boundary effects on localized structures in spatially extended systems abstract we present a general method of analyzing the influence of finite size and boundary effects on the dynamics of localized solutions of non linear spatially extended systems the dynamics of localized structures in infinite systems involve solvability conditions that require projection onto a goldstone mode our method works by extending the solvability conditions to finite sized systems by incorporating the finite sized modifications of the goldstone mode and associated nonzero eigenvalue we apply this method to the special case of non equilibrium domain walls under the influence of dirichlet boundary conditions in a parametrically forced complex ginzburg landau equation where we examine exotic nonuniform domain wall motion due to the influence of boundary conditions

the zeros of derivatives of entire functions and the polya wiman conjecture an entire function f x which assumes only real values on the real axis is said to be a real entire function thus if f is a real entire function then its maclaurin coefficients are all real and consequently the zeros of f are symmetrically located with respect to the real axis one of the intuitive principles underlying the theory of distribution of zeros of successive derivatives of real entire functions was formulated by polya p4 in his celebrated survey article entitled on the zeros of the derivatives of a function and its analytic character in this work p4 p 181 polya states the real axis seems to exert an influence on the complex zeros of f n z it seems to attract these zeros when the order is less than 2 and it seems to repel them when the order is greater than 2 indeed the first confirmation of this principle was made by alander a2 see also p6lya p2 who in 1930 showed that the polya wiman conjecture is true if the order of f x is less than 2 3 in wil and wi2 wiman established the validity of this conjecture for functions f x of order at most 1 while in 1937 polya p3 proved it for functions of order less than 4 3 a general survey of these results and related conjectures may be found in p2 and p4 for more recent surveys of this and related areas of research see boas b2 and prather pr it seems that no progress has been made on the p6lya wiman conjecture since the publication of polya s 4 3 theorem in 1937 our proof of the conjecture is self contained and does not rely on the results cited above in section 2 we will 1 introduce some definitions and notations 2 state some of the properties of functions in the laguerre p6lya class and 3 prove the polya wiman conjecture theorem 3 in the proof of theorem 3 we

rotating chemical waves in the gray scott model a set of reaction diffusion equations is considered known as the gray scott model defined on a circle and the stability of rotating wave solutions formed via hopf bifurcations that break the circular o 2 symmetry is investigated using a hybrid numerical analytical technique center manifold normal form reductions are performed to analyze symmetry breaking hopf bifurcations degenerate hopf bifurcations and hopf hopf mode interactions it is found that stable rotating waves exist over broad ranges of parameter values and that the bifurcation behavior of this relatively simple model can be quite complex e g two and three frequency motions exist

weakly interacting pulses in synaptically coupled neural media we use singular perturbation theory to analyze the dynamics of n weakly interacting pulses in a one dimensional synaptically coupled neuronal network the network is modeled in terms of a nonlocal integro differential equation in which the integral kernel represents the spatial distribution of synaptic weights and the output activity of a neuron is taken to be a mean firing rate we derive a set of n coupled ordinary differential equations odes for the dynamics of individual pulses establishing a direct relationship between the explicit form of the pulse interactions and the structure of the long range synaptic coupling the system of odes is used to explore the existence and stability of stationary n pulses and traveling wave trains

domain structures in fourth order phase and ginzburg landau equations abstract in pattern forming systems competition between patterns with different wave numbers can lead to domain structures which consist of regions with differing wave numbers separated by domain walls for domain structures well above threshold we employ the appropriate phase equation and obtain detailed qualitative agreement with recent experiments close to threshold a fourth order ginzburg landau equation is used which describes a steady bifurcation in systems with two competing critical wave numbers the existence and stability regime of domain structures is found to be very intricate due to interactions with other modes in contrast to the phase equation the ginzburg landau equation allows a spatially oscillatory interaction of the domain walls thus close to threshold domain structures need not undergo the coarsening dynamics found in the phase equation far above threshold and can be stable even without phase conservation we study their regime of stability as a function of their quantized length domain structures are related to zig zags in two dimensional systems the latter are therefore expected to be stable only when quenched far enough beyond the zig zag instability

