controlling correlations in latin hypercube samples abstract monte carlo integration is competitive for high dimensional integrands latin hypercube sampling is a stratification technique that reduces the variance of the integral previous work has shown that the additive part of the integrand is integrated with error op n 1 2 under latin hypercube sampling with n integrand evaluations a bilinear part of the integrand is more accurately estimated if the sample correlations among input variables are negligible other authors have proposed an algorithm for controlling these correlations we show that their method reduces the correlations by roughly a factor of 3 for 10 n 500 we propose a method that based on simulations appears to produce correlations of order op n 3 2 an analysis of the algorithm indicates that it cannot be expected to do better than n 3 2

f expansivity for borel measures abstract we introduce the notion of f expansive measure by making the dynamical ball in 4 to depend on a given subset f of the set of all the reparametrizations h we prove that these measures satisfy some interesting properties resembling the expansive ones these include the equivalence with expansivity when f h the vanishing along the orbits the absence of singularities in the support the f expansivity with respect to time t maps the invariance under equivalence and the characterization for suspensions we also analyze the support of the f expansive measures and prove that there exists a dense subset of measures in the set of f expansive measures all of them with a common support finally we extend to flows the recent result for homeomorphisms in 11

homoclinic tangencies and hyperbolicity for surface diffeomorphisms we prove here that in the complement of the closure of the hyperbolic surface diffeomorphisms the ones exhibiting a homoclinic tangency are c 1 dense this represents a step towards the global understanding of dynamics of surface diffeomorphisms

bayesian prediction of deterministic functions with applications to the design and analysis of computer experiments abstract this article is concerned with prediction of a function y t over a multidimensional domain t given the function values at a set of sites t 1 t 2 t n in t and with the design that is with the selection of those sites the motivating application is the design and analysis of computer experiments where t determines the input to a computer model of a physical or behavioral system and y t is a response that is part of the output or is calculated from it following a bayesian formulation prior uncertainty about the function y is expressed by means of a random function y which is taken here to be a gaussian stochastic process the mean of the posterior process can be used as the prediction function t and the variance can be used as a measure of uncertainty this kind of approach has been used previously in bayesian interpolation and is strongly related to the kriging methods used in geostatistics here emphasis is placed on product linear and product cubic correlation func

interleaved lattice based minimax distance designs summarywe propose a new method to construct maximin distance designs with arbitrary numbers of dimensions and points the proposed designs hold interleaved layer structures and are by far the best maximin distance designs in four or more dimensions applicable to distance measures with equal or unequal weights our method is useful for emulating computer experiments when a relatively accurate a priori guess on variable importance is available

a general approach to analyzing epidemiologic data that contain misclassification errors misclassification is a common source of bias and reduced efficiency in the analysis of discrete data several methods have been proposed to adjust for misclassification using information on error rates i gathered by resampling the study population ii gathered by sampling a separate population or iii assumed a priori we present unified methods for incorporating these types of information into analyses based on log linear models and maximum likelihood estimation general variance expressions are developed examples from epidemiologic studies are used to demonstrate the proposed methodology

measure expansive diffeomorphisms abstract in this paper measure expansive diffeomorphisms are considered and the characterizations of the c 1 interiors of the set of measure expansive diffeomorphisms are obtained

the first approximation algorithm for the maximin latin hypercube design problem in metamodeling the choice of sampling points is crucial for the quality of the model in this context the maximin latin hypercube designs lhd with their space filling and noncollapsing properties are particularly efficient to this day there is no polynomial time algorithm that produces optimal maximin lhds i e in which the minimum distance between two points the separation distance is maximal we are interested in lhds with a separation distance as large as possible the algorithm we propose ies gives an approximate solution to the lhd problem regardless of its dimension and size with a theoretical performance guarantee we introduce two upper bounds for the separation distance to find its approximation ratio its performance is compared with the best metaheuristic algorithm known for this problem an appropriate simulated annealing scheme our algorithm defeats the metaheuristic algorithm for large instances of the problem while having a very short running time

columnwise pairwise algorithms with applications to the construction of supersaturated designs motivated by the construction of supersaturated designs we develop a class of algorithms called columnwise pairwise exchange algorithms they differ from the k exchange algorithms in two respects 1 they exchange columns instead of rows of the design matrix and 2 they employ a pairwise adjustment in the search for a better column the proposed algorithms perform very well in the construction of supersaturated designs both for a single criterion and for multiple criteria they are also applicable to the construction of designs that are not supersaturated

a comparison of three methods for selecting values of input variables in the analysis of output from a computer code two types of sampling plans are examined as alternatives to simple random sampling in monte carlo studies these plans are shown to be improvements over simple random sampling with respect to variance for a class of estimators which includes the sample mean and the empirical distribution function

