extension of the berlekamp massey algorithm to n dimensions abstract we present an algorithm for finding a minimal set of linear recurring relations which are valid for a given n dimensional array over any field where the minimality is defined with respect to the partial order over the n dimensional lattice the algorithm is an extension of our two dimensional version of the berlekamp massey algorithm to more than two dimensions the n dimensional theory is based on more general concepts which can be reduced into those of the two dimensional theory in the previous paper in a typical case the resulting set of polynomials characterizing the minimal linear recurring relations proves to be a groebner basis of the ideal defined by the array and consequently the structure of an n dimensional linear feedback shift register with the minimum number of storage devices which can generate the array is determined by it

on a decoding algorithm for codes on maximal curves a decoding algorithm for algebraic geometric codes that was given by a n skorobogatov and s g vladut preprint inst problems of information transmission 1988 is considered the author gives a modified algorithm with improved performance which he obtains by applying the above algorithm a number of times in parallel he proves the existence of the decoding algorithm on maximal curves by showing the existence of certain divisors however he has so far been unable to give an efficient procedure of finding these divisors

fast decoding of algebraic geometric codes up to the designed minimum distance we present a decoding algorithm for algebraic geometric codes from regular plane curves in particular the hermitian curve which corrects all error patterns of weight less than d 2 with low complexity the algorithm is based on the majority scheme of feng and rao 1993 and uses a modified version of sakata s 1988 generalization of the berlekamp massey algorithm

fast generalized minimum distance decoding of algebraic geometry and reed solomon codes generalized minimum distance gmd decoding is a standard soft decoding method for block codes we derive an efficient general gmd decoding scheme for linear block codes in the framework of error correcting pairs special attention is paid to reed solomon rs codes and one point algebraic geometry ag codes for rs codes of length n and minimum hamming distance d the gmd decoding complexity turns out to be in the order o nd where the complexity is counted as the number of multiplications in the field of concern for ag codes the gmd decoding complexity is highly dependent on the curve in consideration it is shown that we can find all relevant error erasure locating functions with complexity o o sub 1 nd where o sub 1 is the size of the first nongap in the function space associated with the code a full gmd decoding procedure for a one point ag code can be performed with complexity o dn sup 2

covariate adjustment in randomized trials with binary outcomes targeted maximum likelihood estimation covariate adjustment using linear models for continuous outcomes in randomized trials has been shown to increase efficiency and power over the unadjusted method in estimating the marginal effect of treatment however for binary outcomes investigators generally rely on the unadjusted estimate as the literature indicates that covariate adjusted estimates based on the logistic regression models are less efficient the crucial step that has been missing when adjusting for covariates is that one must integrate average the adjusted estimate over those covariates in order to obtain the marginal effect we apply the method of targeted maximum likelihood estimation tmle to obtain estimators for the marginal effect using covariate adjustment for binary outcomes we show that the covariate adjustment in randomized trials using the logistic regression models can be mapped by averaging over the covariate s to obtain a fully robust and efficient estimator of the marginal effect which equals a targeted maximum likelihood estimator this tmle is obtained by simply adding a clever covariate to a fixed initial regression we present simulation studies that demonstrate that this tmle increases efficiency and power over the unadjusted method particularly for smaller sample sizes even when the regression model is mis specified

a generalized forney formula for algebraic geometric codes this correspondence contains a straightforward generalization of decoding of bch codes to the decoding of algebraic geometric codes couched in terms of varieties ideals and grobner bases this consists of 1 a berlekamp massey type lattice shifting row reduction algorithm with majority voting similar to algorithms in the current literature 2 a realization that it produces a minimal grobner basis b for the error locator ideal i v relative to a particular weighted total degree monomial ordering 3 a factoring of that basis into several minimal plex bases that facilitates finding the variety v of error positions and 4 a direct generalization of forney s formula to calculate error magnitudes using functions spl sigma p which are by products of this factoring

on the number of correctable errors for some ag codes an algorithm that for codes from a regular plane curve corrects up to d 2 m sup 2 8 m 4 9 8 errors where d is the designed distance and m is the degree of the curve was presented in an earlier work see ibid vol 35 p 811 21 1989 it is now shown that this bound is the best possible for the algorithm considered

