random attractors for quasi continuous random dynamical systems and applications to stochastic reaction diffusion equations abstract this paper first introduces the so called quasi continuous random dynamical system rds on a separable banach space the quasi continuity is weaker than all the usual continuities and thus is easier to check in practice we then establish a necessary and sufficient condition for the existence of random attractors for the quasi continuous rds we also give a general method to obtain the random attractors for the rds on the banach space l q d for q 2 as an application it is shown that the rds generated by the stochastic reaction diffusion equation possesses a finite dimensional random attractor in l q d for any q 2 a comparison result of fractal dimensions under the different l q norms is also obtained

optimal matching with minimal deviation from fine balance in a study of obesity and surgical outcomes in multivariate matching fine balance constrains the marginal distributions of a nominal variable in treated and matched control groups to be identical without constraining who is matched to whom in this way a fine balance constraint can balance a nominal variable with many levels while focusing efforts on other more important variables when pairing individuals to minimize the total covariate distance within pairs fine balance is not always possible that is it is a constraint on an optimization problem but the constraint is not always feasible we propose a new algorithm which returns a minimum distance finely balanced match when one is feasible and otherwise minimizes the total distance among all matched samples that minimize the deviation from fine balance perhaps we can come very close to fine balance when fine balance is not attainable moreover in any event because our algorithm is guaranteed to come as close as possible to fine balance the investigator may perform one match and on that basis judge whether the best attainable balance is adequate or not we also show how to incorporate an additional constraint the algorithm is implemented in two similar ways first as an optimal assignment problem with an augmented distance matrix second as a minimum cost flow problem in a network the case of knee surgery in the obesity and surgical outcomes study motivated the development of this algorithm and is used as an illustration in that example two of 47 hospitals had too few nonobese patients to permit fine balance for the nominal variable with 47 levels representing the hospital but our new algorithm came very close to fine balance moreover in that example there was a shortage of nonobese diabetic patients and incorporation of an additional constraint forced the match to include all of these nonobese diabetic patients thereby coming as close as possible to balance for this important but recalcitrant covariate

bounding parameter estimates with nonclassical measurement error abstract the bias introduced by errors in the measurement of independent variables has increasingly been a topic of interest among researchers estimating economic parameters however studies typically use the assumption of classical measurement error that is the variable of interest and its measurement error are uncorrelated and the expected value of the mismeasured variable is equal to the expected value of the true measure these assumptions often arise from convenience rather than conviction when a variable is bounded it is likely that the measurement error and the true value of the variable are negatively correlated we consider the case of a noisily measured variable with a negative covariance between the measurement error and the true value of the variable we show that asymptotically the parameter in a univariate regression is bounded between the ordinary least squares ols estimator and an instrumental variables iv estimator further we demonstrate that the ols bound can be improved in

limiting behavior of non autonomous stochastic reaction diffusion equations on thin domains abstract this paper deals with the limiting behavior of stochastic reaction diffusion equations driven by multiplicative noise and deterministic non autonomous terms defined on thin domains we first prove the existence uniqueness and periodicity of pullback tempered random attractors for the equations in an n 1 dimensional narrow domain and then establish the upper semicontinuity of these attractors when a family of n 1 dimensional thin domains collapses onto an n dimensional domain

the uncertainty principle on considere l existence et la regularite des solutions d equations aux derivees partielles la construction de solutions fondamentales explicites et les valeurs propres d operateurs de schrodinger

reverse regression for latent variable models abstract under joint normality of all regressors the errors in variables bounds for linear regression may be extended to probit and related models of censorship and truncation

finite fractal dimensions of random attractors for stochastic fitzhugh nagumo system with multiplicative white noise abstract in this paper we consider the asymptotic behavior of solutions for stochastic non autonomous fitzhugh nagumo system with multiplicative white noise first we prove the existence of random attractor of the random dynamical system generated by the solutions of considered system then we present some conditions for estimating an upper bound of the fractal dimension of a random invariant set of a random dynamical system on a separable banach space and apply these conditions to prove the finiteness of fractal dimension of random attractor

