local existence of solutions to the free boundary value problem for the primitive equations of the ocean lions temam and wang in probleme a frontiere libre pour les modeles couples de l ocean et de l atmosphere acad sci paris c r 318 12 1165 1171 1994 introduced a free surface model for the primitive equations of the ocean in this paper we establish the local well posedness of the model with analytic initial data

adjustments to the mantel haenszel chi square statistic and odds ratio variance estimator when the data are clustered dependence between observations on a dichotomous variable renders invalid the usual chi square tests of independence and inflates the variances of parameter estimates such a situation occurs for example when subjects consist of members of the same family or with repeated observations on the same person in this paper we describe methods of measuring the extent of correlation or clustering we also develop methods of adjusting the mantel haenszel chi square test statistic and the variance of the mantel haenszel estimate of a common odds ratio in sets of 2 2 contingency tables

fundamental limitations for estimating dimensions and lyapunov exponents in dynamical systems we show that values of the correlation dimension estimated over a decade from the grassberger procaccia algorithm cannot exceed the value 2 log10n if n is the number of points in the time series when this bound is saturated it is thus not legitimate to conclude that low dimensional dynamics is present the estimation of lyapunov exponents is also discussed

the analysis of categorical data from complex sample surveys chi squared tests for goodness of fit and independence in two way tables abstract the effect of stratification and clustering on the asymptotic distributions of standard pearson chi squared test statistics for goodness of fit simple hypothesis and independence in a two way contingency table denoted as x 2 and xi 2 respectively is investigated it is shown that both x 2 and xi 2 are asymptotically distributed as weighted sums of independent 1 2 random variables the weights are then related to the familiar design effects deffs used by survey samplers a simple correction to x 2 which requires only the knowledge of variance estimates or deffs for individual cells in the goodness of fit problem is proposed and empirical results on the performance of corrected x 2 provided empirical work on xi 2 indicated that the distortion of nominal significance level is substantially smaller with xi 2 than with x 2 some results under simple models for clustering are also given

odds ratio inference with dependent data summary when data can be presented as a series of k 2 x 2 tables with cell counts xi ni xi yi mi yi it is often assumed that xi and yi are binomially distributed this paper deals with inference for the common odds ratio i l when the binomial assumption is invalid when k increases the consistency and asymptotic normality of the mantel haenszel 1959 estimator is derived the conditional maximum likelihood estimator is shown to be inconsistent and the asymptotic bias is computed when either the first order markov chain or beta binomial model is assumed the mantel haenszel test for testing f 1 is also shown to be inappropriate through some simulation studies two consistent test statistics are proposed and shown to be comparable to each other in terms of size and efficiency some possible further work is described

local in time solvability and space analyticity for the navier stokes equations with bmo type initial data it is proved that there exists a local in time solution u in c 0 t bmo mathbb r d d of the navier stokes equations such that every u t has an analytic extension on a complex domain whose size only depends on t and increases with t and the external force f assuming only that the initial velocity u 0 is a local bmo function our method for proving this is a combination and refinement of the work by grujic and kukavica j funct anal 152 2 447 466 1998 https doi org 10 1006 jfan 1997 3167 guberovic discrete contin dyn syst 27 1 231 236 2010 https doi org 10 3934 dcds 2010 27 231 and kozono et al kyushu j math 57 2 303 324 2003 https doi org 10 2206 kyushujm 57 303 one challenging step is the estimation of the heat and stokes semigroups from bmo type spaces to l infty a result that is itself of independent interest we also apply the idea to the analyticity of vorticity with the assistance of calderon zygmund theory

efficient analysis of case control studies with sample weights analysis of population based case control studies with complex sampling designs is challenging because the sample selection probabilities and therefore the sample weights depend on the response variable and covariates commonly the design consistent weighted estimators of the parameters of the population regression model are obtained by solving sample weighted estimating equations weighted estimators however are known to be inefficient when the weights are highly variable as is typical for case control designs in this paper we propose two alternative estimators that have higher efficiency and smaller finite sample bias compared with the weighted estimator both methods incorporate the information included in the sample weights by modeling the sample expectation of the weights conditional on design variables we discuss benefits and limitations of each of the two proposed estimators emphasizing efficiency and robustness we compare the finite sample properties of the two new estimators and traditionally used weighted estimators with the use of simulated data under various sampling scenarios we apply the methods to the u s kidney cancer case control study to identify risk factors published 2012 this article is a us government work and is in the public domain in the usa