construction and decoding of a class of algebraic geometry codes a class of codes derived from algebraic plane curves is constructed the concepts and results from algebraic geometry that were used are explained in detail no further knowledge of algebraic geometry is needed parameters generator and parity check matrices are given the main result is a decoding algorithm which turns out to be a generalization of the peterson algorithm for decoding bch decoder codes

decoding of codes defined by a single point on a curve a decoding algorithm for certain codes from algebraic curves is presented the dual code which is used for decoding is formed by evaluating rational functions having poles at a single point a theoretical foundation is developed from which an improved bound for the minimum distance and results on decoding up to that bound are derived the decoding is done by a computationally efficient berlekamp massey type algorithm which is intrinsic to the curve

bounded efficient and doubly robust estimation with inverse weighting consider estimating the mean of an outcome in the presence of missing data or estimating population average treatment effects in causal inference a doubly robust estimator remains consistent if an outcome regression model or a propensity score model is correctly specified we build on a previous nonparametric likelihood approach and propose new doubly robust estimators which have desirable properties in efficiency if the propensity score model is correctly specified and in boundedness even if the inverse probability weights are highly variable we compare the new and existing estimators in a simulation study and find that the robustified likelihood estimators yield overall the smallest mean squared errors

enhanced precision in the analysis of randomized trials with ordinal outcomes we present a general method for estimating the effect of a treatment on an ordinal outcome in randomized trials the method is robust in that it does not rely on the proportional odds assumption our estimator leverages information in prognostic baseline variables and has all of the following properties i it is consistent ii it is locally efficient iii it is guaranteed to have equal or better asymptotic precision than both the inverse probability weighted and the unadjusted estimators to the best of our knowledge this is the first estimator of the causal relation between a treatment and an ordinal outcome to satisfy these properties we demonstrate the estimator in simulations based on resampling from a completed randomized clinical trial of a new treatment for stroke we show potential gains of up to 39 in relative efficiency compared to the unadjusted estimator the proposed estimator could be a useful tool for analyzing randomized trials with ordinal outcomes since existing methods either rely on model assumptions that are untenable in many practical applications or lack the efficiency properties of the proposed estimator we provide r code implementing the estimator

periodic solutions for van der pol equation with time delay for van der pol equation with distributed delay when the distributed delay kernel is the general gamma distributed delay kernel the existence and the stability of periodic solution are obtained by using the linear chain trick and geometric singular perturbation theory on the other hand for van der pol equation with discrete delay the existence and the stability are proved by employing a technique which is based on inertial manifold finally numerical simulations are also given to illustrate the results

vector bundles and codes on the hermitian curve the construction of algebraic geometry ag codes can be seen as a distinctly geometric process and yet decoding procedures tend to rely on algebraic ideas that have no direct geometric interpretation recently however trygve johnsen observed that decoding can be viewed in abstract terms of a class of vector bundles on the underlying curve the present paper describes these objects at a concrete computational level for the hermitian codes comega d mpinfin defined over fq 2 q a power of 2 the construction of explicit representations of the vector bundles by transition matrices involves finding functions on the curve that satisfy a certain property in their power series expansions around pinfin computing the image of the corresponding global sections under serre duality and finding a suitable open cover of the curve the cover enables any rational point to be expressed as a line bundle by a simple kind of transition function a special case is considered in which these functions can be realized as ratios of linear forms

δ sequences and evaluation codes defined by plane valuations at infinity we introduce the concept of sequence a sequence generates a well ordered semigroup s in z or r we show how to construct and compute parameters for the dual code of any evaluation code associated with a weight function defined by from the polynomial ring in two indeterminates to a semigroup s as above we prove that this is a simple procedure which can be understood by considering a particular class of valuations of function fields of surfaces called plane valuations at infinity we also give algorithms to construct an unlimited number of sequences of the different existing types and so this paper provides the tools to know and use a new large set of codes

better bootstrap confidence intervals abstract we consider the problem of setting approximate confidence intervals for a single parameter in a multiparameter family the standard approximate intervals based on maximum likelihood theory can be quite misleading in practice tricks based on transformations bias corrections and so forth are often used to improve their accuracy the bootstrap confidence intervals discussed in this article automatically incorporate such tricks without requiring the statistician to think them through for each new application at the price of a considerable increase in computational effort the new intervals incorporate an improvement over previously suggested methods which results in second order correctness in a wide variety of problems in addition to parametric families bootstrap intervals are also developed for nonparametric situations