comment on identification in the linear errors in variables model on considere un modele etudie par kapteyn et wansbeek 1983 et on presente des conditions necessaires et suffisantes d identification

using mixed integer programming for matching in an observational study of kidney failure after surgery this article presents a new method for optimal matching in observational studies based on mixed integer programming unlike widely used matching methods based on network algorithms which attempt to achieve covariate balance by minimizing the total sum of distances between treated units and matched controls this new method achieves covariate balance directly either by minimizing both the total sum of distances and a weighted sum of specific measures of covariate imbalance or by minimizing the total sum of distances while constraining the measures of imbalance to be less than or equal to certain tolerances the inclusion of these extra terms in the objective function or the use of these additional constraints explicitly optimizes or constrains the criteria that will be used to evaluate the quality of the match for example the method minimizes or constrains differences in univariate moments such as means variances and skewness differences in multivariate moments such as correlations between covari

substantial gains in bias reduction from matching with a variable number of controls summary in observational studies that match several controls to each treated subject substantially greater bias reduction is possible if the number of controls is not fixed but rather is allowed to vary from one matched set to another in certain cases matching with a fixed number of controls may remove only 50 of the bias in a covariate whereas matching with a variable number of controls may remove 90 of the bias even though both control groups have the same number of controls in total an example of matching in a study of surgical mortality is discussed in detail

attractors for the stochastic reaction diffusion equation driven by linear multiplicative noise with a variable coefficient abstract by the classic law of iterated logarithm we get a new way to study the existence of random attractors for the stochastic reaction diffusion equation driven by linear multiplicative noise with a variable coefficient and estimate the hausdorff dimensions of the random attractors

minimum distance matched sampling with fine balance in an observational study of treatment for ovarian cancer in observational studies of treatment effects matched samples have traditionally been constructed using two tools namely close matches on one or two key covariates and close matches on the propensity score to stochastically balance large numbers of covariates here we propose a third tool fine balance obtained using the assignment algorithm in a new way we use all three tools to construct a matched sample for an ongoing study of provider specialty in the treatment of ovarian cancer fine balance refers to exact balance of a nominal covariate often one with many categories but it does not require individually matched treated and control subjects for this variable in the example the nominal variable has 72 9 8 categories formed from 9 possible years of diagnosis and 8 geographic locations or seer sites we obtain exact balance on the 72 categories and close individual matches on clinical stage grade year of diagnosis and other variables using a distance and stochastically balance a total of

attractors for random dynamical systems a criterion for existence of global random attractors for rds is established existence of invariant markov measures supported by the random attractor is proved for spde this yields invariant measures for the associated markov semigroup the results are applied to reation diffusion equations with additive white noise and to navier stokes equations with multiplicative and with additive white noise

evidence factors in observational studies some experiments involve more than one random assignment of treatments to units an analogous situation arises in certain observational studies although randomization is not used so each assignment may be biased if each assignment is suspect it is natural to ask whether there are separate pieces of information dependent upon different assumptions and perhaps whether conclusions about treatment effects are not critically dependent upon one or another suspect assumption the design of an observational study contains evidence factors if it permits several statistically independent tests of the same null hypothesis about treatment effects where these tests rely on different assumptions about treatment assignments at several levels of assignment two designs and two empirical examples are considered one example of each design in the dose control design there are matched pairs of a treated subject and an untreated control and doses of treatment vary between pairs for treated subjects this yields two evidence factors in the varied intensity design there are matched sets with two treated subjects and one or more untreated controls where the two treated subjects within the same matched set receive different doses of treatment and in a technically different way the design yields two evidence factors

optimal multilevel matching in clustered observational studies a case study of the effectiveness of private schools under a large scale voucher system abstracta distinctive feature of a clustered observational study is its multilevel or nested data structure arising from the assignment of treatment in a nonrandom manner to groups or clusters of units or individuals examples are ubiquitous in the health and social sciences including patients in hospitals employees in firms and students in schools what is the optimal matching strategy in a clustered observational study at first thought one might start by matching clusters of individuals and then within matched clusters continue by matching individuals but as we discuss in this article the optimal strategy is the opposite in typical applications where the intracluster correlation is not one it is best to first match individuals and once all possible combinations of matched individuals are known then match clusters in this article we use dynamic and integer programming to implement this strategy and extend optimal matching methods to hierarchical and multilevel settings among other match