predictability in the large an extension of the concept of lyapunov exponent we investigate the predictability problem in dynamical systems with many degrees of freedom and a wide spectrum of temporal scales in particular we study the case of three dimensional turbulence at high reynolds numbers by introducing a finite size lyapunov exponent which measures the growth rate of finite size perturbations for sufficiently small perturbations this quantity coincides with the usual lyapunov exponent when the perturbation is still small compared to large scale fluctuations but large compared to fluctuations at the smallest dynamically active scales the finite size lyapunov exponent is inversely proportional to the square of the perturbation size our results are supported by numerical experiments on shell models we find that intermittency corrections do not change the scaling law of predictability we also discuss the relation between the finite size lyapunov exponent and information entropy

fitting logistic models under case control or choice based sampling on compare deux approches dans le cas important de l ajustement des modeles de regression logistique

finite correlation dimension for stochastic systems with power law spectra abstract we discuss a counter example to the traditional view that stochastic processes lead to a non convergence of the correlation dimension in computed or measured time series specifically we show that a simple class of colored random noises characterized by a power law power spectrum have a finite and predictable value for the correlation dimension these results have implications on the experimental study of deterministic chaos as they indicate that the soie observation of a finite fractal dimension from the analysis of a time series is not sufficient to infer the presence of a strange attractor in the system dynamics we demonstrate that the types of random noises considered herein may be given an interpretation in terms of their fractal properties the consequent exploitation of the non gaussian behavior of these random noises leads us to the introduction of a new time series analysis method which we call multivariate scaling analysis we apply this approach to characterize several global properties of random noise

standard errors for attributable risk for simple and complex sample designs adjusted attributable risk ar is the proportion of diseased individuals in a population that is due to an exposure we consider estimates of adjusted ar based on odds ratios from logistic regression to adjust for confounding influence function methods used in survey sampling are applied to obtain simple and easily programmable expressions for estimating the variance of ar these variance estimators can be applied to data from case control cross sectional and cohort studies with or without frequency or individual matching and for sample designs with subject samples that range from simple random samples to sample weighted multistage stratified cluster samples like those used in national household surveys the variance estimation of ar is illustrated with i a weighted stratified multistage clustered cross sectional study of childhood asthma from the third national health and examination survey nhanes iii and ii a frequency matched case control study of melanoma skin cancer

strong chaos without the butterfly effect in dynamical systems with feedback we discuss the predictability of a system that drives a chaotic system with a positive lyapunov exponent in the absence of feedback the driver is regular and fully predictable with a small feedback of strength the state of the driver can be predicted up to a time diverging with a power of although the total system is strongly chaotic the exponential amplification of the uncertainty on the initial conditions of the driver coexists with very long predictability times as illustrated in a model of coupled maps and of three point vortices in a disc

local analyticity radii of solutions to the 3d navier stokes equations with locally analytic forcing abstract we introduce a new method for establishing local analyticity and estimating the local analyticity radius of a solutions to the 3d navier stokes equations at interior points the approach is based on rephrasing the problem in terms of second order parabolic systems which are then estimated using the mild solution approach the estimates agree with the global analyticity radius from 16 up to a logarithm

finite sample properties of some old and some new estimators of a common odds ratio from multiple 2 2 tables abstract a simulation study was used to determine the finite sample properties of various estimators of a common odds ratio from multiple 2 2 tables the maximum likelihood mantel haenszel and woolf estimators plus four variants of each were considered the original woolf estimator and one of its variants are dismissed on the grounds that they often cannot be calculated in terms of minimum bias maximum likelihood is the recommended procedure after adding 25 to each cell

effects of cluster sampling on epidemiologic analysis in population based case control studies we consider population based case control designs in which controls are selected by one of three cluster sampling plans from the entire population at risk the effects of cluster sampling on classical epidemiologic procedures are investigated and appropriately modified procedures are developed in particular modified procedures for testing the homogeneity of odds ratios across strata and for estimating and testing a common odds ratio are presented simulations that use the data from the 1970 health interview survey as a population suggest that classical procedures may be fairly robust in the presence of cluster sampling a more extreme example based on a mixed multinomial model clearly demonstrates that the classical mantel haenszel 1959 journal of the national cancer institute 22 719 748 and woolf haldane tests of no exposure effect may have sizes exceeding nominal levels and confidence intervals with less than nominal coverage under an alternative hypothesis classical estimates of odds ratios may also be biased with non self weighting cluster samples the modified procedures we propose remedy these defects

