regression models for longitudinal binary responses with informative drop outs this paper reviews both likelihood based and non likelihood generalized estimating equations regression models for longitudinal binary responses when there are drop outs throughout it is assumed that the regression parameters for the marginal expectations of the binary responses are of primary scientific interest the association or time dependence between the responses is largely regarded as a nuisance characteristic of the data the performance of the methods is compared in terms of asymptotic bias under mis specification of the association between the responses and the missing data mechanism or drop out process

disordered one dimensional contact process new theoretical and numerical analysis of the one dimensional contact process with quenched disorder are presented we derive new scaling relations different from their counterparts in the pure model which are valid not only at the critical point but also away from it due to the presence of generic scale invariance all the proposed scaling laws are verified in numerical simulations in addition we map the disordered contact process into a non markovian contact process by using the so called run time statistic and write down the associated field theory this turns out to be in the same universality class as one derived by janssen for the quenched system with a gaussian distribution of impurities our findings here support the lack of universality suggested by the field theoretical analysis generic power law behaviors are obtained evidence is shown of the absence of a characteristic time away from the critical point and the absence of universality is put forward the intermediate sublinear regime predicted by bramsom et al is also found

absorbing state phase transitions with quenched disorder quenched disorder in the sense of the harris criterion is generally a relevant perturbation at an absorbing state phase transition point here using a strong disorder renormalization group framework and effective numerical methods we study the properties of random fixed points for systems in the directed percolation universality class for strong enough disorder the critical behavior is found to be controlled by a strong disorder fixed point which is isomorph with the fixed point of random quantum ising systems in this fixed point dynamical correlations are logarithmically slow and the static critical exponents are conjecturedly exact for one dimensional systems the renormalization group scenario is confronted with numerical results on the random contact process in one and two dimensions and satisfactory agreement is found for weaker disorder the numerical results indicate static critical exponents which vary with the strength of disorder whereas the dynamical correlations are compatible with two possible scenarios either they follow a power law decay with a varying dynamical exponent like in random quantum systems or the dynamical correlations are logarithmically slow even for a weak disorder for models in the parity conserving universality class there is no strong disorder fixed point according to our renormalization group analysis

application of gee procedures for sample size calculations in repeated measures experiments derivation of the minimum sample size is an important consideration in an applied research effort when the outcome is measured at a single time point sample size procedures are well known and widely applied the corresponding situation for longitudinal designs however is less well developed in this paper we adapt the generalized estimating equation gee approach of liang and zeger to sample size calculations for discrete and continuous outcome variables the non central version of the wald 2 test is considered we use the damped exponential family of correlation structures described in munoz et al for the working correlation matrix among the repeated measures we present a table of minimum sample sizes for binary outcomes and discuss extensions that account for unequal allocation staggered entry and loss to follow up 1998 john wiley sons ltd

improved perturbation expansion for disordered systems beating griffiths singularities we introduce a new expansion to prove exponential clustering of connected correlations in a large class of disordered systems our expansion converges for values of the temperature and magnetic field where standard cluster expansions diverge due to the presence of griffiths type singularities it is organized inductively over an infinite sequence of increasing distance scales in each induction step one redefines what is means by the unperturbed system a procedure somewhat reminiscent of k a m theory our techniques may be useful in dealing with the so called large field problem in real space renormalization group schemes

statistical properties of functionals of the paths of a particle diffusing in a one dimensional random potential we present a formalism for obtaining the statistical properties of functionals and inverse functionals of the paths of a particle diffusing in a one dimensional quenched random potential we demonstrate the implementation of the formalism in two specific examples 1 where the functional corresponds to the local time spent by the particle around the origin and 2 where the functional corresponds to the occupation time spent by the particle on the positive side of the origin within an observation time window of size t we compute the disorder average distributions of the local time the inverse local time the occupation time and the inverse occupation time and show that in many cases disorder modifies the behavior drastically

the order parameter in a spin glass various possible precise definitions of an edwards anderson type of order parameter for an ising model spin glass are considered using boundary conditions for a finite system states of an infinite system and a duplicate system approach several of these definitions are shown to yield identical results

reaction diffusion models in one dimension with disorder we study a large class of one dimensional reaction diffusion models with quenched disorder using a real space renormalization group method rsrg which yields exact results at large time particles e g of several species undergo diffusion with random local bias sinai model and may react upon meeting we obtain a detailed description of the asymptotic states i e attractive fixed points of the rsrg such as the large time decay of the density of each specie their associated universal amplitudes and the spatial distribution of particles we also derive the spectrum of nontrivial exponents which characterize the convergence towards the asymptotic states for reactions which lead to several possible asymptotic states separated by unstable fixed points we analyze the dynamical phase diagram and obtain the critical exponents characterizing the transitions we also obtain a detailed characterization of the persistence properties for single particles as well as more complex patterns we compute the decay exponents for the probability of no crossing of a given point by respectively the single particle trajectories ensuremath theta or the thermally averaged packets overline ensuremath theta the generalized persistence exponents associated to n crossings are also obtained specifying to the process a stackrel ensuremath rightarrow a ensuremath emptyset or a with probabilities r 1 ensuremath r we compute exactly the exponents ensuremath delta r and ensuremath psi r characterizing the survival up to time t of a domain without any merging or with mergings respectively and the exponents ensuremath delta a r and ensuremath psi a r characterizing the survival up to time t of a particle a without any coalescence or with coalescences respectively overline ensuremath theta ensuremath psi and ensuremath delta obey hypergeometric equations and are numerically surprisingly close to pure system exponents though associated to a completely different diffusion length the effect of additional disorder in the reaction rates as well as some open questions are also discussed

phase diagram and correlation length bounds for mandelbrot aerogels the authors study a variant of the mandelbrot percolation process which is of current use as a model of aerogels the model has two parameters one of them q is the usual multiscale parameter of the mandelbrot percolation process and the other p is a bernoulli percolation parameter that is reserved for the last step of the construction they investigate the phase diagram of this model in the q p plane there are two phases a sol phase and a gel phase classified according to whether a limit of crossing probabilities vanishes or is nonzero in the sol phase they define a correlation length via the rate of decay of a rescaled connectivity function they show that this length scale diverges at the phase boundary furthermore they demonstrate that if the phase boundary is approached with q fixed and p tending up to its critical value pg q then up to logarithmic corrections the divergence is at least as fast as mod pg p mod 2dh where dh 2 mod log q log n mod can be identified as the hausdorff dimension of the background medium