algebraic geometry codes the theory of error correcting codes derived from curves in an algebraic geometry was initiated by the work of goppa as generalizations of bose chaudhuri hocquenghem bch reed solomon rs and goppa codes the development of the theory has received intense consideration since that time and the purpose of the paper is to review this work elements of the theory of algebraic curves at a level sufficient to understand the code constructions and decoding algorithms are introduced code constructions from particular classes of curves including the klein quartic elliptic and hyperelliptic curves and hermitian curves are presented decoding algorithms for these classes of codes and others are considered the construction of classes of asymptotically good codes using modular curves is also discussed

sharp nonparametric bounds and randomization inference for treatment effects on an ordinal outcome in clinical research investigators are interested in inferring the average causal effect of a treatment however the causal parameter that can be used to derive the average causal effect is not well defined for ordinal outcomes although some definitions have been proposed they are limited in that they are not identical to the well defined causal risk for a binary outcome which is the simplest ordinal outcome in this paper we propose the use of a causal parameter for an ordinal outcome defined as the proportion that a potential outcome under one treatment condition would not be smaller than that under the other condition for a binary outcome this proportion is identical to the causal risk unfortunately the proposed causal parameter cannot be identified even under randomization therefore we present a numerical method to calculate the sharp nonparametric bounds within a sample reflecting the impact of confounding when the assumption of independent potential outcomes is included the causal parameter can be identified when randomization is in play then we present exact tests and the associated confidence intervals for the relative treatment effect using the randomization based approach which are an extension of the existing methods for a binary outcome our methodologies are illustrated using data from an emetic prevention clinical trial

efficient forney functions for decoding ag codes using a forney formula to solve for the error magnitudes in decoding algebraic geometric ag codes requires producing functions spl sigma sub p which are 0 at all but one point p of the variety of the error locator ideal the best such function is produced here in a reasonably efficient way from a lex grobner basis this lex basis is in turn produced efficiently from a weighted grevlex basis by using the fglm algorithm these two steps essentially complete the efficient decoding scheme based on a forney formula started in the author s previous work see ibid vol 42 p 1263 8 1996

a code decomposition approach for decoding cyclic and algebraic geometric codes an approach based on code decomposition and partial transform for constructing algorithms for decoding cyclic codes and algebraic geometric ag codes is introduced a general decoding procedure applicable to arbitrary linear codes and their subfield subcodes is then developed in particular we have developed algorithms for error and erasure decoding of cyclic codes up to their actual minimum distance error and erasure decoding of ag codes up to their designed minimum distance and decoding of subfield subcodes of ag codes geometric bch codes moreover a generalization of geometric bch codes is introduced it is shown by an example that for a simple class of ag codes the so called one point codes this generalization brings a better estimate of their minimum distance it is also shown that the algorithms developed in this paper can be applied to decode these codes up to their estimated minimum distance

general principles for the algebraic decoding of cyclic codes this paper provides two theorems for decoding all types of cyclic codes it is shown that from a polynomial ideal point of view the decoding problems of cyclic codes are closely related to the monic generators of certain polynomial ideals this conclusion is also generalized to the decoding problems of algebraic geometry codes

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

a note on hermitian codes over gf q sup 2 properties of codes defined by goppa s algebraic geometric method using hermitian curves are discussed generator and parity check matrices for such codes are derived explicitly results concerning the minimum distance and the weight distribution of the codes are provided

simplified understanding and efficient decoding of a class of algebraic geometric codes an efficient decoding algorithm for algebraic geometric codes is presented for codes from a large class of irreducible plane curves including hermitian curves it can correct up to d 1 2 errors where d is the designed minimum distance with it we also obtain a proof of d sub min spl ges d without directly using the riemann roch theorem the algorithm consists of gaussian elimination on a specially arranged syndrome matrix followed by a novel majority voting scheme a fast implementation incorporating block hankel matrix techniques is obtained whose worst case running time is o mn sup 2 where m is the degree of the curve applications of our techniques to decoding other algebraic geometric codes to decoding bch codes to actual minimum distance and to two dimensional shift register synthesis are also presented