drift bifurcation of dissipative solitons due to a change of shape experiment and theory abstract the subject of this paper is self organized solitary current filaments being observed experimentally in a planar dc gas discharge system with high ohmic barrier we report on the dynamical behavior of these objects which we refer to as dissipative solitons an application of stochastic data analysis methods enables the separation of intrinsic dynamics from stochastic contributions using the externally applied voltage as control parameter we observe a drift bifurcation that is accompanied by a change of shape of the bifurcating dissipative soliton in order to interpret the experimental finding a theoretical model in form of a three component reaction diffusion system is considered allowing for a qualitative understanding of the obtained results we discuss an analytical expression for the velocity of the dissipative soliton as a function of an appropriate control parameter and demonstrate that the change of the shape can induce the drift bifurcation this analytical finding is supported by numerical simulations of the model equations

patterns of propagating pulses the complex dynamics that arise in certain nonlinear partial differential equations in time and in one space dimension are studied in the general case considered the equation admits a solitary wave in the form of a pulse tailing off exponentially fore and aft with possibly oscillatory character complicated solutions are described by a superposition of many such solitary structures in interaction the description is asymptotic in terms of a parameter that becomes exponentially small as the ratio of typical pulse separation to pulse width becomes large the outcome is a set of dynamical equations for the motion of the individual pulses with nearest neighbor interactions this system of ordinary differential equations odes admits a wide range of patterns both regular and chaotic the stability theory of such patterns is sketched and the continuum limit of the lattice dynamical equations of the pulses is given

on a likelihood approach for monte carlo integration the use of estimating equations has been a common approach for constructing monte carlo estimators recently kong et al proposed a formulation of monte carlo integration as a statistical model making explicit what information is ignored and what is retained about the baseline measure from simulated data the baseline measure is estimated by maximum likelihood and then integrals of interest are estimated by substituting the estimated measure for two different situations in which independent observations are simulated from multiple distributions we show that this likelihood approach achieves the lowest asymptotic variance possible by using estimating equations in the first situation the normalizing constants of the design distributions are estimated and meng and wong s bridge sampling estimating equation is considered in the second situation the values of the normalizing constants are known thereby imposing linear constraints on the baseline measure estimating equations including hesterberg s

newton cotes integration for approximating stieltjes generalized euler constants in the laurent expansion s a 1 s 1 k 0 1 k k a k s 1 k 0 1 we also conjecture that limk k 1 2 k k 0 a special case of a more general conjecture relating the values of k a and k a for 0 0 we conjecture that for nonintegral r r is precisely 1 r times the r th weyl fractional derivative at s 1 of the entire function s 1 s 1 1 we also conjecture that g now defined for all real arguments r 0 is smooth our numerical method uses newton cotes integration formulae for very high degree interpolating polynomials it differs in implementation from but compares in error bounding to euler maclaurin summation based methods

adjusting for nonignorable drop out using semiparametric nonresponse models abstract consider a study whose design calls for the study subjects to be followed from enrollment time t 0 to time t t at which point a primary endpoint of interest y is to be measured the design of the study also calls for measurements on a vector v t of covariates to be made at one or more times t during the interval 0 t we are interested in making inferences about the marginal mean 0 of y when some subjects drop out of the study at random times q prior to the common fixed end of follow up time t the purpose of this article is to show how to make inferences about 0 when the continuous drop out time q is modeled semiparametrically and no restrictions are placed on the joint distribution of the outcome and other measured variables in particular we consider two models for the conditional hazard of drop out given v t y where v t denotes the history of the process v t through time t t 0 t in the first model we assume that q t v t y exp 0 y where 0 is a scalar paramet