a parametric family of correlation structures for the analysis of longitudinal data in epidemiological settings we are often faced with numerous short time series and a parsimonious parametrization of the correlation structure is desired in order to optimize the efficiency of the estimation procedure we propose a damped exponential correlation structure for modeling multivariate gaussian outcomes the correlation between two observations separated by s units of time is modeled as gamma s theta where gamma is the correlation between elements separated by one s unit and theta is a damping parameter for theta 0 theta 1 and theta infinity the correlation structures of compound symmetry first order autoregressive and first order moving average processes are obtained although the ar 2 dependency structure and the combination of random effects and ar 1 errors are not special cases of the proposed parametric family these structures can be well approximated within the family for short time series maximum likelihood methods for parameter estimation and interpretations of intermediate models 0 less than theta less than 1 are discussed in the context of modeling pulmonary function in an adult population in the netherlands and t cell subsets in homosexual men infected with human immunodeficiency virus type i

discontinuity of the magnetization in one dimensional 1 x y 2 ising and potts models results from percolation theory are used to study phase transitions in one dimensional ising and q state potts models with couplings of the asymptotic form j sub x y approx const absolute value x y sup 2 for translation invariant systems with well defined lim sub x infinity x sup 2 j sub x j sup possibly o or infinity we establish 1 there is no long range order at inverse temperatures beta with beta j sup less than or equal to1 2 if beta j sup q then by sufficiently increasing j sub 1 the spontaneous magnetization m is made positive 3 in models with 0 j sup infinity the magnetization is discontinuous at the transition point as originally predicted by thouless and obeys m beta sub c less than or equal to 1 beta sub c j sup sup 1 2 4 for ising q 2 models with j sup infinity it is noted that the correlation function decays as beta approx c beta absolute value x y sup 2 whenever beta beta sub c points 1 3 are deduced from previous percolation results by utilizing the fortuin kasteleyn representation which also yields other results of independent interest relating potts models with different values of q

low density series expansions for directed percolation iv temporal disorder we introduce a model for temporally disordered directed percolation in which the probability of spreading from a vertex t x where t is the time and x is the spatial coordinate is independent of x but depends on t using a very efficient algorithm we calculate low density series for bond percolation on the directed square lattice analysis of the series yields estimates for the critical point pc and various critical exponents which are consistent with a continuous change of the critical parameters as the strength of the disorder is increased

annihilating random walks in one dimensional disordered media we study diffusion limited pair annihilation a a to 0 on one dimensional lattices with inhomogeneous nearest neighbour hopping in the limit of infinite reaction rate we obtain a simple exact expression for the particle concentration rho k t of the many particle system in terms of the conditional probabilities p m t l 0 for a single random walker in a dual medium for some disordered systems with an initially randomly filled lattice this leads asymptotically to bar rho t bar p 0 2t 0 0 for the disorder averaged particle density we also obtain interesting exact relations for single particle conditional probabilities in random media related by duality such as random barrier and random trap systems for some specific random barrier systems the smoluchovsky approach to diffusion limited annihilation turns out to fail

critical exponents for branching annihilating random walks with an even number of offspring recently takayasu and tretyakov phys rev lett 68 3060 1992 studied branching annihilating random walks baws with n 1 char21 5 offspring these models exhibit a continuous phase transition to an absorbing state for odd n the models belong to the universality class of directed percolation for even n the particle number is conserved modulo 2 and the critical behavior is not compatible with directed percolation in this article i study the baw with n 4 using time dependent simulations and finite size scaling obtaining precise estimates for various critical exponents the results are consistent with the conjecture ensuremath beta ensuremath nu mathrm ensuremath perp 1 2 ensuremath nu mathrm ensuremath parallel ensuremath nu mathrm ensuremath perp 7 4 ensuremath gamma 0 ensuremath delta 2 7 ensuremath eta 0 and mathrm ensuremath delta mathit h 9 2 these critical exponents characterize respectively the dependence of the order parameter ensuremath beta ensuremath nu mathrm ensuremath perp and relaxation time ensuremath nu mathrm ensuremath parallel ensuremath nu mathrm ensuremath perp on system size the growth of fluctuations ensuremath gamma close to the critical point the long time behavior of the probability of survival ensuremath delta and average number of particles ensuremath eta when starting at time zero with just two particles and finally the decay of the order parameter mathrm ensuremath delta mathit h at the critical point in the presence of an external source

non equilibrium dynamics of disordered systems understanding the broad continuum of relevant time scales via a strong disorder rg in configuration space we show that an appropriate description of the non equilibrium dynamics of disordered systems is obtained through a strong disorder renormalization procedure in configuration space that we define for any master equation with transitions rates between configurations the idea is to eliminate iteratively the configuration with the highest exit rate to obtain renormalized transition rates between the remaining configurations the multiplicative structure of the new generated transition rates suggests that for a very broad class of disordered systems the distribution of renormalized exit barriers defined as will become broader and broader upon iteration so that the strong disorder renormalization procedure should become asymptotically exact at large time scales we have checked numerically this scenario for the non equilibrium dynamics of a directed polymer in a two dimensional random medium

energy dynamics in the sinai model abstract we study the time dependent potential energy w t u x 0 u x t of a particle diffusing in a one dimensional random force field the sinai model using the real space renormalization group method rsrg we obtain the exact large time limit of the probability distribution of the scaling variable w w t t ln t this distribution exhibits a non analytic behaviour at w 1 these results are extended to a small non zero applied field using the constrained path integral method we moreover compute the joint distribution of energy w t and position x t at time t in presence of a reflecting boundary at the starting point with possibly some drift in the direction the rsrg very simply yields the one time and aging two time behaviour of this joint probability it exhibits differences in behaviour compared to the unbounded motion such as analyticity relations with some magnetization distributions in the 1d spin glass are discussed

qualitative analysis of the dynamics and stability properties for axiom a maps abstract assume that f c1 x x is an axiom a mapping from a nontrivial interval x into itself i e f satisfies the conditions a the nonwandering set f can be split up into at most two but at least one nonempty positively f invariant compact sets say f a f e f such that the restriction of f to a f is contracting and the restriction of f to e f is expanding b the periodic points for f are dense in f then we have 1 a the nonwandering set of f decomposes into finitely many positively f invariant sets and f is one sided topologically transitive on each of these basic sets 2 b the map f is c1 stable 3 c there exists a positive integer p such that almost every point in x is asymptotically periodic with period p provided that f x is bounded and that f is of class c1 for some positive real number 4 d the map f is c2 structurally stable provided that f satisfies some suitable conditions finally it will turn out that maps with nonpositive schwarzian derivative are under reasonable assumptions axiom a maps