bounds for maximin latin hypercube designs latin hypercube designs lhds play an important role when approximating computer simulation models to obtain good space filling properties the maximin criterion is frequently used unfortunately constructing maximin lhds can be quite time consuming when the number of dimensions and design points increase in these cases we can use heuristical maximin lhds in this paper we construct bounds for the separation distance of certain classes of maximin lhds these bounds are useful for assessing the quality of heuristical maximin lhds until now only upper bounds are known for the separation distance of certain classes of unrestricted maximin designs i e for maximin designs without a latin hypercube structure the separation distance of maximin lhds also satisfies these unrestricted bounds by using some of the special properties of lhds we are able to find new and tighter bounds for maximin lhds within the different methods used to determine the upper bounds a variety of combinatorial optimization techniques are employed mixed integer programming the traveling salesman problem and the graph covering problem are among the formulations used to obtain the bounds besides these bounds also a construction method is described for generating lhds that meet baer s bound for the l distance measure for certain values of n

the asymptotic efficiency of tests using misclassified data in contingency tables a simple expression is given for the approximate upper bound of the asymptotic relative efficiency of tests between nested loglinear models using misclassified data versus those using data with no classification errors this efficiency depends on the probabilities of data being misclassified into the wrong cells of the contingency table an example demonstrates that the loss of efficiency due to misclassification can be substantial

on the dynamics of dominated splitting let f m m be a c 2 dieomorphism of a compact surface we give a complete description of the dynamics of any compact invariant set having dominated splitting in particular we prove a spectral decomposition theorem for the limit set l f under the assumption of dominated splitting moreover we describe all the bifurcations that these systems can exhibit and the dierent types of dynamics that could follow for small c r perturbations

a model for multinomial response error applied to labor flows abstract a model for the response error associated with reported categorical data is developed the model is used to construct estimators for the interior cells of a two way table with marginals subject to independent response error the estimation procedure is applied to the month to month table of employment status obtained from the u s current population survey

finding maximin latin hypercube designs by iterated local search heuristics the maximin lhd problem calls for arranging n points in a k dimensional grid so that no pair of points share a coordinate and the distance of the closest pair of points is as large as possible in this paper we propose to tackle this problem by heuristic algorithms belonging to the iterated local search ils family and show through some computational experiments that the proposed algorithms compare very well with different heuristic approaches in the established literature

maximin latin hypercube designs in two dimensions the problem of finding a maximin latin hypercube design in two dimensions can be described as positioning n nonattacking rooks on an n a n chessboard such that the minimal distance between pairs of rooks is maximized maximin latin hypercube designs are important for the approximation and optimization of black box functions in this paper general formulas are derived for maximin latin hypercube designs for general n when the distance measure is l or l1 furthermore for the distance measure l2 we obtain maximin latin hypercube designs for n 70 and approximate maximin latin hypercube designs for other values of n all these maximin latin hypercube designs can be downloaded from the website http www spacefillingdesigns nl we show that the reduction in the maximin distance caused by imposing the latin hypercube design structure is small this justifies the use of maximin latin hypercube designs instead of unrestricted designs

on the ergodicity of partially hyperbolic systems pugh and shub have conjectured that essential accessibility implies ergodicity for a c partially hyperbolic volume preserving diffeomorphism we prove this conjecture under a mild center bunching assumption which is satisfied in particular by all partially hyperbolic systems with 1 dimensional center bundle we also obtain ergodicity results for c 1ci partially hyperbolic systems

hierarchical log linear models not preserved by classification error abstract a model of bross 1954 for classification error in 2 2 contingency tables is extended to higher dimensional tables it is known mote and anderson 1965 that the usual hypothesis tests of independence for a sampled two dimensional table have the nominal significance level in the presence of misclassification a simple criterion is given to determine which hierarchical log linear models in higher dimensional tables do not share this property that is are not preserved by classification error

log linear models for doubly sampled categorical data fitted by the em algorithm abstract double sampling experiments can be expressed as incomplete multiway contingency tables and analyzed by using techniques appropriate for fitting log linear models the framework described can be applied to experiments with any number of factors and measurement devices maximum likelihood estimation via the em algorithm leads to straightforward expressions for covariances of estimates of the parameters and functions of the parameters

asymptotic measure expansive diffeomorphisms abstract in this paper the notion of asymptotic measure expansiveness is introduced and its relationship with dominated splitting is considered it is proved that if a diffeomorphism admits a co dimension one dominated splitting then it is asymptotic measure expansive also a diffeomorphism with a homoclinic tangency can be perturbed to a non asymptotic measure expansive diffeomorphism