asymptotic normality and consistency of semi nonparametric regression estimators using an upwards f test truncation rule abstract the consistency and asymptotic normality of semi nonparametric regression estimators are shown when the truncation parameter is selected by an upwards f test moreover the same statements are also shown to apply to a large class of linear estimators the article concludes with a discussion of f test critical value settings and includes results from a simulation study which demonstrates that confidence interval coverage can be increased by varying the critical values in a nonstandard way

mixed effects nonlinear regression for unbalanced repeated measures repeated measures data such as clinical pharmacokinetic data growth data and dose response data are often inherently nonlinear with respect to a given response function and are frequently incomplete and or unbalanced nonlinear random effects models together with a variety of estimation procedures have been proposed for the analysis of such data this paper is concerned with a straightforward procedure for estimating and comparing the parameters of a generalized mixed effects nonlinear regression model the asymptotic properties of the proposed estimators are given and large sample tests of hypothesis provided the results are applied to in vitro data on the water transport kinetics of hemodialyzers used in the treatment of patients with chronic renal failure

illustration of bayesian inference in normal data models using gibbs sampling abstract the use of the gibbs sampler as a method for calculating bayesian marginal posterior and predictive densities is reviewed and illustrated with a range of normal data models including variance components unordered and ordered means hierarchical growth curves and missing data in a crossover trial in all cases the approach is straightforward to specify distributionally and to implement computationally with output readily adapted for required inference summaries

seshadri constants and periods of polarized abelian varieties the purpose of this paper is to study the seshadri constants of abelian varieties consider a polarized abelian variety a l of dimension g over the field of complex numbers one can associate to a l a real number e a l its seshadri constant which in effect measures how much of the positivity of l can be concentrated at any given point of a the number e a l can be defined as the rate of growth in k of the number of jets that one can specify in the linear series oa kl alternatively one considers the blow up f x blx x x of x at a point x with exceptional divisor e x over x and defines e a l def sup e r f l ee is nef

seshadri constants on abelian varieties we show that on a complex abelian variety of dimension two or greater the seshadri constant of an ample line bundle is at least one moreover the seshadri constant is equal to one if and only if the polarized abelian variety splits as a product of a principally polarized elliptic curve and a polarized abelian subvariety of codimension one we also examine the case when the seshadri constant is not one and obtain lower bounds when the dimension of the abelian variety is small

the single machine weighted mean squared deviation problem abstract this paper studies a single machine problem related to the just in time jit production objective in which the goal is to minimize the sum of weighted mean squared deviation of the completion times with respect to a common due date in order to solve the problem several structural and dominance properties of the optimal solution are investigated these properties are then integrated within a branch and cut approach to solve a time indexed formulation of the problem the results of a computational experiment with the proposed algorithm show that the method is able to optimally solve instances with up to 300 jobs within reduced running times improving other integer programming approaches

heuristics for multimachine scheduling problems with earliness and tardiness costs we consider multimachine scheduling problems with earliness and tardiness costs we first analyze problems in which the cost of a job is given by a general nondecreasing convex function f of the absolute deviation of its completion time from a common unrestrictive due date and the objective is to minimize the sum of the costs incurred for all n jobs a special case to which considerable attention is given is the completion time variance problem we derive an easily computable lower bound for the minimum cost value and a simple alternating schedule heuristic both of which are computable in on log n time under mild technical conditions with respect to f we show that the worst case optimality accuracy gap of the heuristic lower bound is bounded by a constant as well as by a simple function of a single measure of the dispersion among the processing times we also show that the heuristic bound is asymptotically optimal accurate and characterize the convergence rate as on 2 under very general conditions with respect to the function f in addition we report on a numerical study showing that the average gap is less than 1 even for problems with 30 jobs and that it falls below 0 1 for problems with 90 or more jobs this study also establishes that the empirical gap is almost perfectly proportional with n 2 as verified by a regression analysis finally we generalize the heuristic to settings with a possibly restrictive due date and general asymmetric and possibly nonconvex earliness and tardiness cost functions and demonstrate its excellent performance via a second numerical study

