering a diffusion coefficient with spatial and time dependence the presence of external forces and time fractional derivatives we obtain new exact classes of solutions for a linear anisotropic fractional diffusion equation and investigate the time scaling behavior and an asymptotic solution for a nonlinear anisotropic fractional diffusion equation we connect the asymptotic solution obtained with the distribution that emerges from the nonextensive statistics to the nonlinear case we also verify different diffusive behavior for instance subdiffusion and superdiffusion in each direction

the generalized cattaneo equation for the description of anomalous transport processes the cattaneo equation which describes a diffusion process with a finite velocity of propagation is generalized to describe anomalous transport three possible generalizations are proposed each one supported by a different scheme continuous time random walks non local transport theory and delayed flux force relation the properties of these generalizations are studied in both the long time and the short time regimes in the long time limit we recover the mean square displacement which is characteristic for these anomalous processes as expected the short time behaviour is modified in comparison to generalized diffusion equations

on the multiplication of free n tuples of noncommutative random variables let a1 a n b 1 b n be random variables in a noncommutative probability space such that a1 a n is free from b1 b n we show how the joint distribution of the n tuple a1b1 a n b n can be described in terms of the joint distributions of a1 a n a nd b 1 b n by using the combinatorics of the n dimensional r transform we point out a few applications that can be easily derived from our result concerning the left and right translation with a semicircular element see sections 1 6 1 10 and the compression with a projection see sections 1 11 1 14 of an n tuple of noncommutative random variables a different approach to two of these applications is presented by dan voiculescu in an appendix to the paper introduction the theory of free random variables was developed in a se quence of papers of d voiculescu see 17 or the recent survey in 16 as an instrument for approaching free products of operator algebras its particular aspect addressed in the present paper is the one concerning the addition and multiplica tion of free random variables as shown by voiculescu in 13 14 a powerful method in the study of these operations is the use of transforms that convert them respectively into addition and multiplication of complex analytic func tions or in an algebraic framework of formal power series in an indeterminate z the precise definitions of these transforms called r transform for the addition problem and s transform for the multiplication problem will be reviewed in the sections 1 2 1 3 below in the present paper we are pursuing a combination of two ideas that have appeared recently in the study of the r and s transforms the first idea is that the connection between the r and the s transform is closer than one might suspect at first glance a way of making this precise was pointed out in our paper 6 in the form of the equation s r for a distribution with nonvan ishing mean and where is a combinatorial object with a precise significance the fourier transform for multiplicative functions on noncrossing partitions a byproduct of our result in 6 is the remark that the multiplication of free

characterizing additively closed discrete models by a property of their maximum likelihood estimators with an application to generalized hermite distributions this article reports on two parameter count distributions satisfying very general conditions that are closed under addition so that their maximum likelihood estimator mle of the population mean is the sample mean the most important of these in practice the generalized hermite distribution is analyzed and a necessary and sufficient condition is given to ensure that the mle is the solution of likelihood equations score test to contrast the poisson assumption is studied and two examples of applications are given

waiting times for random walks on regular and fractal lattices we use the exact renormalization procedure introduced by machta phys rev b 24 5260 1981 to evaluate the waiting time density for a walker to jump to one of its nearest neighbors on a decimated lattice in terms of the original waiting time densities on the nondecimated lattice we explicitly identify all the fixed points and their corresponding domain of attraction for the one dimensional case and for the sierpinsky gasket

solutions for a generalized fractional anomalous diffusion equation in this paper we investigate the solutions for a generalized fractional diffusion equation that extends some known diffusion equations by taking a spatial time dependent diffusion coefficient and an external force into account which subjects to the natural boundaries and the generic initial condition we obtain explicit analytical expressions for the probability distribution and study the relation between our solutions and those obtained within the maximum entropy principle by using the tsallis entropy

an application of compound poisson modelling to biological dosimetry in this paper the rth order univariate hermite distributions are proposed to model the number of dicentrics in biological dosimetry these families of distributions are introduced from compound poisson process modelling regression models appropriate for analysing the number of dicentrics as a function of doses of radiation are presented and an example of application is also given

modelling hospital length of stay using convolutive mixtures distributions length of hospital stay los is an important indicator of the hospital activity and management of health care the skewness in the distribution of los poses problems in statistical modelling because it fails to adequately follow the usual traditional distribution of positive variables such as the log normal distribution we present in this paper a model using the convolution of two distributions a technique well known in the signal processing community the specificity of that model is that the variable of interest is considered to be the resulting sum of two random variables with different distributions one of the variables features the patient related factors in terms of their need to recover from their admission condition while the other models the hospital management process such as the discharging process two estimation procedures are proposed one is the classical maximum likelihood while the other relates to the expectation maximization algorithm we present some results obtained by applying this model to a set of real data from a group of hospitals in victoria australia copyright 2016 john wiley sons ltd