parameter shifted shadowing property for geometric lorenz attractors in this paper we will show that any geometric lorenz flow in a definite class satisfies the parameter shifted shadowing property

monte carlo study of the triangular blume capel model under bond randomness the effects of bond randomness on the universality aspects of a two dimensional d 2 blume capel model embedded in the triangular lattice are discussed the system is studied numerically in both its first and second order phase transition regimes by a comprehensive finite size scaling analysis for a particularly suitable value of the disorder strength we find that our data for the second order phase transition emerging under random bonds from the second order regime of the pure model are compatible with the universality class of the two dimensional 2d random ising model furthermore we find evidence that the second order transition emerging under bond randomness from the first order regime of the pure model belongs again to the same universality class although the first finding reinforces the scenario of strong universality in the 2d ising model with quenched disorder the second is in difference from the critical behavior emerging under randomness in the cases of the ex first order transitions of the potts model finally our results verify previous renormalization group calculations on the blume capel model with disorder in the crystal field coupling

the exact distribution of the oscillation period in the underdamped one dimensional sinai model we consider the newtonian dynamics of a massive particle in a one dimensional random potential which is a brownian motion in space this is the zero temperature nondamped sinai model as there is no dissipation the particle oscillates between two turning points where its kinetic energy becomes zero the period of oscillation is a random variable fluctuating from sample to sample of the random potential we compute the probability distribution of this period exactly and show that it has a power law tail for large period p t t 5 3 and an essential singularity p t exp 1 t as t 0 our exact results are confirmed by numerical simulations and also via a simple scaling argument

analysis of repeated categorical data using generalized estimating equations moment methods for analysing repeated binary responses have been proposed by liang and zeger and extended by prentice and zhao and prentice in these estimating equations models are proposed for the correlation between the repeated binary responses we extend liang and zeger s method to models for the correlation between repeated nominal or ordinal categorical responses in particular when the repeated responses are binary our methods reduce to liang and zeger s method our method is illustrated with two datasets one dataset contains repeated observations of self assessment of arthritis an ordered variable with three categories collected during a randomized comparative study of alternative treatments of patients with rheumatoid arthritis the second dataset is a longitudinal study of the health effects of air pollution in which the repeated ordered multinomial response is the wheezing status no wheeze wheeze with cold wheeze apart from cold of a child at ages 9 10 11 and 12 years

crossovers from parity conserving to directed percolation universality the crossover behavior of various models exhibiting phase transition to absorbing phase with parity conserving class has been investigated by numerical simulations and cluster mean field method in case of models exhibiting z 2 symmetric absorbing phases the cellular automaton version of the nonequilibrium kinetic ising model nekimca and a stochastic cellular automaton invented by grassberger krause and von der twer j phys a 17 l105 1984 the introduction of an external symmetry breaking field causes a crossover to kink parity conserving models characterized by dynamical scaling of the directed percolation dp and the crossover exponent 1 phi approximately equal to 0 53 2 in the case of a branching and annihilating random walk model with an even number of offspring dual to nekimca the introduction of spontaneous particle decay destroys the parity conservation and results in a crossover to the dp class characterized by the crossover exponent 1 phi approximately equal to 0 205 5 the two different kinds of crossover operators cannot be mapped onto each other and the resulting models show a diversity within the dp universality class in one dimension these subclasses differ in cluster scaling exponents

spin models on random lattices under certain conditions phase transitions in systems with quenched disorder are expected to exhibit a dierent behaviour than in the corresponding pure system here we discuss a series of monte carlo studies of a special type of such disordered systems namely spin models dened on quenched random lattices exhibiting geometrical disorder in the connectivity of the lattice sites in two dimensions we present results for the q state potts model on random tri valent 3 planar graphs which appear quite naturally in the dynamically triangulated random surface dtrs approach to quantum gravity as well as on poissonian random lattices of voronoi delaunay type both cases q64 and 4 are discussed which in the pure model without disorder give rise to second and rst order phase transitions respectively in three dimensions results for the ising model on poissonian random lattices are briey described we conclude with a comparison of the two types of connectivity disorder with the more standard case of bond disorder and a discussion of the distinguishing dierences c 2000 elsevier science b v all rights reserved

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

cluster mean field study of the parity conserving phase transition the phase transition of the branching and annihilating random walk with even offspring is studied by n cluster mean field approximations on one dimensional lattices by allowing the system to reach zero branching rate a phase transition can be seen for any n ensuremath leqslant 12 coherent anomaly extrapolations applied for the series of approximations results in ensuremath nu ensuremath perp 1 85 3 and ensuremath beta 0 96 2

computing the topological entropy of maps we give an algorithm for determining the topological entropy of a unimodal map of the interval given its kneading sequence we also show that this algorithm converges exponentially in the number of letters of the kneading sequence

is every approximate trajectory of some process near an exact trajectory of a nearby process this paper deals with the problem can a noisy orbit be tracked by a real orbit in particular we will study the one parameter family of tent maps and the one parameter family of quadratic maps we writeg for eitherf orf withf x x forx 1 2 andf x 1 x forx 1 2 andf x x 1 x for a given we will say g permits increased parameter shadowing if for each x 0 there exists some 0 and some f 0 such that every f pseudog orbit starting in some invariant interval can be x shadowed by a realg orbit with we show thatg typically permits increased parameter shadowing

sample size for repeated measures studies with binary responses we consider the sample size required for repeated measures studies when the response variable is binary we propose the use of weighted least squares wls for calculating the minimum sample size required to detect some minimum clinically important treatment effect we provide tabulated values of the estimated sample sizes for a simple example and we discuss some practical considerations in determination of sample size with repeated binary responses