on the period matrix of a riemann surface of large genus with an appendix by j h conway and n j a sloane riemann showed that a period matrix of a compact riemann surface of genusg 1 satisfies certain relations we give a further simple combinatorial property related to the length of the shortest non zero lattice vector satisfied by such a period matrix see 1 13 in particular it is shown that for large genus the entire locus of jacobians lies in a very small neighborhood of the boundary of the space of principally polarized abelian varieties

heteroscedastic nonlinear regression several parameter estimation methods for dealing with heteroscedasticity in nonlinear regression are described these include variations on ordinary weighted iteratively reweighted extended and generalized least squares some of these variations are new and one of them in particular modified extended iteratively reweighted least squares meirls allows parameters of an assumed heteroscedastic variance model to be estimated with an adjustment for bias due to estimation of the regression parameters the context of the discussion is primarily that of pharmacokinetic type data although an example is given involving chemical reaction data using simulated data from 21 heteroscedastic pharmacokinetic type models some of the methods are compared in terms of mean absolute error and 95 confidence interval coverage from these comparisons meirls and the variations on generalized least squares emerge as the methods of choice

on the asymptotic normality of fourier flexible form estimates abstract rates of increase in the number of parameters of a fourier factor demand system that imply asymptotically normal elasticity estimates are characterized this is the multivariate analog of work by andrews 1991 our proof strategy is new and consists of relating the minimum eigenvalue of the sample sum of squares and cross products matrix to the minimum eigenvalue of the population matrix via a uniform strong law with rate that is established using results from the empirical processes literature in its customary form the minimum eigenvalue of the fourier sum of squares and cross products matrix considered as a function of the number of parameters decreases faster than any polynomial the consequence is that the rate at which parameters may increase is slower than any fractional power of the sample size in this case we get the same rate as andrews when our results are applied to multivariate regressions with a minimum eigenvalue that is bounded or declines at a polynomial rate the rate on the parameters is a fractional power of the sample size in this case our method of proof gives faster rates than andrews andrews results cover the heteroskedastic case ours do not

seshadri constants on the self product of an elliptic curve abstract the purpose of this paper is to study seshadri constants on the self product e e of an elliptic curve e we provide explicit formulas for computing the seshadri constants of all ample line bundles on the surfaces considered as an application we obtain a good picture of the behaviour of the seshadri function on the nef cone

earliness tardiness scheduling problems i weighted deviation of completion times about a common due date this paper and its companion part ii concern the scheduling of jobs with cost penalties for both early and late completion in part i we consider the problem of minimizing the weighted sum of earliness and tardiness of jobs scheduled on a single processor around a common due date d we assume that d is not early enough to constrain the scheduling decision the weight of a job does not depend on whether the job is early or late but weights may vary between jobs we prove that the recognition version of this problem is np complete in the ordinary sense we describe optimality conditions and present a computationally efficient dynamic programming algorithm when the weights are bounded by a polynomial function of the number of jobs a fully polynomial approximation scheme is given we also describe four special cases for which the problem is polynomially solvable part ii provides similar results for the unweighted version of this problem where d is arbitrary

a maximum likelihood estimation method for random coefficient regression models summary a method for estimating the distribution of the parameters of a random coefficient regression model is proposed this distribution accounting for interindividual variability is assumed to lie in a wide class of probability distributions rather than in a given parametric class estimation is based on observations from a sample of individuals and likelihood is the estimation criterion experimental designs may be different among individuals allowing the method to apply to routinely collected data the problem has strong connections with the theory of optimum design of experiments conditions are given under which the problem has a unique solution which then corresponds to a discrete distribution a simple pharmacokinetic model involving two parameters is used as an example these parameters have a bimodal distribution as statistical specification moreover only one observation is available per individual thus the method applies even when the model is not identifiable