estimating tails of probability distributions we study the asymptotic properties of estimators of the tail of a distribution based on the excesses over a threshold a key idea is the use of pickands generalised pareto distribution and its fitting in most cases by the method of maximum likelihood the results cover all three limiting types of extreme value theory we propose a new estimator for an index of regular variation and show that it often performs better than hill s estimator we give new results for estimating the endpoint of a distribution extending earlier work by hall and by smith and weissman finally we give detailed results for the domain of attraction of exp e x and show that in most cases our proposed estimator is more efficient than two others one based on the exponential distribution and the other due to davis and resnick we also touch briefly on the problem of large deviations from a statistical point of view the results make extensive use of existing work on rates of convergence

asymptotic distribution of test statistics in the analysis of moment structures under inequality constraints summary the analysis of moment structural models has become an important tool of investigation in behavioural educational and economic studies the chi squared largesample test is routinely employed to assess the goodness of fit of the model considered however in order to invoke the standard asymptotic distribution theory certain regularity conditions have to be met here we consider the case where the population value of the parameter vector is a boundary point of the feasible region we show that in this case the asymptotic distribution of test statistic is a mixture of chi squared distributions the problem of finding the corresponding weights is discussed

on the propagator of sierpinski gaskets the authors present numerical calculations for the propagator p r t the probability to reach a distance r at time t having started at the origin at t 0 on sierpinski gaskets the results are confronted with approximate analytical expressions it is shown that p r t approximately t ds 2 pi xi where xi is the scaling variable xi r t1 dw in the short xi regime the scaling function follows the form pi xi approximately exp c1 xi dw while for large xi pi xi is given asymptotically by pi xi approximately xi alpha exp c2 xi nu with alpha df dw 2 dw 1 and nu dw dw 1 this result extends the previously derived expressions the numerically observed oscillations which are superimposed on the power law decay of the autocorrelation function p r 0 t are analysed in terms of typical residence times on hierarchical substructures

analytical solutions for diffusion on fractal objects a generalization of the euclidean diffusion equation is proposed for diffusion on fractals on the basis of a scaling argument a renormalization group theory for the green s function and numerical tests conjectures on the applicability to natural fractals such as porous media are presented

pseudo maximum likelihood estimation theory and applications abstract pseudo maximum likelihood estimation easily extends to k parameter models and is of interest in problems in which the likelihood surface is ill behaved in higher dimensions but well behaved in lower dimensions several signal plus noise or convolution models are examined which exhibit such behavior and satisfy the regularity conditions of the asymptotic theory for specific models a numerical comparison of asymptotic variances suggests that a psuedo maximum likelihood estimate of the signal parameter is uniformly more efficient than estimators that have been advanced by previous authors a number of other potential applications are noted

description of diffusion on discrete arrays through system of piecewise linear maps abstract it is shown that diffusion s dynamic on any discrete array including fractals can be described by piecewise linear maps the proposed method which is geometric in its nature allows to construct a system of piecewise linear maps based on the nearest neighbor coupling matrix of cosenza and kapral we propose that the dynamics of the map system describes the diffusion dynamics on the array which in our case is the sierpinski gasket due to the existence of an intrinsic homeomorphism between them it is found that there is a one to one correspondence between the partitions of the map and the cells of the fractal this fact allows to generate specific diffusion trajectories on the fractal in order to study the particle dwell time distribution since the method proposed here is completely deterministic the diffusion on the map is anomalous the mean square displacement scales with time to a power very near to 2 it is also shown that as a consequence of the lattice autosimilarity and the finite precision of the calculations this parameter remains fixed for several levels of construction of the sierpinski gasket

extreme value statistics of brain networks importance of balanced condition despite the key role played by inhibitory excitatory couplings in the functioning of brain networks the impact of a balanced condition on the stability properties of underlying networks remains largely unknown we investigate properties of the largest eigenvalues of networks having such couplings and find that they follow completely different statistics when in the balanced situation based on numerical simulations we demonstrate that the transition from weibull to frechet via the gumbel distribution can be controlled by the variance of the column sum of the adjacency matrix which depends monotonically on the denseness of the underlying network as a balanced condition is imposed the largest real part of the eigenvalue emulates a transition to the generalized extreme value statistics independent of the inhibitory connection probability furthermore the transition to the weibull statistics and the small world transition occur at the same rewiring probability reflecting a more stable system