critical behavior of an even offspringed branching and annihilating random walk cellular automaton with spatial disorder a stochastic cellular automaton exhibiting a parity conserving class transition has been investigated in the presence of quenched spatial disorder by large scale simulations numerical evidence has been found that weak disorder causes irrelevant perturbation for the universal behavior of the transition and the absorbing phase of this model this opens up the possibility for experimental observation of the critical behavior of a nonequilibrium phase transition to absorbing state for very strong disorder the model breaks up into blocks with exponential size distribution and continuously changing critical exponents are observed for strong disorder the randomly distributed diffusion walls introduce another transition within the inactive phase of the model in which residual particles survive the extinction the critical dynamical behavior of this transition has been explored

on a sharp transition from area law to perimeter law in a system of random surfaces we introduce and study a phase transition which is associated with the spontaneous formation of infinite surface sheets in a bernoulli system of random plaquettes the transition is manifested by a change in the asymptotic behavior of the probability of the formation of a surface spanning a prescribed loop as such this transition offers a generalization of the bond percolation phenomenon at low plaquette densities the probability for large loops is shown to decay exponentially with the loops area whereas for high densities the decay is by a perimeter law furthermore we show that the two phases of the three dimensional plaquette system are in a precise correspondence with the two phases of the dual system of random bonds thus if a natural conjecture about the phase structure of the bond percolation model is true then there is a sharp transition in the asymptotic behavior of the surface events our analysis incorporates block variables in terms of which a non critical system is transformed into one which is close to a trivial high or low density fixed point stochastic geometric effects like those discussed here play an important role in lattice gauge theories

critical region for droplet formation in the two dimensional ising model we study the formation dissolution of equilibrium droplets in finite systems at parameters corresponding to phase coexistence specifically we consider the 2d ising model in volumes of size l2 inverse temperature c and overall magnetization conditioned to take the value m l2 2m vl where c 1 is the critical temperature m m is the spontaneous magnetization and vl is a sequence of positive numbers we find that the critical scaling for droplet formation dissolution is when vl3 2l 2 tends to a definite limit specifically we identify a dimensionless parameter proportional to this limit a non trivial critical value c and a function such that the following holds for c there is a single wulff shaped droplet containing a fraction c 2 3 of the magnetization deficit and there are no other droplets beyond the scale of log l moreover and are related via a universal equation that apparently is independent of the details of the system

a new type of kinetic critical phenomenon the authors study a new critical phenomenon in an non thermal one dimensional lattice model it is characterised by the transition from stability to instability of kinks between ordered states below the critical point the kinks are stable and move by annihilating random walks above the critical point they are unstable against creation of kink antikink pairs the spontaneous production of pairs is assumed to be absent at the critical point p pcr the density of kinks decreases like n approximately talpha with alpha 0 27 or 0 08 above the critical point the density of kinks in the stationary state is approximately p pcr beta with beta 0 06 or 0 2 possible extensions to two or more dimensions and possible applications are discussed

improved cost functions for modelling of noisy chaotic time series abstract standard least squares cost functions yield unbiased results only if the independent variables are noise free which is not the case in time series analysis new minimization problems for the determination of the dynamics underlying noisy chaotic data are formulated which can overcome the problem of noise in the independent variables for a given model these improved cost functions give the chance to estimate its parameters with a strongly reduced bias in the case of large amplitude measurement noise the method is illustrated by the help of numerical and experimental examples results for dynamical noise are discussed

power and sample size calculations for exact conditional tests with ordered categorical data we develop an algorithm for computing sample sizes equal or unequal for categorical data we illustrate its use in the two sample setting using the wilcoxon rank sum statistic but the algorithm accommodates the entire class of linear rank statistics and can be extended to include nonlinear rank statistics as well the sample size determinations can be based on either exact power or on a very precise monte carlo estimate of it to reduce the computations further power can be computed as a function of asymptotic critical values when the number of categories is not too small for the wilcoxon statistic we show that this approximation works well if there are more than five response categories

preservation of shadowing in discrete dynamical systems abstract we look at the preservation of various notions of shadowing in discrete dynamical systems under inverse limits products factor maps and the induced maps for symmetric products and hyperspaces the shadowing properties we consider are the following shadowing h shadowing eventual shadowing orbital shadowing strong orbital shadowing the first and second weak shadowing properties limit shadowing s limit shadowing orbital limit shadowing and inverse shadowing

universality class for domain growth in random magnets a 2d ising model with random ferromagnetic bonds is studied by monte carlo simulation following a quench from t infinity to t tc the domain size grows as l t approximately in t to x at late times the data are consistent with the theoretical prediction chi 4 the exponent defined by si 0 si t approximately l t and the scaling functions for the spatial correlations are very close to those of the pure system suggesting that pure and random systems belong to the same universality class

non algebraic domain growth in random magnets a cell dynamical approach the authors develop a novel numerical approach based on a computationally efficient cell dynamical system cds model for studying the kinetics of ordering in systems described by a non conserved order parameter with quenched disorder evolving from unstable initial states they use this model to study the kinetics of domain growth in a coarse grained version of the random exchange ising model their numerical data strongly indicate quantitative agreement with the theoretically predicted asymptotic growth law over a limited range of disorder amplitudes they also compare their observations with those in laboratory experiments and make important predictions regarding dynamical scaling in these systems

exact asymptotic results for persistence in the sinai model with arbitrary drift we obtain exact asymptotic results for the disorder averaged persistence of a brownian particle moving in a biased sinai landscape we employ a method that maps the problem of computing the persistence to the problem of finding the energy spectrum of a single particle quantum hamiltonian which can be subsequently found our method allows us analytical access to arbitrary values of the drift bias thus going beyond the previous methods that provide results only in the limit of vanishing drift we show that on varying the drift the persistence displays a variety of rich asymptotic behaviors including in particular interesting qualitative changes at some special values of the drift

sensitivity of long periodic orbits of chaotic systems the properties of long numerically determined periodic orbits of two low dimensional chaotic systems the lorenz equations and the kuramoto sivashinsky system in a minimal domain configuration are examined the primary question is to establish whether the sensitivity of period averaged quantities with respect to parameter perturbations computed over long orbits can be used as a sufficiently good proxy for the response of the chaotic state to finite amplitude parameter perturbations to address this question an inventory of thousands of orbits at least two orders of magnitude longer than the shortest admissible cycles is constructed the expectation of period averages floquet exponents and sensitivities over such set is then obtained it is shown that all these quantities converge to a limiting value as the orbit period is increased however while period averages and floquet exponents appear to converge to analogous quantities computed from chaotic trajectories the limiting value of the sensitivity is not necessarily consistent with the response of the chaotic state similar to observations made with other shadowing algorithms