toward a curse of dimensionality appropriate coda asymptotic theory for semi parametric models we argue that due to the curse of dimensionality there are major difficulties with any pure or smoothed likelihood based method of inference in designed studies with randomly missing data when missingness depends on a high dimensional vector of variables we study in detail a semi parametric superpopulation version of continuously stratified random sampling we show that all estimators of the population mean that are uniformly consistent or that achieve an algebraic rate of convergence no matter how slow require the use of the selection randomization probabilities we argue that in contrast to likelihood methods which ignore these probabilities inverse selection probability weighted estimators continue to perform well achieving uniform n 1 2 rates of convergence we propose a curse of dimensionality appropriate coda asymptotic theory for inference in non and semi parametric models in an attempt to formalize our arguments we discuss whether our results constitute a fatal blow to the likelihood principle and study the attitude toward these that a committed subjective bayesian would adopt finally we apply our coda theory to analyse the effect of the curse of dimensionality in several interesting semi parametric models including a model for a two armed randomized trial with randomization probabilities depending on a vector of continuous pretreatment covariates x we provide substantive settings under which a subjective bayesian would ignore the randomization probabilities in analysing the trial data we then show that any statistician who ignores the randomization probabilities is unable to construct nominal 95 per cent confidence intervals for the true treatment effect that have both i an expected length which goes to zero with increasing sample size and ii a guaranteed expected actual coverage rate of at least 95 per cent over the ensemble of trials analysed by the statistician during his or her lifetime however we derive a new interval estimator depending on the randomization probabilities that satisfies i and ii

the role of curvature and wavefront interactions in spiral wave dynamics abstract a theory of rotating spiral waves in excitable media is presented that allows the study of dynamical aspects such as nonsteady rotation an approximate spiral wave solution is proposed in the form of a superposition of curved solitary wavefronts parallel to each other this form is used by means of singular perturbation theory to derive an evolution equation for the spiral arm numerical solutions of that equation are found that describe one and two frequency rotations the transition to two frequency dynamics tip meandering is attributed to a destabilizing curvature effect

on the number of nonreal zeros of real entire functions and the fourier polya conjecture this paper is concerned with a general theorem on the number of nonreal zeros of transcendental functions j fourier formulated the theorem in his work analyse des equations determineesin 1831 but he did not give a proof roughly speaking the theorem states that if a real entire function f x can be expressed as a product of linear factors then we can count the nonreal zeros of f x by observing the behavior of the derivatives of f x on the real axis alone as we shall see in the sequel this theorem completely justifies his former argument by which he tried to prove that the function j0 2 x has only real zeros it seems that no complete proof of the theorem is known and no general theorem has been published that justifies the argument later in 1930 g polya published a paper entitled some problems connected with fourier s work on transcendental equations p3 in this paper polya conjectured two hypothetical theorems that are closely related to fourier s unproved theorem in fact he conjectured three but he proved that two of them are equivalent to each other the first hypothetical theorem is a modernized formulation of the theorem and it justifies fourier s argument completely the second conjecture was proved in 1990 but it is impossible to justify the argument using the conjecture alone in the present paper we prove polya s formulation of the theorem his first conjecture as well as its extensions give a very simple and direct proof of the second conjecture mentioned above and exhibit some applications of the results in particular we completely justify fourier s argument by our general theorems acknowledgments professor fefferman has encouraged and helped us to publish this paper the authors truly thank him for this the authors also thank professor csordas for his kind interest in the results and his valuable suggestions on the proof of the polya wiman conjecture 1 historical introduction in this section we briefly explain our results as well as their background a real entire function is an entire function that assumes only real values on the real axis fourier s unproven theorem asserts that we can know the number of nonreal zeros of such real entire functions by counting their critical points which are defined as follows let f x be a real analytic function defined in an open