some relations between dimension and lyapounov exponents we consider differentiable maps and compact invariant sets we introduce dimensional quantities related to the ergodic invariant measures and prove some simple relations

entropy chaos and weak horseshoe for infinite dimensional random dynamical systems in this paper we study the complicated dynamics of infinite dimensional random dynamical systems that include deterministic dynamical systems as their special cases in a polish space without assuming any hyperbolicity we prove if a continuous random map has a positive topological entropy then it contains a topological horseshoe we also show that the positive topological entropy implies the chaos in the sense of li yorke the complicated behavior exhibited here is induced by the positive entropy but not the randomness of the system 2017 wiley periodicals inc

random attractors for damped non autonomous wave equations with memory and white noise abstract we first prove the existence of random attractors for the continuous random dynamical systems generated by stochastic damped non autonomous wave equations with linear memory and additive white noise when the nonlinearity has a critically growing exponent then we study the upper semicontinuity of random attractors when the coefficient of random term approaches zero

regressor diagnostics for the classical errors in variables model abstract a series of diagnostics are developed which can be used to probe the sensitivity of regression coefficient estimates to measurement error in each regressor when all the regressors may be measured with error the diagnostics are based on the large sample properties of the classical errors in variables model the diagnostics provide information about the bounds on the measurement error variances of the regressors needed to bound any coefficient to a desired interval algorithms to compute the diagnostics are provided and the use of the diagnostics is illustrated in an example

random exponential attractor for stochastic reaction diffusion equation with multiplicative noise in r3 abstract in this paper we first improve the existing conditions for the existence of a random exponential attractor for a continuous cocycle on a separable banach space then we consider the existence of a random exponential attractor for stochastic non autonomous reaction diffusion equation with multiplicative noise defined in r 3 which implies the existence of a random attractor with finite fractal dimension the essential difficulty here is the continuity of the spectrum of the linear part of the equation which can be overcome by the tail estimation of solutions of equation and carefully decomposing the solution into a sum of three parts of whose one part is finite dimensional and other two parts are quickly decay in mean sense

characteristic exponents and invariant manifolds in hilbert space the multiplicative ergodic theorem and the construction almost everywhere of stable and unstable manifolds pesin theory are extended to differentiable dynamical systems on hilbert manifolds under some compactness assumptions the results apply to partial differential equations of evolution and also to non invertible maps of compact manifolds

classical and quantum probability we follow the development of probability theory from the beginning of the last century emphasizing that quantum theory is really a generalization of this theory the great achievements of probability theory such as the theory of processes generalized random fields estimation theory and information geometry are reviewed their quantum versions are then described

large volume limit of the distribution of characteristic exponents in turbulence for spatially extended conservative or dissipative physical systems it appears natural that a density of characteristic exponents per unit volume should exist when the volume tends to infinity in the case of a turbulent viscous fluid however this simple idea is complicated by the phenomenon of intermittency in the present paper we obtain rigorous upper bounds on the distribution of characteristic exponents in terms of dissipation these bounds have a reasonable large volume behavior for two dimensional fluids a particularly striking result is obtained the total information creation is bounded above by a fixed multiple of the total energy dissipation at fixed viscosity the distribution of characteristic exponents is estimated in an intermittent model of turbulence see 7 and it is found that a change of behavior occurs at the valued 2 6 of the self similarity dimension

on the largest lyapunov exponent for products of gaussian matrices the paper provides a new integral formula for the largest lyapunov exponent of gaussian matrices which is valid in the real complex and quaternion valued cases this formula is applied to derive asymptotic expressions for the largest lyapunov exponent when the size of the matrix is large and compare the lyapunov exponents in models with a spike and no spikes

a finite dimensional attractor of the moore greitzer pde model the moore greitzer pde model with viscosity is presented and the equations are rewritten as an evolution equation on a hilbert space it is proven that the model has a unique global solution which is smooth in space and time furthermore it is proven that there exists a global attractor i e a compact set which attracts all bounded sets finally it is shown that the attractor has a finite fractal dimension