extinction survival and dynamical phase transition of branching annihilating random walk we analyze statistical properties of random walkers which disappear when they meet and make offsprings by a controllable rate numerical results for one two and three dimensions and for the sierpinski gasket are assessed in view of the mean field theory predictions universality classes are found to depend on the number of offsprings in space dimension less than 3

phase transitions and singularities in random quantum systems random quantum systems that exhibit unusual behavior associated with infinite randomness fixed points are discussed focusing on the random quantum ising model this system undergoes a transition at zero temperature from a phase with infinite susceptibility and continuously variable exponents to a ferromagnetic phase via a quantum critical point characterized by tunneling scaling with energy and length scales l related by 1n l exact results in one dimension and a scaling picture in higher dimensions are derived from a simple renormalization group other random quantum critical points and quantum disordered phases that can exhibit similar features are discussed briefly

sample size calculations for ordered categorical data many clinical trials yield data on an ordered categorical scale such as very good good moderate poor under the assumption of proportional odds such data can be analysed using techniques of logistic regression in simple comparisons of two treatments this approach becomes equivalent to the mann whitney test in this paper sample size formulae consistent with an eventual logistic regression analysis are derived the influence on efficiency of the number and breadth of categories will be examined effects of misclassification and of stratification are discussed and examples of the calculations are given

small random perturbations of dynamical systems and the definition of attractors the strange attractors plotted by computers and seen in physical experiments do not necessarily have an open basin of attraction in view of this we study a new definition of attractors based on ideas of conley we argue that the attractors observed in the presence of small random perturbations correspond to this new definition

impact of the updating scheme on stationary states of networks from boolean networks it is well known that the number of attractors as a function of the system size depends on the updating scheme which is chosen either synchronously or asynchronously in this contribution we report on a systematic interpolation between synchronous and asynchronous updating in a one dimensional chain of ising spins the stationary state for fully synchronous updating is antiferromagnetic the interpolation allows us to locate a phase transition between phases with an absorbing and a fluctuating stationary state the associated universality class is that of parity conservation we also report on a more recent study of asynchronous updates applied to the yeast cell cycle network compared to the synchronous update the basin of attraction of the largest attractor considerably shrinks and the convergence to the biological pathway slows down and is less dominant both examples illustrate how sensitively the stationary states and the properties of attractors can depend on the updating mode of the algorithm

phase transition between synchronous and asynchronous updating algorithms we update a one dimensional chain of ising spins of length l with algorithms which are parameterized by the probability p for a certain site to get updated in one time step the result of the update event itself is determined by the energy change due to the local change in the configuration in this way we interpolate between the metropolis algorithm at zero temperature when p is of the order of 1 l and l is large and a synchronous deterministic updating procedure for p 1 as a function of p we observe a phase transition between the stationary states to which the algorithm drives the system these are non absorbing stationary states with antiferromagnetic domains for p p c and absorbing states with ferromagnetic domains for p p c this means that above this transition the stationary states have lost any remnants of the ferromagnetic ising interaction a measurement of the critical exponents shows that this transition belongs to the universality class of parity conservation

iterated maps on discretized meshes of the unit interval this paper takes a new approach to the problem of numerical processes with finite mantissa arithmetic and uses completely elementary techniques we study discretized numerical versions of unimodal maps from the unit interval to itself analogues of continuity and an intermediate value theorem are used to construct return points rather than periodic orbits floating point versions of differentiation of discretized unimodal functions and a mean value theorem do however provide a framework for showing the existence of periodic regimes for more general unimodal mappings the treatment could be loosely described as a floating point version of the analytic program of lanford

power sample size calculations for generalized linear models an approach for estimating power sample size is described within the framework of generalized linear models this approach is based on an asymptotic approximation to the power of the score test under contiguous alternatives and is applicable to tests of composite null hypotheses an implementation is described for the special case of logistic regression models simulation studies are presented which indicate that the asymptotic approximation to the finite sample situation is good over a range of parameter configurations

random walk in a two dimensional self affine random potential properties of the anomalous diffusion phase at small external force we study the dynamical response to an external force f for a particle performing a random walk in a two dimensional quenched random potential of hurst exponent h 1 2 we present numerical results on the statistics of first passage times that satisfy closed backward master equations we find that there exists a zero velocity phase in a finite region of the external force 0lfl f c where the dynamics follows the anomalous diffusion law x t ensuremath sim ensuremath xi f t ensuremath mu f the anomalous exponent 0l ensuremath mu f l1 and the correlation length ensuremath xi f vary continuously with f in the limit of vanishing force f ensuremath rightarrow 0 we measure the following power laws the anomalous exponent vanishes as ensuremath mu f ensuremath propto f a with a ensuremath simeq 0 6 instead of a 1 in dimension d 1 and the correlation length diverges as ensuremath xi f ensuremath propto f ensuremath ensuremath nu with ensuremath nu ensuremath simeq 1 29 instead of ensuremath nu 2 in dimension d 1 our main conclusion is thus that the dynamics renormalizes onto an effective directed trap model where the traps are characterized by a typical length ensuremath xi f along the direction of the force and by a typical barrier 1 ensuremath mu f the fact that these traps are smaller in linear size and in depth than in dimension d 1 means that the particle uses the transverse direction to find lower barriers

critical behavior and griffiths effects in the disordered contact process we study the nonequilibrium phase transition in the one dimensional contact process with quenched spatial disorder by means of large scale monte carlo simulations for times up to 10 9 and system sizes up to 10 7 sites in agreement with recent predictions of an infinite randomness fixed point our simulations demonstrate activated exponential dynamical scaling at the critical point the critical behavior turns out to be universal even for weak disorder however the approach to this asymptotic behavior is extremely slow with crossover times of the order of 10 4 or larger in the griffiths region between the clean and the dirty critical points we find power law dynamical behavior with continuously varying exponents we discuss the generality of our findings and relate them to a broader theory of rare region effects at phase transitions with quenched disorder