transient behavior of collapsing ring solutions in the critical nonlinear schrodinger equation abstract the critical nonlinear schrodinger equation nls possesses nearly self similar ring profile solutions we address the question of whether this profile is maintained all the way until the point of singularity a perturbative analysis of the rescaled pde and the resulting self similar profile uncover slow dynamics that eventually drive the ring structure to the classical peak shaped collapse instead a numerical scheme capable of resolving self similar behavior to high resolutions confirms our analysis we also consider ring type blowup arising either from azimuthally polarized solutions of a coupled nls system or as vortex solutions of the usual nls in this case the ring profile is maintained up to the time of singularity

oscillations of fronts and front pairs in two and three component reaction diffusion systems abstract we investigate multi co ponent reaction diffusion systems on a finite one dimensional domain the first component is assumed both to react on a short time scale and to have a small diffusion length leading to patterns with sharp fronts to analyze stability we apply the slep method by nishiura and fujii this method is superior to standard perturbation methods we illustrate this using a two component system in the three component system in a situation where both the influence of the first component on the other components and the interaction of the latter is only weak we show that there is a unique hopf destabilization of stationary fronts when changing time constants as an example we treat a system with global coupling used e g for semi conductor devices for filaments front pairs we find two types of hopf destabilizations breathing and swinging the global coupling controls which type occurs this corresponds to recent experimental results and is confirmed via numerical calculations

local stability theory of solitary pulses in an active medium abstract if the spatio temporal chaos of an extended active medium is driven by repulsive or attractive interaction among localized coherent structures such as kinks and pulses its dynamics can often be described by a low dimensional dynamical system this welcomed reduction in the degrees of freedom only occurs when the localized structures remain stable during their mutual interaction it is shown that the structures can be destroyed by two types of local disturbance an expanding radiation packet and a localized disturbance which travels with the structure these two instabilities and the bifurcations they induce select the proper coherent structure and specify the dynamics of the generalized kuramoto sivashinsky gks equation in an extended domain the possibility of describing pulse radiation interaction by resonance poles also suggests that a more general coherent structure theory can be developed

improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data considerable recent interest has focused on doubly robust estimators for a population mean response in the presence of incomplete data which involve models for both the propensity score and the regression of outcome on covariates the usual doubly robust estimator may yield severely biased inferences if neither of these models is correctly specified and can exhibit nonnegligible bias if the estimated propensity score is close to zero for some observations we propose alternative doubly robust estimators that achieve comparable or improved performance relative to existing methods even with some estimated propensity scores close to zero

replication variance estimation for two phase stratified sampling in two phase sampling the second phase sample is often a stratified sample based on the information observed in the first phase sample for the total of a population characteristic either the double expansion estimator or the reweighted expansion estimator can be used given a consistent first phase replication variance estimator we propose a consistent variance estimator that is applicable to both the double expansion estimator and the reweighted expansion estimator the proposed method can be extended to multiphase sampling

modeling discrete choice with response error food stamp participation abstract validation of food stamp program participation by marquis and moore revealed net bias of 13 in mean estimates of participation in the 1984 survey of income and program participation we extend the analysis incorporating demographic and economic covariates in models for underreporting and overreporting we use the resulting models of response error to refine estimates of participation models using pseudo maximum likelihood estimation methods we find that the probability of underreporting rises with increased family income estimates of the participation model indicate the presence of substantial bias in income and asset related parameters compared to values obtained without incorporating response error

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

estimation of regression coefficients when some regressors are not always observed abstract in applied problems it is common to specify a model for the conditional mean of a response given a set of regressors a subset of the regressors may be missing for some study subjects either by design or happenstance in this article we propose a new class of semiparametric estimators based on inverse probability weighted estimating equations that are consistent for parameter vector 0 of the conditional mean model when the data are missing at random in the sense of rubin and the missingness probabilities are either known or can be parametrically modeled we show that the asymptotic variance of the optimal estimator in our class attains the semiparametric variance bound for the model by first showing that our estimation problem is a special case of the general problem of parameter estimation in an arbitrary semiparametric model in which the data are missing at random and the probability of observing complete data is bounded away from 0 and then deriving a representation for the efficient score