the central role of the propensity score in observational studies for causal effects abstract the results of observational studies are often disputed because of nonrandom treatment assignment for example patients at greater risk may be overrepresented in some treatment group this paper discusses the central role of propensity scores and balancing scores in the analysis of observational studies the propensity score is the estimated conditional probability of assignment to a particular treatment given a vector of observed covariates both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates applications include matched sampling on the univariate propensity score which is equal percent bias reducing under more general conditions than required for discriminant matching multivariate adjustment by subclassification on balancing scores where the same subclasses are used to estimate treatment effects for all outcome variables and in all subpopulations and visual representation of multivariate adjustment by a two dimensional plot author

random exponential attractor for cocycle and application to non autonomous stochastic lattice systems with multiplicative white noise abstract we first establish some sufficient conditions for constructing a random exponential attractor for a continuous cocycle on a separable banach space and weighted spaces of infinite sequences then we apply our abstract result to study the existence of random exponential attractors for non autonomous first order dissipative lattice dynamical systems with multiplicative white noise

estimation of average treatment effects with misclassification this paper considers identification and estimation of the effect of a mismeasured binary regressor in a nonparametric or semiparametric regression or the conditional average effect of a binary treatment or policy on some outcome where treatment may be misclassified failure to account for misclassification is shown to result in attenua tion bias in the estimated treatment effect an identifying assumption that overcomes this bias is the existence of an instrument for the binary regressor that is conditionally independent of the treatment effect a discrete instrument suffices for nonparametric identification this paper provides conditions for identification and estimation of the av erage effect conditioned on covariates of a binary treatment program or pol icy on a scalar outcome when treatment may be misclassified more generally what is provided is an estimator of the effect of a binary regressor in a con ditional mean regression which may also include other regressors when the binary regressor is observed with error this equals the conditional average treatment effect given a weak unconfoundedness assumption misclassification occurs when a binary variable the treatment indicator is measured with error that is some units are reported to have received treat ment when they actually have not and vice versa for example in a returns to schooling analysis the outcome could be wages the binary variable could be attaining a college degree and misclassification could arise from school tran script reporting errors see e g kane and rouse 1995 and kane rouse and staiger 1999 bollinger 1996 considers misclassification of union status in wage equations if treatment is a job training program misclassification may arise if individuals assigned to the program fail to attend or if those not as signed obtain training elsewhere similarly for medical treatment individuals assigned a drug might fail to take it and those assigned a placebo might obtain treatment from another source more generally misclassification describes any binary variable that is sometimes mismeasured this paper first shows that misclassification causes attenuation bias in esti mated treatment effects analogous to the attenuation bias of classically mis measured variables in linear regression models additional assumptions on

random attractor for the ladyzhenskaya model with additive noise this paper studies the dynamical behavior of the ladyzhenskaya model with additive noise with some conditions we prove that the generated random dynamical system has a compact random attractor which is a random compact set absorbing any bounded nonrandom subset of the phase space

partial identification of probability distributions with misclassified data abstract this paper addresses the problem of data errors in discrete variables when data errors occur the observed variable is a misclassified version of the variable of interest whose distribution is not identified inferential problems caused by data errors have been conceptualized through convolution and mixture models this paper introduces the direct misclassification approach the approach is based on the observation that in the presence of classification errors the relation between the distribution of the true but unobservable variable and its misclassified representation is given by a linear system of simultaneous equations in which the coefficient matrix is the matrix of misclassification probabilities formalizing the problem in these terms allows one to incorporate any prior information into the analysis through sets of restrictions on the matrix of misclassification probabilities such information can have strong identifying power the direct misclassification approach fully exploits it to derive identification regions for any real functional of the distribution of interest a method for estimating the identification regions and construct their confidence sets is given and illustrated with an empirical analysis of the distribution of pension plan types using data from the health and retirement study

