transition phenomena in cellular automata rule space abstract we define several qualitative classes of cellular automata ca behavior based on various statistical measures and describe how the space of all cellular automata is organized as a cellular automaton is changed by varying entries in its rule table abrupt changes in qualitative behavior may occur these abrupt changes have the character of bifurcations in smooth dynamical systems or of phase transitions in statistical mechanical systems the most complex ca rules exhibit many of the characteristics of second order transitions suggesting an association between computation complexity and critical phenomena

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

annealed and quenched inhomogeneous cellular automata inca a probabilistic one dimensional cellular automaton model by domany and kinzel is mapped into an inhomogeneous cellular automaton with the boolean functions xor and and as transition rules wolfram s classification is recovered by varying the frequency of these two simple rules and by quenching or annealing the inhomogeneity in particular class 4 is related to critical behavior in directed percolation also the critical slowing down of second order phase transitions is related to a stochastic version of the classical halting problem of computation theory

failure time regression with continuous covariates measured with error summary we consider failure time regression analysis with an auxiliary variable in the presence of a validation sample we extend the nonparametric inference procedure of zhou and pepe to handle a continuous auxiliary or proxy covariate we estimate the induced relative risk function with a kernel smoother and allow the selection probability of the validation set to depend on the observed covariates we present some asymptotic properties for the kernel estimator and provide some simulation results the method proposed is illustrated with a data set from an on going epidemiologic study

universality and complexity in cellular automata abstract cellular automata are discrete dynamical systems with simple construction but complex self organizing behaviour evidence is presented that all one dimensional cellular automata fall into four distinct universality classes characterizations of the structures generated in these classes are discussed three classes exhibit behaviour analogous to limit points limit cycles and chaotic attractors the fourth class is probably capable of universal computation so that properties of its infinite time behaviour are undecidable

bias analysis and simex approach in generalized linear mixed measurement error models abstract we consider generalized linear mixed models glmms for clustered data when one of the predictors is measured with error when the measurement error is additive and normally distributed and the error prone predictor is itself normally distributed we show that the observed data also follow a glmm but with a different fixed effects structure from the original model a different and more complex random effects structure and restrictions on the parameters this characterization enables us to compute the biases that result in common glmms when one ignores measurement error for instance in one common situation the biases in parameter estimates become larger as the number of observations within a cluster increases both for regression coefficients and for variance components parameter estimation is described using the simex method a relatively new functional method that makes no assumptions about the structure of the unobservable predictors simulations and an example illustrate the results

emergent properties in random complex automata abstract studies of large randomly assembled binary boolean node automata have demonstrated that such systems can spontaneously exhibit enormously ordered dynamical behavior an important approach to characterizing these behaviors has consisted of studying ensembles of automata ensemble specifications have been based on 1 choice of boolean function regulating each node in the automaton 2 random or biased mappings of the 2 n automata states into themselves 3 the numbers of inputs k per node this article briefly reviews these approaches reports new results on the expected behavior of threshold automata and automata with a particular class of biased mappings in addition it discusses emergent highly ordered dynamical behavior in random automata rich in a specific class of canalizing boolean functions due to the crystallization of powerful subautomata called forcing structures the ordered behaviors may be of importance in biological evolution in physics and in the design of adaptive automata

co evolving non uniform cellular automata to perform computations a major impediment of cellular automata ca stems from the difficulty of utilizing their complex behavior to perform useful computations recent studies by packard and mitchell et al have shown that cas can be evolved to perform a computational task in this paper non uniform cas are studied where each cell may contain a different rule in contrast to the original uniform model we describe experiments in which non uniform cas are evolved to perform the computational task using a local co evolutionary algorithm for radius r 3 we attain peak performance values of 0 92 comparable to those obtained for uniform cas 0 93 0 95 this is notable considering the huge search spaces involved much larger than the uniform case smaller radius cas previously unstudied in this context attain performance values of 0 93 0 94 for r 1 this is considerably higher than the maximal possible uniform ca performance of 0 83 suggesting that non uniformity reduces connectivity requirements we thus demonstrate that 1 non uniform cas can attain high computational performance and 2 such systems can be evolved rather than designed

directed percolation a finite size renormalisation group approach the finite size renormalisation group technique introduced by nightingale 1976 is applied to the directed percolation problem the decay of correlations is anisotropic in this model and finite size scaling is extended to treat such anisotropy precise estimates for critical exponents and percolation probabilities are obtained for site bond and site bond percolation on the square lattice with bonds directed along the positive axes both free boundary conditions for which the results converge linearly with 1 n as n to infinity and helical boundary conditions for which unexpectedly the results converge linearly with 1 n3 are considered

covariate measurement errors and parameter estimation in a failure time regression model summary estimation in cox s failure time regression model is considered when the regression vector is subject to measurement error a hazard function model is induced for the failure rate given the measured covariate and a partial likelihood function is derived for the relative risk parameters this partial likelihood function may involve the baseline hazard function as well as the regression parameter but useful inference techniques arise for testing whether the regression parameter equals zero and for more general inferences in important special cases explicit consideration is given to testing equality of survival curves when group membership is subject to misclassification and to relative risk estimation with normally distributed covariates approaches to regression estimation using the overall likelihood function and a marginal likelihood function based on failure time ranks are also indicated illustration of the possible effect of covariate errors on relative risk estimation is provided

asymptotics for the simex estimator in nonlinear measurement error models abstract cook and stefanski have described a computer intensive method the simex method for approximately consistent estimation in regression problems with additive measurement error in this article we derive the asymptotic distribution of their estimators and show how to compute estimated standard errors these standard error estimators can either be used alone or as prepivoting devices in a bootstrap analysis we also give theoretical justification to some of the phenomena observed by cook and stefanski in their simulations