localization properties of the anomalous diffusion phase in the directed trap model and in the sinai diffusion with a bias we study the localization properties of the anomalous diffusion phase x approximately t micro with 0 0 and corresponds to the golosov localization for finite micro we thus generalize the usual real space renormalization method to allow for the spreading of the thermal packet over many renormalized valleys our construction allows one to compute exact series expansions in micro for all observables to compute observables at order micro n it is sufficient to consider in each sample a spreading of the thermal packet onto at most 1 n traps so our approach provides a description of the structure of the thermal packet sample by sample and a full statistical characterization of the important traps at a given order in micro for the directed trap model we show explicitly up to order micro 2 how to recover the exact expressions for the diffusion front the thermal width and the localization parameter y2 we then use our method to derive exact results for the localization parameters y k for arbitrary k the correlation function of two particles and the generating function of thermal cumulants we then explain how these results apply to the sinai diffusion with bias by deriving the quantitative mapping between the large scale renormalized descriptions of the two models finally we study the internal structure of the effective traps for the sinai model via path integral methods

self averaging distribution of pseudocritical temperatures and finite size scaling in critical disordered systems we evaluate by monte carlo simulations various singular thermodynamic quantities x for ensembles of quenched random ising and ashkin teller models the measurements are taken at t c and we study how the distributions p x and in particular their relative squared width r x over the ensemble depend on the system size l the ashkin teller model was studied in the regime where bond randomness is irrelevant and we found weak self averaging r x ensuremath sim l ensuremath alpha ensuremath nu ensuremath rightarrow 0 where ensuremath alpha l0 and ensuremath nu are the exponents of the pure model fixed point governing the transition for the site dilute ising model on a cubic lattice known to be governed by a random fixed point we find that r x tends to a constant as predicted by aharony and harris we tested whether this constant is universal however this constant is different for canonical and grand canonical disorder we identify the pseudocritical temperature of each sample i t c i l as the temperature at which the susceptibility reaches its maximal value ensuremath chi mathrm max the distribution of these sample dependent t c i l was investigated we found that its variance scales as ensuremath delta t c l 2 ensuremath sim l ensuremath 2 ensuremath nu our previously proposed finite size scaling ansatz for disordered systems was tested and found to hold we did observe deviations from a single function which imply that sample dependent scaling functions are needed these deviations are however relatively small and hence to obtain a fixed statistical error it may be more computationally efficient to measure ensuremath chi mathrm max than the commonly used ensuremath chi t c ensuremath infty

infinite randomness critical point in the two dimensional disordered contact process we study the nonequilibrium phase transition in the two dimensional contact process on a randomly diluted lattice by means of large scale monte carlo simulations for times up to 10 10 and system sizes up to 8000 x8000 sites our data provide strong evidence for the transition being controlled by an exotic infinite randomness critical point with activated exponential dynamical scaling we calculate the critical exponents of the transition and find them to be universal i e independent of disorder strength the griffiths region between the clean and the dirty critical points exhibits power law dynamical scaling with continuously varying exponents we discuss the generality of our findings and relate them to a broader theory of rare region effects at phase transitions with quenched disorder our results are of importance beyond absorbing state transitions because according to a strong disorder renormalization group analysis our transition belongs to the universality class of the two dimensional random transverse field ising model

sample size calculations for studies with correlated observations correlated data occur frequently in biomedical research examples include longitudinal studies family studies and ophthalmologic studies in this paper we present a method to compute sample sizes and statistical powers for studies involving correlated observations this is a multivariate extension of the work by self and mauritsen 1988 biometrics 44 79 86 who derived a sample size and power formula for generalized linear models based on the score statistic for correlated data we appeal to a statistic based on the generalized estimating equation method liang and zeger 1986 biometrika 73 13 22 we highlight the additional assumptions needed to deal with correlated data some special cases that are commonly seen in practice are discussed followed by simulation studies

strange attractors across the boundary of hyperbolic systems we study a bifurcation of axiom a hyperbolic vector fields in dimension three leading to robust strange attractors with singularities the axiom a vector fields involved in the bifurcation exhibit a basic set equivalent to the suspension of a three symbol subshift the attractors arising from this kind of bifurcation are not equivalent to the geometric lorenz attractors

the phase boundary in dilute and random ising and potts ferromagnets the authors present an approach to dilute ising and potts models based on the fortuin kasteleyn random cluster representation which is simultaneously rigorous intuitive and surprisingly simple their analysis yields with no dimensional restrictions or other caveats the following asymptotic form of the phase boundary for the regular dilute model in which bonds have constant ferromagnetic coupling j with probability p and are vacant with probability 1 p the critical temperature scales as exp j ktc p approximately mod p pc mod implying that the crossover exponent is phi 1 if the constant couplings are replaced by a distribution f j with mass near j 0 quite different crossover behaviour is observed for example if f j approximately jalpha then for p near pc tc p approximately mod p pc mod 1 alpha

equivalent classes of integrable nonlinear evolution equations and generalised miura transformations the authors write down the recursion operator which defines the class of integrable nonlinear evolution equations nee associated with a spectral problem sp for matrices of rank 2 depending quadratically on the spectral parameter then they show the existence of four different transformations which transform the given sp into the well known one of zakharov and shabat zs 1972 by composing these transformations they recover among others the so called elementary backlund transformations for the zs sp under some restrictions one is able to prove the complete equivalence of the given glass of nee to the one associated with the zs sp

pseudo orbit shadowing in the family of tent maps on montre que les applications en tente ont la propriete d ombrage pour presque tous les parametres s mais elles n ont pas cette propriete pour un ensemble dense non denombrable des parametres on montre que pour une application tente chaque pseudo orbite peut etre approchee par une orbite actuelle d une application en tente avec une boucle peut etre legerement plus grande

analysis of semiparametric regression models for repeated outcomes in the presence of missing data abstract we propose a class of inverse probability of censoring weighted estimators for the parameters of models for the dependence of the mean of a vector of correlated response variables on a vector of explanatory variables in the presence of missing response data the proposed estimators do not require full specification of the likelihood they can be viewed as an extension of generalized estimating equations estimators that allow for the data to be missing at random but not missing completely at random these estimators can be used to correct for dependent censoring and nonrandom noncompliance in randomized clinical trials studying the effect of a treatment on the evolution over time of the mean of a response variable the likelihood based parametric g computation algorithm estimator may also be used to attempt to correct for dependent censoring and nonrandom noncompliance but because of possible model misspecification the parametric g computation algorithm estimator in contrast with the proposed w