turbulent transport and the random occurrence of coherent events abstract we suggest that the transport properties and dissipation rates of a wide class of turbulent flows are determined by the random occurrence of coherent events which correspond to certain orbits which we call homoclinic excursions in the high dimensional strange attractor homoclinic excursions are trajectories in the noncompact phase space that are attracted to special orbits which connect saddle points in the finite region of phase space to infinity and represent organized structures in the flow field this picture also suggests that one can compute fluxes using a relatively low dimensional description of the flow a method for extracting the organized structures from a time series is given and provides a local analogue of the notion of lyapunov exponents

bounding the effects of measurement error in regressions involving dichotomous variables abstract in a multiple regression involving dichotomous independent variables the effects of measurement error in the dichotomous variables is analyzed unlike the case of classical i e white noise measurement error the measurement error in a dichotomous variable must be correlated with the true variable and any other variables correlated with the true variable nonetheless it is shown that the results for the classical errors in variables model can be used to analyze the implications of measurement error in dichotomous variables it is shown how the bounding procedure developed by klepper and leamer 1984 for the classical errors in variables model can be adapted to bound the coefficients when the regression contains mismeasured dichotomous variables the classical results are also used to analyze the inconsistency in least squares regression coefficient estimators computed from data on the mismeasured variables

evaluation of subset matching methods and forms of covariate balance this paper conducts a monte carlo simulation study to evaluate the performance of multivariate matching methods that select a subset of treatment and control observations the matching methods studied are the widely used nearest neighbor matching with propensity score calipers and the more recently proposed methods optimal matching of an optimally chosen subset and optimal cardinality matching the main findings are i covariate balance as measured by differences in means variance ratios kolmogorov smirnov distances and cross match test statistics is better with cardinality matching because by construction it satisfies balance requirements ii for given levels of covariate balance the matched samples are larger with cardinality matching than with the other methods iii in terms of covariate distances optimal subset matching performs best iv treatment effect estimates from cardinality matching have lower root mean square errors provided strong requirements for balance specifically fine balance or strength k balance plus close mean balance in standard practice a matched sample is considered to be balanced if the absolute differences in means of the covariates across treatment groups are smaller than 0 1 standard deviations however the simulation results suggest that stronger forms of balance should be pursued in order to remove systematic biases due to observed covariates when a difference in means treatment effect estimator is used in particular if the true outcome model is additive then marginal distributions should be balanced and if the true outcome model is additive with interactions then low dimensional joints should be balanced copyright 2016 john wiley sons ltd

the kuramoto sivashinsky equation a bridge between pde s and dynamical systems abstract through extensive numerical simulation we have characterized the transition to chaos of the solutions to the kuramoto sivashinsky equation the attracting solution manifolds undergo a complex bifurcation sequence including multimodal fixed points invariant tori traveling wave trains and homoclinic orbits we relate this behavior to earlier work where the kuramoto sivashinsky equation was shown to behave as a finite dimensional dynamical system of ordinary differential equations

sufficient and necessary criteria for existence of pullback attractors for non compact random dynamical systems abstract we study pullback attractors of non autonomous non compact dynamical systems generated by differential equations with non autonomous deterministic as well as stochastic forcing terms we first introduce the concepts of pullback attractors and asymptotic compactness for such systems we then prove a sufficient and necessary condition for existence of pullback attractors we also introduce the concept of complete orbits for this sort of systems and use these special solutions to characterize the structures of pullback attractors for random systems containing periodic deterministic forcing terms we show the pullback attractors are also periodic under certain conditions as an application of the abstract theory we prove the existence of a unique pullback attractor for reaction diffusion equations on r n with both deterministic and random external terms since sobolev embeddings are not compact on unbounded domains the uniform estimates on the tails of solutions are employed to establish the asymptotic compactness of solutions