differentiation evens out zero spacings if f is a polynomial with all of its roots on the real line then the roots of the derivative f are more evenly spaced than the roots of f the same holds for a real entire function of order 1 with all its zeros on a line in particular we show that if f is entire of order 1 and has sufficient regularity in its zero spacing then under repeated differentiation the function approaches after normalization the cosine function we also study polynomials with all their zeros on a circle and we find a close analogy between the two situations this sheds light on the spacing between zeros of the riemann zeta function and its connection to random matrix polynomials

on the exponentially slow motion of a viscous shock using formal asymptotic methods we study the internal layer behavior associated with the following viscous shock problem in the limit e 0 the convex nonlinearity f u satisfies f f for the steady problem we show that the method of matched asymptotic expansions fails to uniquely determine the location of the equilibrium shock layer solution this indeterminacy resulting from neglecting certain exponentially small effects is eliminated by using the projection method which exploits certain properties of the spectrum associated with the linearized operator for the time dependent problem we show that the viscous shock which is formed from initial data drifts towards the equilibrium solution on an exponentially long time interval of the order o ec e for some c 0 this exponentially slow behavior is analyzed by deriving an equation of motion for the location of the viscous shock for burgers equation f u u2 2 the results give an analytical characterization of the slow shock layer motion observed numerically in kreiss and kreiss see 11 we also show that the shock layer behavior is very sensitive to small changes in the boundary operator in addition using a wkb type method the slow viscous shock motion is studied numerically for small e the results comparing favorably with corresponding analytical results finally we relate the slow viscous shock motion to similar slow internal layer motion for the allen cahn equation

semiparametric regression for repeated outcomes with nonignorable nonresponse abstract we consider inference about the parameter indexing the conditional mean of a vector of correlated outcomes given a vector of explanatory variables when some of the outcomes are missing in a subsample of the study and the probability of response depends on both observed and unobserved data values that is nonresponse is nonignorable we propose a class of augmented inverse probability of response weighted estimators that are consistent and asymptotically normal can for estimating when the response probabilities can be parametrically modeled and a can estimator exists the proposed estimators do not require full specification of a parametric likelihood and their computation does not require numerical integration our estimators can be viewed as an extension of generalized estimating equation estimators that allows for nonignorable nonresponse we show that our class essentially consists of all can estimators of we also show that the asymptotic variance of the optimal estimator in our

a paradox concerning nuisance parameters and projected estimating functions summary this paper is concerned with a paradox associated with parameter estimation in the presence of nuisance parameters in a statistical model with unknown nuisance parameters the efficiency of an estimator of a parameter usually increases when the nuisance para meters are known however the opposite phenomenon can sometimes occur in this paper we elucidate the occurrence of this paradox by examining estimating functions in particular we focus on the projected estimating function which is defined by the projection of the score function on to a given estimating function a sufficient condition for the paradox to occur is the orthogonality of the two components of the projected estimating functions corresponding to parameters of interest and nuisance parameters in addition a numerical assessment is conducted in the context of a simple model to investigate the improvement of the asymptotic efficiency of estimators

asymptotic estimation of ξ 2n 1 2 on a conjecture of farmer and rhoades we verify a very recent conjecture of farmer and rhoades on the asymptotic rate of growth of the derivatives of the riemann xi function at s 1 2 we give two separate proofs of this result with the more general method not restricted to s 1 2 we briefly describe other approaches to our results give a heuristic argument and mention supporting numerical evidence

intrinsic efficiency and multiple robustness in longitudinal studies with drop out intrinsic efficiency and multiple robustness are desirable properties in missing data analysis we establish both for estimating the mean of a response at the end of a longitudinal study with drop out the idea is to calibrate the estimated missingness probability at each visit using data from past visits we consider one working model for the missingness probability and multiple working models for the data distribution intrinsic efficiency guarantees that when the missingness probability is correctly modelled the multiple data distribution models combined with data prior to the end of the study are optimally accommodated to maximize efficiency the efficiency generally increases with the number of data distribution models except where one such model is correctly specified as well in which case all the proposed estimators attain the semiparametric efficiency bound multiple robustness ensures estimation consistency if the missingness probability model is misspecified but one data distribution model is correct our proposed estimators are all convex combinations of the observed responses and thus always fall within the parameter space