on determining the independent point set for doubly periodic arrays and encoding two dimensional cyclic codes and their duals for the purpose of encoding two dimensional cyclic tdc codes an effective algorithm for finding the independent point set of an arbitrary module of doubly periodic dp arrays is proposed in addition a method for determining the characteristic ideal of a given set of dp arrays is exhibited with the aid of these methods it is possible to specify the structure of the generator and check ideals of tdc codes by applying this algorithm to nonsemisimple binary tdc codes with small areas several optimal linear codes have been found and their previously unknown tdc structures have been exhibited

error locator ideals for algebraic geometric codes the error locations for an algebraic geometric code c d mp are exactly the common zeros that is a projective variety v i of a set ideal i of error locator functions the paper gives a one dimensional berlekamp massey version of the feng rao 1993 algorithm for decoding algebraic geometric codes c d mp this produces a generating set for i as an ideal of size at most spl rho the smallest positive pole order at p of any function in l mp relative to any error of weight at most e

chaos controlling of extended nonlinear lienard system based on the melnikov theory abstract chaos control may have a dual function to generate chaos or to suppress it by the melnikov theory two criterions of controlling chaos for a class of nonlinear lienard system are established according to the criterions we implement chaos control using non feedback method two illustrative examples a duffing rayleigh oscillator imposed with a weak bounded noise control and a duffing van der pol oscillator subject to a harmonic parametric control are presented here to illustrate the validity of the criterions to better support the results obtained above some indicators are used namely the lyapunov exponent phase portrait poincare cross section and time evolution both two methods lead to fully consistent results

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

improved geometric goppa codes i basic theory in this paper we present a construction of improved geometric goppa codes which for the case of r 2g are often more efficient than the current geometric goppa codes derived from some varieties which include algebraic curves hyperplanes surfaces and other varieties for the special case of a plane in a three dimensional projective space the improved geometric goppa codes are reduced to linear multilevel codes for these improved geometric goppa codes a designed minimum distance can be easily determined and a decoding procedure which corrects up to half the designed minimum distance is also given

stability and chaotic behavior of a pid controlled inverted pendulum subjected to harmonic base excitations by using the normal form theory abstract in this paper we investigate the stability and the onset of chaotic oscillations around the pointing up position for a simple inverted pendulum that is driven by a control torque and is harmonically excited in the vertical and horizontal directions the driven control torque is defined as a proportional plus integral plus derivative pid control of the deviation angle with respect to the pointing down equilibrium position the parameters of the pid controller are tuned by using the routh criterion to obtain a stable weak focus around the pointing up position whose stability is investigated by using the normal form theory the normal form theory is also used to deduce a simplified mathematical model that can be resolved analytically and compared with the numerical simulation of the complete mathematical model from the harmonic prescribed motions for the pendulum base necessary conditions for chaotic motion are deduced by means of the melnikov function when the pendulum is close to the unstable pointing up position the pid parameters are changed and the chaotic motion is destroyed which is achieved by employing very small control signals even in the presence of random noise the results of the analytical calculations are verified by full numerical simulations

decoding of hermitian codes the key equation and efficient error evaluation this paper presents a generalization of the key equation to hermitian codes the syndrome is interpreted as a power series and the product of this power series with a locator polynomial gives the error evaluator polynomial the computation of the evaluator polynomial may be done iteratively using a modified version of a previously published computationally efficient algorithm for computing locator polynomials

doubly robust inference for targeted minimum loss based estimation in randomized trials with missing outcome data missing outcome data is a crucial threat to the validity of treatment effect estimates from randomized trials the outcome distributions of participants with missing and observed data are often different which increases bias causal inference methods may aid in reducing the bias and improving efficiency by incorporating baseline variables into the analysis in particular doubly robust estimators incorporate 2 nuisance parameters the outcome regression and the missingness mechanism ie the probability of missingness conditional on treatment assignment and baseline variables to adjust for differences in the observed and unobserved groups that can be explained by observed covariates to consistently estimate the treatment effect one of these nuisance parameters must be consistently estimated traditionally nuisance parameters are estimated using parametric models which often precludes consistency particularly in moderate to high dimensions recent research on missing data has focused on data adaptive estimation to help achieve consistency but the large sample properties of such methods are poorly understood in this article we discuss a doubly robust estimator that is consistent and asymptotically normal under data adaptive estimation of the nuisance parameters we provide a formula for an asymptotically exact confidence interval under minimal assumptions we show that our proposed estimator has smaller finite sample bias compared to standard doubly robust estimators we present a simulation study demonstrating the enhanced performance of our estimators in terms of bias efficiency and coverage of the confidence intervals we present the results of an illustrative example a randomized double blind phase 2 3 trial of antiretroviral therapy in hiv infected persons