mutual information based matching for causal inference with observational data this paper presents an information theory driven matching methodology for making causal inference from observational data the paper adopts a potential outcomes framework view on evaluating the strength of cause effect relationships the population wide average effects of binary treatments are estimated by comparing two groups of units the treated and untreated control to reduce the bias in such treatment effect estimation one has to compose a control group in such a way that across the compared groups of units treatment is independent of the units covariates this requirement gives rise to a subset selection matching problem this paper presents the models and algorithms that solve the matching problem by minimizing the mutual information mi between the covariates and the treatment variable such a formulation becomes tractable thanks to the derived optimality conditions that tackle the non linearity of the sample based mi function computational experiments with mixed integer programming formulations and four matching algorithms demonstrate the utility of mi based matching for causal inference studies the algorithmic developments culminate in a matching heuristic that allows for balancing the compared groups in polynomial close to linear time thus allowing for treatment effect estimation with large data sets

inertial manifolds associated to partly dissipative reaction diffusion systems abstract in a previous work we established the existence of finite dimensional attractors for partly dissipative reaction diffusion systems of two types systems with a polynomial growth nonlinearity and systems admitting an invariant region the aim of this article is to show that these problems possess inertial manifolds in space dimension n 2 these inertial manifolds contain the universal attractor attract exponentially all the solutions as time goes to infinity and due to the weak dissipation are here infinite dimensional our results are applied to several classical systems borrowed from mathematical biology physics and chemistry

hausdorff dimension of attractors for the two dimensional navier stokes equations with boundary conditions we consider a viscous incompressible fluid enclosed in a region of ir2 and subject to boundary conditions we obtain explicit bounds depending only on the data for the entropy kolmogorov sinai invariant and the hausdorff dimension of attracting sets

random attractors of reaction diffusion equations with multiplicative noise in lp in this paper we study the random dynamical system rds generated by the reaction diffusion equation with multiplicative noise and prove the existence of a random attractor for such rds in l p d for any p 2

a new u statistic with superior design sensitivity in matched observational studies summary in an observational or nonrandomized study of treatment effects a sensitivity analysis indicates the magnitude of bias from unmeasured covariates that would need to be present to alter the conclusions of a naive analysis that presumes adjustments for observed covariates suffice to remove all bias the power of sensitivity analysis is the probability that it will reject a false hypothesis about treatment effects allowing for a departure from random assignment of a specified magnitude in particular if this specified magnitude is no departure then this is the same as the power of a randomization test in a randomized experiment a new family of u statistics is proposed that includes wilcoxon s signed rank statistic but also includes other statistics with substantially higher power when a sensitivity analysis is performed in an observational study wilcoxon s statistic has high power to detect small effects in large randomized experiments that is it often has good pitman efficiency but small effects are invariably sensitive to small unobserved biases members of this family of u statistics that emphasize medium to large effects can have substantially higher power in a sensitivity analysis for example in one situation with 250 pair differences that are normal with expectation 1 2 and variance 1 the power of a sensitivity analysis that uses wilcoxon s statistic is 0 08 while the power of another member of the family of u statistics is 0 66 the topic is examined by performing a sensitivity analysis in three observational studies using an asymptotic measure called the design sensitivity and by simulating power in finite samples the three examples are drawn from epidemiology clinical medicine and genetic toxicology

random attractor for stochastic reaction diffusion equation with multiplicative noise on unbounded domains abstract in this paper we study the asymptotic dynamics for stochastic reaction diffusion equation with multiplicative noise defined on unbounded domains we investigate the existence of a random attractor for the random dynamical system associated with the equation the asymptotic compactness of the random dynamical system is established by using uniform a priori estimates for far field values of solutions and a cut off technique

bayesian moment based inference in a regression model with misclassification error we present a bayesian analysis of a regression model with a binary covariate that may have classification measurement error prior research demonstrates that the regression coefficient is only partially identified we take a bayesian approach which adds assumptions in the form of priors on the unknown misclassification probabilities the approach is intermediate between the frequentist bounds of previous literature and strong assumptions which achieve point identification and thus preferable in many settings we present two simple algorithms to sample from the posterior distribution when the likelihood function is not fully parametric but only satisfies a set of moment restrictions we focus on how varying amounts of information contained in a prior distribution on the misclassification probabilities change the posterior of the parameters of interest while the priors add information to the model they do not necessarily tighten the identified set however the information is sufficient to tighten bayesian inferences we also consider the case where the mismeasured binary regressor is endogenous we illustrate the use of our bayesian approach in a simulated data set and an empirical application investigating the association between narcotic pain reliever use and earnings