universal oscillations of high derivatives differentiation generates oscillations for the n th derivative f n t of a function f t that is analytic in a strip including the real t axis the oscillations occupy a t interval that gets larger as n increases the oscillations are studied in detail using integral representations and large n asymptotics for functions with singularities poles or branch points in the complex t plane the oscillations of high derivatives are determined by the singularities for entire functions the oscillations originate in complex saddle points in a wide class of cases the oscillations are contained in a gaussian envelope in the t interval where f n t is largest with the envelope including about graphic 1 oscillations examples of the universal oscillations are given for f t with a simple pole competing branch points a single saddle competing pole and saddle and where the zeros are confined to half the real axis 1 embed inline graphic 1 gif

multi hump pulses in systems with reflection and phase invariance abstract we investigate the existence and stability of standing and travelling multi hump waves in partial differential equations with reflection and phase symmetries we focus on 2 and 3 pulse solutions that arise near bi foci and apply our results to the complex cubic quintic ginzburg landau equation

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

solitary wave interactions in dispersive equations using manton s approach we generalize the approach first proposed by manton nucl phys b 150 397 1979 to compute solitary wave interactions in translationally invariant dispersive equations that support such localized solutions the approach is illustrated using as examples solitons in the korteweg de vries equation standing waves in the nonlinear schr odinger equation and kinks as well as breathers of the sine gordon equation

assessing sensitivity to an unobserved binary covariate in an observational study with binary outcome this paper proposes a simple technique for assessing the range of plausible causal con clusions from observational studies with a binary outcome and an observed categorical covariate the technique assesses the sensitivity of conclusions to assumptions about an unobserved binary covariate relevant to both treatment assignment and response a medical study of coronary artery disease is used to illustrate the technique inevitably the results of clinical studies are subject to dispute in observational studies one basis for dispute is obvious since patients were not assigned to treatments at random patients at greater risk may be over represented in some treatment groups this paper proposes a method for assess ing the sensitivity of causal conclusions to an unmeasured patient characteristic relevant to both treatment assignment and response despite their limitations observational studies will continue to be a valuable source of information and therefore it is prudent to develop appropriate methods of analysis for them our sensitivity analysis consists of the estimation of the average effect of a treatment on a binary outcome variable after adjustment for observed categorical covariates and an unobserved binary covariate u under several sets of assumptions about u both cornfield et al 1959 and bross 1966 have proposed guidelines for determining whether an unmeasured binary covariate having specified properties could explain all of the apparent effect of a treatment that is whether the treatment effect after adjustment for u could be zero our method has two advantages first cornfield et al 1959 and bross 1966 adjust only for the unmeasured binary covariate u whereas we adjust for measured covariates in addition to the unmeasured covariate u second cornfield et al 1959 and bross 1966 1967 only judge whether the effect of the treatment could be zero having adjusted for u where cornfield et al 1959 employ an implicit yet extreme assumption about u in contrast we provide actual estimates of the treatment effect adjusted for both u and the observed categorical covariates under any assumption about u in principle the ith of the n patients under study has both a binary response r1i that would have resulted if he had received the new treatment and a binary response ro0 that would have resulted if he had received the control treatment in this formulation treatment effects are comparisons of r1i and roi such as r1i roi since each patient receives only one treatment either rli or ro0 is observed but not both and therefore comparisons of rli and roi imply some degree of speculation treatment effects defined as comparisons of the two potential responses r1i and roi of individual patients are implicit in fisher s 1953 randomization test of the sharp null