a rapid dynamical monte carlo algorithm for glassy systems we present a dynamical monte carlo algorithm which is applicable to systems satisfying a clustering condition during the dynamical evolution the system is mostly trapped in deep local minima as happens in glasses pinning problems etc we compare the algorithm to the usual monte carlo algorithm using as an example the bernasconi model in this model a straightforward implementation of the algorithm gives an improvement of several orders of magnitude in computational speed with respect to a recent already very efficient implementation of the algorithm of bortz et al 1975

stochastic lattice models with several absorbing states we study two models with n equivalent absorbing states that generalize the domany kinzel cellular automaton and the contact process numerical investigations show that for n 2 both models belong to the same universality class as branching annihilating walks with an even number of offspring unlike previously known models these models have no explicit parity conservation law

distribution of dynamical quantities in the contact process random walks and quantum spin chains in random environments we study the distribution of dynamical quantities in various one dimensional disordered models the critical behavior of which is described by an infinite randomness fixed point in the disordered contact process the survival probability mathcal p t is found to show multiscaling in the critical point meaning that mathcal p t t ensuremath ensuremath delta where the environment and time dependent exponent ensuremath delta has a universal limit distribution when t ensuremath rightarrow ensuremath infty the limit distribution is determined by the strong disorder renormalization group method analytically in the end point of a semi infinite lattice where it is found to be exponential while in the infinite system conjectures on its limiting behaviors for small and large ensuremath delta which are based on numerical results are formulated by the same method the survival probability in the problem of random walks in random environments is also shown to exhibit multiscaling with an exponential limit distribution in addition to this the imaginary time spin spin autocorrelation function of the random transverse field ising chain is found to have a form similar to that of survival probability of the contact process at the level of the renormalization approach consequently a relationship between the corresponding limit distributions in the two problems can be established finally the distribution of the spontaneous magnetization in this model is also discussed

sample size estimation for gee method for comparing slopes in repeated measurements data sample size calculation is an important component at the design stage of clinical trials controlled clinical trials often use a repeated measurement design in which individuals are randomly assigned to treatment groups and followed up for measurements at intervals across a treatment period of fixed duration in studies with repeated measurements one of the popular primary interests is the comparison of the rates of change in a response variable between groups statistical models for calculating sample sizes for repeated measurement designs often fail to take into account the impact of missing data correctly in this paper we propose to use the generalized estimating equation gee method in comparing the rates of change in repeated measurements and introduce closed form formulae for sample size and power that can be calculated using a scientific calculator since the sample size formula is based on asymptotic theory we investigate the performance of the estimated sample size in practical settings through simulations

quenched randomness at first order transitions abstract a rigorous theorem due to aizenman and wehr asserts that there can be no latent heat in a two dimensional system with quenched random impurities we examine this result and its possible extensions to higher dimensions in the context of several models for systems whose pure versions undergo a strong first order transition we show that there is an asymptotically exact mapping to the random field ising model at the level of the interface between the ordered and disordered phases this provides a physical explanation for the above result and also implies a correspondence between the problems in higher dimensions including scaling relations between their exponents the particular example of the q state potts model in two dimensions has been considered in detail by various authors and we review the numerical results obtained for this case turning to weak fluctuation driven first order transitions we describe analytic renormalization group calculations which show how the continuous nature of the transition is restored by randomness in two dimensions

discontinuity of the spin wave stiffness in the two dimensional xy model using a graphical representation based on the wolff algorithm the classical d dimensional xy model and some related spin systems are studied it is proved that in d 2 the predicted discontinuity in the spin wave stiffness indeed occurs further the critical properties of the spin system are related to percolation properties of the graphical representation in particular a suitably defined notion of percolation in the graphical representation is proved to be the necessary and sufficient condition for positivity of the spontaneous magnetization

exact results on sinai s diffusion we study the continuum version of sinai s problem of a random walker in a random force field in one dimension a method of stochastic representation is used to represent various probability distributions in this problem mean probability density function and first passage time distributions this method reproduces already known rigorous results and also confirms directly some recent results derived using approximation schemes we demonstrate clearly in the sinai scaling regime that the disorder dominates the problem and that the thermal distributions tend to zero one laws

sample size and power determination for clustered repeated measurements it is common in epidemiological and clinical studies that each subject has repeated measurements on a single common variable while the subjects are also clustered to compute sample size or power of a test we have to consider two types of correlation correlation among repeated measurements within the same subject and correlation among subjects in the same cluster we develop based on generalized estimating equations procedures for computing sample size and power with clustered repeated measurements explicit formulae are derived for comparing two means two slopes and two proportions under several simple correlation structures

shadowing internal chain transitivity and α limit sets abstract let f x x be a continuous map on a compact metric space x and let f f and i c t f denote the set of limit sets limit sets and nonempty closed internally chain transitive sets respectively we show that if the map f has shadowing then every element of i c t f can be approximated to any prescribed accuracy by both the limit set and the limit set of a full trajectory furthermore if f is additionally expansive then every element of i c t f is equal to both the limit set and the limit set of a full trajectory in particular this means that shadowing guarantees that f f i c t f where the closures are taken with respect to the hausdorff topology on the space of compact sets whilst the addition of expansivity entails f f i c t f we progress by introducing novel variants of shadowing which we use to characterise both maps for which f i c t f and maps for which f i c t f

numerical analysis of the rebellious voter model the rebellious voter model introduced by sturm and swart 2008 is a variation of the standard one dimensional voter model in which types that are locally in the minority have an advantage it is related both through duality and through the evolution of its interfaces to a system of branching annihilating random walks that is believed to belong to the parity conservation universality class this paper presents numerical data for the rebellious voter model and for a closely related one sided version of the model both models appear to exhibit a phase transition between noncoexistence and coexistence as the advantage for minority types is increased for the one sided model but not for the original two sided rebellious voter model it appears that the critical point is exactly a half and two important functions of the process are given by simple explicit formulas a fact for which we have no explanation

symbolic dynamics of noisy chaos abstract one model of randomness observed in physical systems is that low dimensional deterministic chaotic attractors underly the observations a phenomenological theory of chaotic dynamics requires an accounting of the information flow from the observed system to the observer the amount of information available in observations and just how this information affects predictions of the system s future behavior in an effort to develop such a description we discuss the information theory of highly discretized observations of random behavior metric entropy and topological entropy are well defined invariant measures of such an attractor s level of chaos and are computable using symbolic dynamics real physical systems that display low dimensional dynamics are however inevitably coupled to high dimensional randomless e g thermal noise we investigate the effects of such fluctuations coupled to deterministic chaotic systems in particular the metric entropy s response to the fluctuations we find that the entropy increases with a power law in the noise level and that the convergence of the entropy and the effect of fluctuations can be cast as a scaling theory we also argue that in addition to the metric entropy there is a second scaling invariant quantity that characterizes a deterministic system with added fluctuations i0 the maximum average information obtainable about the initial condition that produces a particular sequence of measurements or symbols