balance optimization subset selection boss an alternative approach for causal inference with observational data scientists in all disciplines attempt to identify and document causal relationships those not fortunate enough to be able to design and implement randomized control trials must resort to observational studies to make causal inferences outside the experimental realm researchers attempt to control for bias sources by postprocessing observational data finding the subset of data most conducive to unbiased or least biased treatment effect estimation is a challenging complex problem however the rise in computational power and algorithmic sophistication leads to an operations research solution that circumvents many of the challenges presented by methods employed over the past 30 years

random attractors for stochastic reaction diffusion equations on unbounded domains the existence of a pullback attractor is established for a stochastic reaction diffusion equation on all n dimensional space the nonlinearity is dissipative for large values of the state and the stochastic nature of the equation appears as spatially distributed temporal white noise the reaction diffusion equation is recast as a random dynamical system and asymptotic compactness for this is demonstrated by using uniform a priori estimates for far field values of solutions

continuity and random dynamics of the non autonomous stochastic fitzhugh nagumo system on rn abstract in this article we use the so called difference estimate method to investigate the continuity and random dynamics of the non autonomous stochastic fitzhugh nagumo system with a general nonlinearity firstly under weak assumptions on the noise coefficient we prove the existence of a pullback attractor in l 2 r n l 2 r n by using the tail estimate method and a certain compact embedding on bounded domains secondly although the difference of the first component of solutions possesses at most p times integrability where p is the growth exponent of the nonlinearity we overcome the absence of higher order integrability and establish the continuity of solutions in l p r n h 1 r n l 2 r n with respect to the initial values belonging to l 2 r n l 2 r n as an application of the result on the continuity the existence of a pullback attractor in l p r n h 1 r n l 2 r n is proved for arbitrary n 1 and p 2

amplification of sensitivity analysis in matched observational studies a sensitivity analysis displays the increase in uncertainty that attends an inference when a key assumption is relaxed in matched observational studies of treatment effects a key assumption in some analyses is that subjects matched for observed covariates are comparable and this assumption is relaxed by positing a relevant covariate that was not observed and not controlled by matching what properties would such an unobserved covariate need to have to materially alter the inference about treatment effects for ease of calculation and reporting it is convenient that the sensitivity analysis be of low dimension perhaps indexed by a scalar sensitivity parameter but for interpretation in specific contexts a higher dimensional analysis may be of greater relevance an amplification of a sensitivity analysis is defined as a map from each point in a low dimensional sensitivity analysis to a set of points perhaps a curve in a higher dimensional sensitivity analysis such that the possible inferences are

determining nodes for partly dissipative reaction diffusion systems abstract in this paper we study the long time dynamical properties of the solutions of partly dissipative reaction diffusion systems of the form u t d u f x u g x v 0 x r n t 0 v t v h x u 0 the main result is that under appropriate assumptions the large time behavior of a solution is completely determined in certain sense if the large time behavior of the solution is known on a densely chosen yet finite set of points which are called determining nodes a concept initially introduced by foias and temam for the navier stokes equations math comput 43 1984 117

random attractors for the stochastic fitzhugh nagumo system on unbounded domains abstract the existence of a random attractor for the stochastic fitzhugh nagumo system defined on an unbounded domain is established the pullback asymptotic compactness of the stochastic system is proved by uniform estimates on solutions for large space and time variables these estimates are obtained by a cut off technique

characteristic exponents for a viscous fluid subjected to time dependent forces we consider a viscous incompressible fluid enclosed in a bounded region of 2 or 3 and subjected to time dependent forces using bound state estimates for the schrodinger operator we obtain rigorous bounds for the characteristic exponents entropy kolmogorov sinai invariant and hausdorff dimension of attracting sets our methods are of potential use for more general time evolutions described by nonlinear partial differential equations

on characteristic exponents in turbulence ruelle has found upper bounds to the magnitude and to the number of non negative characteristic exponents for the navier stokes flow of an incompressible fluid in a domain the latter is particularly important because it yields an upper bound to the hausdorff dimension of attracting sets however ruelle s bound on the number has three deficiences i it relies on some unproved conjectures about certain constants ii it is valid only in dimensions 3 and not 2 iii it is valid only in the limit in this paper these deficiences are remedied and in addition the final constants in the inequality are improved