nonlinearity saturation as a singular perturbation of the nonlinear schroźdinger equation saturation of a kerr type nonlinearity in the nonlinear schro dinger equation nlse can be regarded as a singular perturbation which regularizes the well known blow up phenomenon in the cubic nlse an asymptotic expansion is proposed which takes into account multiple scale behavior both in the longitudinal and transverse directions in one dimension this leads to a free boundary problem reduction where the solitary wave acts solely to reflect impinging waves and is accelerated by an elastic transfer of momentum in two dimensions we find that interaction of a solitary wave and an adjacent wave field is governed by behavior of certain eigenfunctions of the linearized fast scale operator this leads to an outer solution with a free logarithmic singularity whose position evolves by virtue of a large transfer of momentum between the ambient and solitary waves however for a certain value of wave power we find there is essentially no interaction and the solitary wave is asymptotically transparent to the ambient field we test our results by numerical simulation of both the full equation and free boundary reductions

an efficient method of estimation for longitudinal surveys with monotone missing data panel attrition is frequently encountered in panel sample surveys when it is related to the observed study variable the classical approach of nonresponse adjustment using a covariate dependent dropout mechanism can be biased we consider an efficient method of estimation with monotone panel attrition when the response probability depends on the previous values of study variable as well as other covariates because of the monotone structure of the missing pattern the response mechanism is missing at random the proposed estimator is asymptotically optimal in the sense that it minimizes the asymptotic variance of a class of estimators that can be written as a linear combination of the unbiased estimators of the panel estimates for each wave and incorporates all available information using generalized least squares variance estimation is discussed and results from a simulation study are presented copyright 2012 oxford university press

landau siegel zeros and zeros of the derivative of the riemann zeta function abstract we show that if the derivative of the riemann zeta function has sufficiently many zeros close to the critical line then the zeta function has many closely spaced zeros this gives a condition on the zeros of the derivative of the zeta function which implies a lower bound of the class numbers of imaginary quadratic fields

model based direct adjustment abstract direct adjustment or standardization applies population weights to subclass means in an effort to estimate population quantities from a sample that is not representative of the population direct adjustment has several attractive features but when there are many subclasses it can attach large weights to small quantities of data often in a fairly erratic manner in the extreme direct adjustment can attach infinite weight to nonexistent data a noticeable inconvenience in practice this article proposes a method of model based direct adjustment that preserves the attractive features of conventional direct adjustment while stabilizing the weights attached to small subclasses the sample mean and conventional direct adjustment are both special cases of model based direct adjustment under two different extreme models for the subclass specific selection probabilities the discussion of this method provides some insights into the behavior of true and estimated propensity scores the estimated scores

missing responses in generalised linear mixed models when the missing data mechanism is nonignorable summary we propose a method for estimating parameters in the generalised linear mixed model with nonignorable missing response data and with nonmonotone patterns of missing data in the response variable we develop a monte carlo em algorithm for estimating the parameters in the model via the gibbs sampler for the normal random effects model we derive a novel analytical form for the e and m steps which is facilitated by integrating out the random effects this form leads to a computationally feasible and extremely efficient monte carlo em algorithm for computing maximum likelihood estimates and standard errors in addition we propose a very general joint multinomial model for the missing data indicators which can be specified via a sequence of one dimensional conditional distributions this multinomial model allows for an arbitrary correlation structure between the missing data indicators and has the potential of reducing the number of nuisance parameters real datasets from the international breast cancer study group and an environmental study involving dyspnoea in cotton workers are presented to illustrate the proposed methods

variance estimation for survey data with composite imputation and nonnegligible sampling fractions abstract this article considers variance estimation for horvitz thompson type estimated totals based on survey data with imputed non respondents and with nonnegligible sampling fractions a method based on a variance decomposition is proposed our method can be applied to complicated situations where a composite of some deterministic and or random imputation methods is used including using imputed data in subsequent imputations although here linearization or taylor expansion type techniques are adopted replication methods such as the jackknife balanced repeated replication and random groups can also be used in applying our method to derive variance estimators using our method variance estimators can be derived under either the customary design based approach or the model assisted approach and are asymptotically unbiased and consistent the transportation annual survey conducted at the u s census bureau in which nonrespondents are imputed using a composite of cold deck and ratio type imputation m