correlation length bounds for disordered ising ferromagnets thed dimensional nearest neighbor disordered ising ferromagnet h sum j ij sigma i sigma j is studied as a function of both temperature t and a disorder parameter which measures the size of fluctuations of couplingsjij 0 a finite size scaling correlation length f t is defined in terms of the magnetic response of finite samples this correlation length is shown to be equivalent in the scaling sense to the quenched average correlation length t defined as the asymptotic decay rate of the quenched average two point function furthermore the magnetic response criterion which defines f is shown to have a scale invariant property at the critical point the above results enable us to prove that the quenched correlation length satisfies c left log xi t right xi t geqq left t t c right 2 mathord left vphantom 2 d right kern nulldelimiterspace d which implies the boundv 2 d for the quenched correlation length exponent

on the concept of attractor this note proposes a definition for the concept of attractor based on the probable asymptotic behavior of orbits the definition is sufficiently broad so that every smooth compact dynamical system has at least one attractor

sample size calculations for studies with correlated ordinal outcomes correlated ordinal response data often arise in public health studies sample size power calculations are a crucial step in designing such studies to ensure an adequate sample to detect a significant effect here we extend rochon s method of sample size estimation with a repeated binary response to the ordinal case the proposed sample size calculations are based on an analysis with generalized estimating equations gee and inference with the wald test simulation results demonstrate the merit of the proposed power calculations analysis of an arthritis clinical trial is used for illustration

field theory of branching and annihilating random walks we develop a systematic analytic approach to the problem of branching and annihilating random walks equivalent to the diffusion limited reaction processes 2a and a m 1 a where m 1 starting from the master equation a field theoretic representation of the problem is derived and fluctuation effects are taken into account via diagrammatic and renormalization group methods for d 2 the mean field rate equation which predicts an active phase as soon as the branching process is switched on applies qualitatively for both even and odd m but the behavior in lower dimensions is shown to be quite different for these two cases for even m and d near 2 the active phase still appears immediately but with nontrivial crossover exponents which we compute in an expansion in 2 d and with logarithmic corrections in d 2 however there exists a second critical dimension d c 4 3 below which a nontrivial inactive phase emerges with asymptotic behavior characteristic of the pure annihilation process this is confirmed by an exact calculation in d 1 the subsequent transition to the active phase which represents a new nontrivial dynamic universality class is then investigated within a truncated loop expansion which appears to give a correct qualitative picture the model with m 2 is also generalized to n species of particles which provides yet another universality class and which is exactly solvable in the limit n for odd m we show that the fluctuations of the annihilation process are strong enough to create a nontrivial inactive phase for all d 2 in this case the transition to the active phase is in the directed percolation universality class finally we study the modification when the annihilation reaction is 3a when m 0 mod 3 the system is always in its active phase but with logarithmic crossover corrections for d 1 while the other cases should exhibit a directed percolation transition out of a fluctuation driven inactive phase

random walkers in one dimensional random environments exact renormalization group analysis sinai s model of diffusion in one dimension with random local bias is studied by a real space renormalization group which yields exact results at long times the effects of an additional small uniform bias force are also studied we obtain analytically the scaling form of the distribution of the position x t of a particle the probability of it not returning to the origin and the distributions of first passage times in an infinite sample as well as in the presence of a boundary and in a finite but large sample we compute the distribution of the meeting time of two particles in the same environment we also obtain a detailed analytic description of the thermally averaged trajectories by computing quantities such as the joint distribution of the number of returns and of the number of jumps forward these quantities obey multifractal scaling characterized by generalized persistence exponents ensuremath theta g which we compute in the presence of a small bias the number of returns to the origin becomes finite characterized by a universal scaling function which we obtain the full statistics of the distribution of successive times of return of thermally averaged trajectories is obtained as well as detailed analytical information about correlations between directions and times of successive jumps the two time distribution of the positions of a particle x t and x t ensuremath with tg t ensuremath is also computed exactly it is found to exhibit aging with several time regimes characterized by different behaviors in the unbiased case for t ensuremath t ensuremath ensuremath sim t ensuremath ensuremath alpha with ensuremath alpha g1 it exhibits a mathrm ln t mathrm ln t ensuremath scaling with a singularity at coinciding rescaled positions x t x t ensuremath this singularity is a novel feature and corresponds to particles that remain in a renormalized valley for closer times ensuremath alpha l1 the two time diffusion front exhibits a quasiequilibrium regime with a mathrm ln t ensuremath t ensuremath mathrm ln t ensuremath behavior which we compute the crossover to a t t ensuremath aging form in the presence of a small bias is also obtained analytically rare events corresponding to intermittent splitting of the thermal packet between separated wells which dominate some averaged observables are also characterized in detail connections with the green function of a one dimensional schr odinger problem and quantum spin chains are discussed

anomalous diffusion localization aging and subaging effects in trap models at very low temperature we study in detail the dynamics of the one dimensional symmetric trap model via a real space renormalization procedure which becomes exact in the limit of zero temperature in this limit the diffusion front in each sample consists of two delta peaks which are completely out of equilibrium with each other the statistics of the positions and weights of these delta peaks over the samples allows to obtain explicit results for all observables in the limit t 0 we first compute disorder averages of one time observables such as the diffusion front the thermal width the localization parameters the two particle correlation function and the generating function of thermal cumulants of the position we then study aging and subaging effects our approach reproduces very simply the two different aging exponents and yields explicit forms for scaling functions of the various two time correlations we also extend the real space renormalization group method to include systematic corrections to the previous zero temperature procedure via a series expansion in t we then consider the generalized trap model with parameter alpha in 0 1 and obtain that the large scale effective model at low temperature does not depend on alpha in any dimension so that the only observables sensitive to alpha are those that measure the local persistence such as the probability to remain exactly in the same trap during a time interval finally we extend our approach at a scaling level for the trap model in d 2 and obtain the two relevant time scales for aging properties