first passage time survival probability and propagator on deterministic fractals the first passage time density psi r t defined as the probability density for the time spent by a random walker to travel for the first time the distance r that separates the starting site from its nearest neighbours and the survival probability s r t i e the probability that a random walker who starts at a site has not been absorbed by traps located on its nearest neighbours at distance r in the time interval 0 t were calculated for the class of deterministic fractals in which sites are isolated from the rest of the lattice by their nearest neighbours the large xi identical to r square root 2dt 1dw asymptotic expressions for these quantities are psi r t approximately a xi nu 2 dw exp c xi nu and h r t 1 s r t approximately a c dw 1 xi nu 2 exp c xi nu with v dw dw 1 a and c being characteristic constants for each fractal the asymptotic expression for s r t is used to justify that for this class of deterministic fractals the propagator or green function is given asymptotically by p r t t ds 2 xi alpha exp c xi nu for large xi with alpha nu 2 df this value of alpha differs from others proposed recently

continuum diffusion on networks trees with hyperbranched trunks and fractal branches the probability that a random walker returns to its origin for large times scales as t d over 2 where d over is the spectral dimension we calculate d over for a class of tree structures using a renormalization technique on an infinite continued fraction we consider a wide range of homogeneous networks based on replacing the branches of a self similar tree with arbitrary fractals and composite fractals we also consider a new class of inhomogeneous hyperbranched trees

latent change classes in dichotomous data changes in dichotomous data caused by treatments can be analyzed by means of the so called linear logistic model with relaxed assumptions llra the llra does not require observable criteria representing a single underlying latent trait but it postulates the generalizability of the treatment effects over criteria and subjects to test this latter crucial assumption the mixture llra was proposed that allows directly unobservable types of subjects to have different treatment effects as the earlier methods for estimating the parameters of the mixture llra have specific drawbacks a further method based on the conditional maximum likelihood principle will be presented here in contrast to the earlier conditional methods it uses all of the dichotomous change data while having fewer parameters further its goodness of fit tests become more sensitive to a falsely specified number of change types even though the treatment effects are biased for typically occurring small to moderate sample sizes however parametric bootstrapping of the distributions of the fit statistics is recommended for performing hypotheses tests finally three applications of the new method to empirical data are described first about the effect of the so called trager psychophysical integration second about the effect of autogenic therapy on patients with psychosomatic symptoms and third about the effect of religious education on the attitude towards sects

the analysis of asthma control under a markov assumption with use of covariates in studies of disease states and their relation to evolution data on the state are usually obtained at in frequent time points during follow up moreover in many applications there are measured covariates on each individual under study and interest centres on the relationship between these covariates and the disease evolution we developed a continuous time markov model with use of time dependent covariates and a markov model with piecewise constant intensities to model asthma evolution methods to estimate the effect of covariates on transition intensities to test the assumption of time homogeneity and to assess goodness of fit are proposed we apply these methods to asthma control we consider a three state model and we discuss in detail the analysis of asthma control evolution copyright 2003 john wiley sons ltd

extreme matrices or how an exponential map links classical and free extreme laws using our proposed approach to describe extreme matrices we find an explicit exponentiation formula linking the classical extreme laws of frechet gumbel and weibull given by the fisher tippet gnedenko classification and free extreme laws of free frechet free gumbel and free weibull of ben arous and voiculescu we also develop an extreme random matrix formalism in which refined questions about extreme matrices can be answered in particular we demonstrate explicit calculations for several more or less known random matrix ensembles providing examples of all three free extreme laws finally we present an exact mapping showing the equivalence of free extreme laws to the peak over threshold method in classical probability

finite time and asymptotic behaviour of the maximal excursion of a random walk we evaluate the limit distribution of the maximal excursion of a random walk in any dimension for homogeneous environments and for self similar supports under the assumption of spherical symmetry this distribution is obtained in closed form and is an approximation of the exact distribution comparable to that obtained by real space renormalization methods we then focus on the early time behaviour of this quantity the instantaneous diffusion exponent n exhibits a systematic overshooting of the long time exponent exact results are obtained in one dimension up to third order in n 1 2 in two dimensions on a regular lattice and on the sierpinski gasket we find numerically that the analytic scaling n an holds