the analysis of longitudinal ordinal data with nonrandom drop out a model is proposed for longitudinal ordinal data with nonrandom drop out which combines the multivariate dale model for longitudinal ordinal data with a logistic regression model for drop out since response and drop out are modelled as conditionally independent given complete data the resulting likelihood can be maximised relatively simply using the em algorithm which with acceleration is acceptably fast and with appropriate additions can produce estimates of precision the approach is illustrated with an example such modelling of nonrandom drop out requires caution because the interpretation of the fitted models depends on assumptions that are unexaminable in a fundamental sense and the conclusions cannot be regarded as necessarily robust the main role of such modelling may be as a component of a sensitivity analysis

crystallization of random trigonometric polynomials we give a precise measure of the rate at which repeated differentiation of a random trigonometric polynomial causes the roots of the function to approach equal spacing this can be viewed as a toy model of crystallization in one dimension in particular we determine the asymptotics of the distribution of the roots around the crystalline configuration and find that the distribution is not gaussian

frozen spatial chaos induced by boundaries csic uib e 07071 palma de mallorca spain received 4 june 1999 we show that rather simple but nontrivial boundary conditions could induce the appearance of spatial chaos that is stationary stable but spatially disordered con gurations in extended dynamical systems with verysimple dynamics we exemplify the phenomenon with a nonlinear reaction diffusion equation in a two dimensional undulated domain concepts from the theory of dynamical systems and a transverse single modeapproximation are used to describe the spatially chaotic structures s1063 651x 99 01812 7 pacs number s 05 45 2ai introduction

statistics and causal inference abstract problems involving causal inference have dogged at the heels of statistics since its earliest days correlation does not imply causation and yet causal conclusions drawn from a carefully designed experiment are often valid what can a statistical model say about causation this question is addressed by using a particular model for causal inference holland and rubin 1983 rubin 1974 to critique the discussions of other writers on causation and causal inference these include selected philosophers medical researchers statisticians econometricians and proponents of causal modeling

a distributional approach for causal inference using propensity scores drawing inferences about the effects of treatments and actions is a common challenge in economics epidemiology and other fields we adopt rubin s potential outcomes framework for causal inference and propose two methods serving complementary purposes one can be used to estimate average causal effects assuming no confounding given measured covariates the other can be used to assess how the estimates might change under various departures from no confounding both methods are developed from a nonparametric likelihood perspective the propensity score plays a central role and is estimated through a parametric model under the assumption of no confounding the joint distribution of covariates and each potential outcome is estimated as a weighted empirical distribution expectations from the joint distribution are estimated as weighted averages or equivalently to first order regression estimates the likelihood estimator is at least as efficient and the regression estimator is at least as efficient and r

on the zeros of the derivatives of real entire functions and wiman s conjecture let f be an entire function of finite order real on the real axis and possessing only real zeros a classical problem proposed by g p6lya 9 10 and a wiman 1 is to determine from the hadamard canonical representation of the function the number of nonreal zeros of the higher derivatives of f in this paper we shall prove the following conjecture of wiman which has been open since 1915

a unified approach to linearization variance estimation from survey data after imputation for item nonresponse variance estimation after imputation is an important practical problem in survey sampling when deterministic imputation or stochastic imputation is used we show that the variance of the imputed estimator can be consistently estimated by a unifying linearize and reverse approach we provide some applications of the approach to regression imputation fractional categorical imputation multiple imputation and composite imputation results from a simulation study under a factorial structure for the sampling response and imputation mechanisms show that the proposed linearization variance estimator performs well in terms of relative bias assuming a missing at random response mechanism