slow and fast dynamics in coupled systems a time series analysis view abstract we study the dynamics of systems with different timescales when access only to the slow variables is allowed we use the concept of finite size lyapunov exponent fsle and consider both the cases when the equations of motion for the slow components are known and the situation when a scalar time series of one of the slow variables has been measured a discussion on the effects of parametrizing the fast dynamics is given we show that although the computation of the largest lyapunov exponent can be practically infeasible in complex dynamical systems the computation of the fsle allows to extract information on the characteristic time and on the predictability of the large scale slow time dynamics even with moderate statistics and unresolved small scales

macroscopic chaos in globally coupled maps abstract we study the coherent dynamics of globally coupled maps showing macroscopic chaos with this term we indicate the hydrodynamical like irregular behavior of some global observables with typical times much longer than the times related to the evolution of the single or microscopic elements of the system the usual lyapunov exponent is not able to capture the essential features of this macroscopic phenomenon using the recently introduced notion of finite size lyapunov exponent we characterize in a consistent way these macroscopic behaviors basically at small values of the perturbation we recover the usual microscopic lyapunov exponent while at larger values a sort of macroscopic lyapunov exponent emerges which can be much smaller than the former a quantitative characterization of the chaotic motion at hydrodynamical level is then possible even in the absence of the explicit equations for the time evolution of the macroscopic observables

distinguishing between low dimensional dynamics and randomness in measured time series the success of current attempts to distinguish between low dimensional chaos and random behavior in a time series of observations is considered first we discuss stationary stochastic processes which produce finite numerical estimates of the correlation dimension and k2 entropy under naive application of correlation integral methods we then consider several straightforward tests to evaluate whether correlation integral methods reflect the global geometry or the local fractal structure of the trajectory this determines whether the methods are applicable to a given series if they are we evaluate the significance of a particular result for example by considering the results of the analysis of stochastic signals with statistical properties similar to those of observed series from the examples considered it is clear that the correlation integral should not be used in isolation but as one of a collection of tools to distinguish chaos from stochasticity

adjustments to the mantel haenszel test for data from stratified multistage surveys the usual form of the mantel haenszel test statistic assumes independent observations this is inappropriate for data from a stratified multistage survey two alternative adjustments to the test statistic are developed to deal with this a a modification of the effective sample size for each row of each table using the design effects extending a method proposed by donald and donner for familial aggregation studies b a taylor series approximation to the variance of the square root of the numerator of the mantel haenszel statistic both methods are evaluated by application to both simulated and real data the two methods perform equally well and offer a considerable improvement over the unadjusted test statistic when observations from the same cluster are highly correlated a simplified adjustment is also considered as is the need for correction to the variance of the odds ratio estimator

analyticity of solutions for a generalized euler equation abstract we consider the so called lake and great lake equations which are shallow water equations that describe the long time motion of an inviscid incompressible fluid contained in a shallow basin with a slowly spatially varying bottom a free upper surface and vertical side walls under the influence of gravity and in the limit of small characteristic velocities and very small surface amplitude if these equations are posed on a space periodic domain and the initial data are real analytic the solution remains real analytic for all times the proof is based on a characterization of gevrey classes in terms of decay of fourier coefficients in particular our result recovers known results for the euler equations in two and three spatial dimensions we believe the proof is new

characterization of strange attractors a new measure of strange attractors is introduced which offers a practical algorithm to determine their character from the time series of a single observable the relation of this new measure to fractal dimension and information theoretic entropy is discussed

determining lyapunov exponents from a time series we present the first algorithms that allow the estimation of non negative lyapunov exponents from an experimental time series lyapunov exponents which provide a qualitative and quantitative characterization of dynamical behavior are related to the exponentially fast divergence or convergence of nearby orbits in phase space a system with one or more positive lyapunov exponents is defined to be chaotic our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems we monitor the long term growth rate of small volume elements in an attractor the method is tested on model systems with known lyapunov spectra and applied to data for the belousov zhabotinskii reaction and couette taylor flow