nonparametric identification of a binary random factor in cross section data suppose v and u are two independent mean zero random variables where v has an asymmetric distribution with two mass points and u has a symmetric distribution we show that the distributions of v and u are nonparametrically identifled just from observing the sum v u and provide a rate root n estimator we apply these results to the world income distribution to measure the extent of convergence over time where the values v can take on correspond to country types i e wealthy versus poor countries we also extend our results to include covariates x showing that we can nonparametrically identify and estimate cross section regression models of the form y g x d u where d is an unobserved

existence of inertial manifolds for partly dissipative reaction diffusion systems in higher space dimensions abstract in this paper we prove the existence of inertial manifolds for a partly dissipative reaction diffusion system of the form formula where is a rectangular domain in r 2or a cubic domain in r 3 the proof is based on an abstract invariant manifold theorem for semiflows in a hilbert space which is proved by using the graph transform method the principle of spatial averaging also plays an important role in the proof

bounding mean regressions when a binary regressor is mismeasured in this paper i examine identification and estimation of mean regression models when a binary regressor is mismeasured i prove that bounds for the model parameters are identified and provide simple estimators which are consistent and asymptotically normal when stronger prior information about the probability of misclassification is available the bounds can be made tighter again a simple estimator for these cases is provided all results apply to parametric and nonparametric models the paper concludes with a short empirical example

asymptotic analysis of the navier stokes equations abstract new bounds are established on the number of modes which determine the solutions of the navier stokes equations in two dimensions the best bound available at present is nearly proportional to the generalized grashof number defined in the paper and less than logarithmically dependent on the spatial structure or the shape of the force driving the flow to the extent than for the case of 2 dimensional rayleigh benard convection the generalized grashof number may be identified with the usual grashof number the resulting bound on the number of modes is found to differ only slightly from a bound obtained earlier on heuristic grounds

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

finite reductions for dissipative systems and viscous fluid dynamic models on t2 abstract we reconsider the reduction method introduced for hamiltonian systems by amann conley and zehnder we propose an extension of these techniques to evolutive pde systems of dissipative type and prove that under suitable regularity conditions a finite number of spectral modes controls exactly the time evolution of the complete problem the problem of finite reduction for a two dimensional modified navier stokes equations is considered and an estimate of the dimension of the reduced space is given valid for any time t 0 comparison is made with the asymptotic finite dimension that has been obtained for the true navier stokes equations

bounding parameters in a linear regression model with a mismeasured regressor using additional information this paper discusses a linear regression model with a mismeasured regressor in which the measurement error is correlated with both the latent variable and the regression error we use a linear structure to capture the correlation between the measurement error and the latent variable this paper shows that the variance of the latent variable is very useful for revealing information on the parameters which otherwise cannot be obtained with such a nonclassical measurement error the main result is that the finite bounds on the parameters can be found using the variance of the latent variable regardless of how severely the measurement error and the regression error are correlated if the mismeasured regressor contains enough information on the latent one this paper also discusses the special but interesting case of the latent variable being dichotomous in this case the mean of the latent variable may even reveal information on the correlation between the measurement error and the regression error all the bounds developed in the paper are tight

full matching in an observational study of coaching for the sat among matching techniques for observational studies full matching is in principle the best in the sense that its alignment of comparable treated and control subjects is as good as that of any alternate method and potentially much better this article evaluates the practical performance of full matching for the first time modifying it in order to minimize variance as well as bias and then using it to compare coached and uncoached takers of the sat in this new version with restrictions on the ratio of treated subjects to controls within matched sets full matching makes use of many more observations than does pair matching but achieves far closer matches than does matching with k 2 controls prior to matching the coached and uncoached groups are separated on the propensity score by 1 1 sds full matching reduces this separation to 1 or 2 of an sd in older literature comparing matching and regression cochran expressed doubts that any method of adjustment could substantially reduce observed bias