pragmatical adaptive chaos control from a new double van der pol system to a new double duffing system a new pragmatical adaptive control method for different chaotic systems is proposed traditional chaos control is limited to decrease chaos of one chaotic system this method enlarges the effective scope of chaos control we can control a chaotic system e g a new chaotic double van der pol system to a given chaotic or regular system e g a new chaotic double duffing system or to a damped simple harmonic system by a pragmatical theorem of asymptotical stability based on an assumption of equal probability of initial point an adaptive control law is derived such that it can be proved strictly that the common zero solution of error dynamics and of parameter dynamics is asymptotically stable numerical simulations are given to show the effectiveness of the proposed scheme

steady state self oscillations and chaotic behavior of a controlled electromechanical device by using the first lyapunov value and the melnikov theory abstract in this paper regular and chaotic oscillations in a controlled electromechanical transducer are investigated the nonlinear control laws are defined by an electric tension excitation and an external force applied to the mobile piece of the transducer the paper shows that an andronov poincare hopf bifurcation appears as long as adequate parameters are chosen for the nonlinear control laws the stability of the weak focuses associated to such bifurcation is examined according to the sign of the first lyapunov value showing that chaotic behavior can arise when the first lyapunov value is varied harmonically the appearance of a homoclinic orbit is investigated assuming an approximated model for the device on the basis of the parametric equations of the homoclinic orbit and the presence of harmonic disturbances on the platform it is demonstrated that chaotic oscillations can also appear and they have been examined by means of the melnikov theory chaotic behavior is corroborated by means of the sensitive dependence lyapunov exponents and power spectral density and it is applied to drive the transducer mobile piece to a predefined set point assuming that noise due to the measurement process can appear in the control signals the steady state error associated to such random noise is eliminated by adding a pi linear controller to the control force numerical simulations are used to corroborate the analytical results

decoding algebraic geometric codes up to the designed minimum distance a simple decoding procedure for algebraic geometric codes c sub omega d g is presented this decoding procedure is a generalization of peterson s decoding procedure for the bch codes it can be used to correct any d 1 2 or fewer errors with complexity o n sup 3 where d is the designed minimum distance of the algebraic geometric code and n is the codelength

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

nonparametric regression with missing outcomes using weighted kernel estimating equations we consider nonparametric regression of a scalar outcome on a covariate when the outcome is missing at random mar given the covariate and other observed auxiliary variables we propose a class of augmented inverse probability weighted aipw kernel estimating equations for nonparametric regression under mar we show that aipw kernel estimators are consistent when the probability that the outcome is observed that is the selection probability is either known by design or estimated under a correctly specified model in addition we show that a specific aipw kernel estimator in our class that employs the fitted values from a model for the conditional mean of the outcome given covariates and auxiliaries is double robust that is it remains consistent if this model is correctly specified even if the selection probabilities are modeled or specified incorrectly furthermore when both models happen to be right this double robust estimator attains the smallest possible asymptotic variance of all aipw kernel

adaptive variable structure control for chaos suppression of unified chaotic systems this paper investigates the chaos suppression problem for a class of unified chaotic systems subject to uncertainties and control input with dead zone nonlinearity using the variable structure control technique a robust adaptive control law is established to suppress chaos in a class of unified chaotic systems even with unknown uncertainties and dead zone nonlinearity in input in particular a switching surface is newly proposed to simplify the task of ensuring the stability of the closed loop system in the sliding mode numerical results validate the effectiveness of the proposed adaptive control scheme

global asymptotic stability of nonautonomous systems of lienard type this paper deals with nonautonomous lienard type systems sufficient conditions are given for the zero solution of the systems to be globally asymptotically stable the main result is proved by means of phase plane analysis with a liapunov function examples are included to contrast our theorem with results which were presented by hatvani and cantarelli some global phase portraits are also attached