on using the cox proportional hazards model with missing covariates summary we propose two methods for handling missing covariates in using the cox proportional hazards model the maximum partial likelihood estimator based only on study subjects having complete covariates does not utilise all available information also it is biased when the probability of missingness depends on the failure or censoring time our suggestion is to impute the conditional expectation of the statistic involving missing covariates given the available information the proposed method provides a consistent regression parameter estimator when the probability of missingness depends on the failure or censoring time as well as on the observed covariates also the proposed estimator is more efficient than the estimator suggested previously by lin ying 1993 when data are missing completely at random

regression calibration in failure time regression in this paper we study a regression calibration method for failure time regression analysis when data on some covariates are missing or mismeasured the method estimates the missing data based on the data structure estimated from a validation data set a random subsample of the study cohort in which covariates are always observed ordinary cox 1972 journal of the royal statistical society series b 34 187 220 regression is then applied to estimate the regression coefficients using the observed covariates in the validation data set and the estimated covariates in the nonvalidation data set the method can be easily implemented we present the asymptotic theory of the proposed estimator finite sample performance is examined and compared with an estimated partial likelihood estimator and other related methods via simulation studies where the proposed method performs well even though it is technically inconsistent finally we illustrate the method with a mouse leukemia data set

from equilibrium spin models to probabilistic cellular automata the general equivalence betweend dimensional probabilistic cellular automata pca and d 1 dimensional equilibrium spin models satisfying a disorder condition is first described in a pedagogical way and then used to analyze the phase diagrams the critical behavior and the universality classes of some automata diagrammatic representations of time dependent correlation functions of pca are introduced two important classes of pca are singled out for which these correlation functions simplify 1 quasi hamiltonian automata which have a current carrying steady state and for which some correlation functions are those of ad dimensional static model pca satisfying the detailed balance condition appear as a particular case of these rules for which the current vanishes 2 linear and more generally affine pca for which the diagrammatics reduces to a random walk problem closely related to d 1 dimensional directed saws both problems display a critical behavior with mean field exponents in any dimension the correlation length and effective velocity of propagation of excitations can be calculated for affine pca as is shown on an explicitd 1 example we conclude with some remarks on nonlinear pca for which the diagrammatics is related to reaction diffusion processes and which belong in some cases to the universality class of reggeon field theory

simulation extrapolation the measurement error jackknife abstract this article provides theoretical support for our simulation based estimation procedure simex for measurement error models we do so by establishing a strong relationship between simex estimation and jackknife estimation a result of our investigation is the identification of a variance estimation method for simex that parallels jackknife variance estimation data from the framingham heart study are used to illustrate the variance estimation procedure in logistic regression measurement error models

critical growth phenomena in cellular automata abstract we study a one parameter family of probabilistic cullular automata on square and triagular lattices above a critical parameter value a new dominant invariant phase appears resulting in domain growth in the growth regime a second critical threshold is found above which domains grow at a maximal rate and facet this phenomenon is shown to be equivalent to a certain one dimensional directed percolation problem studied by domany and kinzel 1984 tight bounds are given to the critical probabilities which depend on the lattice these models are of special interest since their behavior corresponds extremely closely to that of certain simple purely deterministic cellular automata

measurement error in covariates in the marginal hazards model for multivariate failure time data nous nous interessons aux erreurs de mesure des covariables dans un modele marginal du risque pour des donnees de survie multivariees nous examinons le biais genere par une erreur de mesure additive normalesans faire d hypothese de distribution pour la vraie covariable sous jacente pour corriger le biais genere par les erreurs de mesures dans l estimation du coefficient de regression du modele marginal nous proposons d utiliser la methode simex et etudions ses proprietes pour des grands et petits echantillons en supposant la variance des erreurs de mesure soit connue soit estimee nous illustrons cette methode avec des donnees de l essai de prevention primaire coronaire des centres de recherche sur les lipides le cholesterol total est la covariable mesuree avec erreur et les delais d apparition d une angine de poitrine et d un infarctus du myocarde sont les criteres correles etudies

phenomenology of nonlocal cellular automata dynamical systems with nonlocal connections have potential applications to economic and biological systems this paper studies the dynamics of nonlocal cellular automata in particular all two state three input nonlocal cellular automata are classified according to the dynamical behavior starting from random initial configurations and random wirings although it is observed that sometimes a rule can have different dynamical behaviors with different wirings the nonlocal cellular automata rule space is studied using a mean field parametrization which is ideal for the situation of random wiring nonlocal cellular automata can be considered as computers carrying out computation at the level of each component their computational abilities are studied from the point of view of whether they contain many basic logical gates in particular i ask the question of whether a three input cellular automaton rule contains the three fundamental logical gates two input rules and and or and one input rule not a particularly interesting edge of chaos nonlocal cellular automaton the rule 184 is studied in detail it is a system of coupled selectors or multiplexers it is also part of the fredkin s gate a proposed fundamental gate for conservative computations this rule exhibits irregular fluctuations of density large coherent structures and long transient times

cox regression with incomplete covariate measurements abstract this article provides a general solution to the problem of missing covariate data under the cox regression model the estimating function for the vector of regression parameters is an approximation to the partial likelihood score function with full covariate measurements and reduces to the pseudolikelihood score function of self and prentice in the special setting of case cohort designs the resulting parameter estimator is consistent and asymptotically normal with a covariance matrix for which a simple and consistent estimator is provided extensive simulation studies show that the large sample approximations are adequate for practical use the proposed approach tends to be more efficient than the complete case analysis especially for large cohorts with infrequent failures for case cohort designs the new methodology offers a variance covariance estimator that is much easier to calculate than the existing ones and allows multiple subcohort augmentations to improve efficiency real data taken f