on the decoding of algebraic geometric codes this paper provides a survey of the existing literature on the decoding of algebraic geometric codes definitions theorems and cross references will be given we show what has been done discuss what still has to be done and pose some open problems

sub quadratic decoding of one point hermitian codes we present the first two sub quadratic complexity decoding algorithms for one point hermitian codes the first is based on a fast realization of the guruswami sudan algorithm using state of the art algorithms from computer algebra for polynomial ring matrix minimization the second is a power decoding algorithm an extension of classical key equation decoding which gives a probabilistic decoding algorithm up to the sudan radius we show how the resulting key equations can be solved by the matrix minimization algorithms from computer algebra yielding similar asymptotic complexities

decoding geometric goppa codes using an extra place decoding geometric goppa codes can be reduced to solving the key congruence of a received word in an affine ring if the codelength is smaller than the number of rational points on the curve then this method can correct up to 1 2 d l 2 s errors where d is the designed minimum distance of the code and s is the clifford defect the affine ring with respect to a place p is the set of all rational functions which have no poles except at p and it is somehow similar to a polynomial ring for a special kind of geometric goppa code namely c sub omega d mp the decoding algorithm is reduced to solving the key equation in the affine ring which can be carried out by the subresultant sequence in the affine ring with complexity o n sup 3 where n is the length of codewords

doubly robust estimation in missing data and causal inference models the goal of this article is to construct doubly robust dr estimators in ignorable missing data and causal inference models in a missing data model an estimator is dr if it remains consistent when either but not necessarily both a model for the missingness mechanism or a model for the distribution of the complete data is correctly specified because with observational data one can never be sure that either a missingness model or a complete data model is correct perhaps the best that can be hoped for is to find a dr estimator dr estimators in contrast to standard likelihood based or nonaugmented inverse probability weighted estimators give the analyst two chances instead of only one to make a valid inference in a causal inference model an estimator is dr if it remains consistent when either a model for the treatment assignment mechanism or a model for the distribution of the counterfactual data is correctly specified because with observational data one can never be sure that a model for the treatment assignment mechanism or a model for the counterfactual data is correct inference based on dr estimators should improve upon previous approaches indeed we present the results of simulation studies which demonstrate that the finite sample performance of dr estimators is as impressive as theory would predict the proposed method is applied to a cardiovascular clinical trial

on the classification of lienard systems with amplitude independent periods abstract we consider conditions under which the second order differential equation x f x x g x 0 has a family of periodic orbits with constant period this condition is equivalent to seeking conditions under which the two dimensional autonomous system x y y g x f x y has a center with constant period i e an isochronous center in turn this is equivalent to the latter system being locally linearizable we give a simple necessary and sufficient condition for this when f and g are analytic functions in the case where when f and g are polynomials we show that this reduces to a finitely determinable system of equations a complete classification is given of all such systems of degree 34 or less

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

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

on the decoding of algebraic geometric codes over f sub q for q or 16 it is proved that for algebraic geometric codes on a curve over f sub q for q or 37 or on a curve of sufficiently large genus over f sub q for q or 16 there exists a polynomial decoding algorithm up to d 1 2 errors d being the designed minimum distance

improved double robust estimation in missing data and causal inference models recently proposed double robust estimators for a population mean from incomplete data and for a finite number of counterfactual means can have much higher efficiency than the usual double robust estimators under misspecification of the outcome model in this paper we derive a new class of double robust estimators for the parameters of regression models with incomplete cross sectional or longitudinal data and of marginal structural mean models for cross sectional data with similar efficiency properties unlike the recent proposals our estimators solve outcome regression estimating equations in a simulation study the new estimator shows improvements in variance relative to the standard double robust estimator that are in agreement with those suggested by asymptotic theory

fast decoding of codes from algebraic plane curves improvement to an earlier decoding algorithm for codes from algebraic geometry is presented for codes from an arbitrary regular plane curve the authors correct up to d 2 m sup 2 8 m 4 9 8 errors where d is the designed distance of the code and m is the degree of the curve the complexity of finding the error locator is o n sup 7 3 where n is the length of the code for codes from hermitian curves the complexity of finding the error values given the error locator is o n sup 2 and the same complexity can be obtained in the general case if only d 2 m sup 2 2 errors are corrected