minimizing mean squared deviation of completion times about a common due date this paper addresses a nonpreemptive single machine scheduling problem where all jobs have a common due date and have zero ready time the scheduling objective is to minimize mean squared deviation msd of job completion times about the due date this nonregular measure of performance is appropriate when earliness and tardiness are both penalized and when large deviations of completion time from the due date are undesirable a special case of the msd problem referred to as the unconstrained msd problem is shown to be equivalent to the completion time variance problem ctv studied by merten and muller merten a g m e muller 1972 variance minimization in single machine sequencing problems management sci 18september 518 528 and schrage schrage l 1975 minimizing the time in system variance for a finite jobset management sci 21may 540 543 strong results for this latter problem are combined with several new propositions to develop a reasonably efficient procedure for solving the unconstrained msd problem this enables us to improve the existing procedures for the ctv problem we also propose a branching procedure for the constrained msd problem and present computational results

some simple methods for estimating intraindividual variability in nonlinear mixed effects models methods are proposed to improve both population and individual inference within the nonlinear random coefficient regression framework by incorporating possible heterogeneity in the intraindividual variance structure these methods extend existing variance function estimation techniques by pooling information across individuals the methods are appropriate when it is reasonable to assume that there exists a common intraindividual variance structure

the nonlinear mixed effects model with a smooth random effects density summary the fixed parameters of the nonlinear mixed effects model and the density of the random effects are estimated jointly by maximum likelihood the density of the random effects is assumed to be smooth but is otherwise unrestricted the method uses a series expansion that follows from the smoothness assumption to represent the density and quadrature to compute the likelihood standard algorithms are used for optimization empirical bayes estimates of random coefficients are obtained by computing posterior modes the method is applied to data from pharmacokinetics and properties of the method are investigated by application to simulated data

on the minimization of completion time variance with a bicriteria extension we discuss a single machine scheduling problem where the objective is to minimize the variance of job completion times to date the problem has not been solved in polynomial time this paper presents a dynamic programming algorithm that is pseudopolynomial in complexity we also propose a fully polynomial approximation scheme and derive a lower bound that is useful in its implementation furthermore we show that the dynamic programming solution is easy to extend to a bicriteria version of the problem in which it is desired to simultaneously minimize the mean completion time

scheduling about a given common due date to minimize mean squared deviation of completion times abstract in this paper the problem of minimizing the mean squared deviation msdp of job completion times about a given common due date in n job single machine scheduling is considered the release times for all jobs are assumed to be zero no polynomial time algorithms have been found to identify an optimal solution to msdp for the tightly restricted version of msdp no even pseudo polynomial time algorithms have been found to identify an optimal solution we present some dominance properties for msdp based on which a pseudo polynomial dynamic programming algorithm which is an extension of the dynamic programming algorithm proposed by lee danusaputro and lin is presented to optimally solve the tightly restricted version of msdp computational results show that the proposed dynamic programming algorithm can optimally solve tightly restricted instances of msdp with up to 100 jobs in less than two seconds

remarks on seshadri constants which is called the seshadri constant of l at x here the infimum is taken over all irreducible curves c passing through x and mx c is the multiplicity of c at x for example if l is very ample then e l x 1 there has been recant interest in trying to give lower bounds for this invariant at a general point ein and lazarsfeld el show that if x is a surface then e l x 1 for very general x x in higher dimension n 3 ein kuchle and lazarsfeld ekl prove that e l x 1 n for a very general point we say that a point x x is very general if x is in the complement x z of z a countably union of proper subvarieties examples of miranda show that e l x can take arbitrarily small values in codimension two i e codim z 2 even for an ample line bundle one may expect that this general bounds are not optimal an elementary observation see remark 1 below for the proof shows that e l x n ln a natural question is are there conditions which guarantee equality even in relative simple cases it turns out to be hard to give an answer recently xu xu improved the surface bound given by ein and lazarsfeld he showed that if l2 3 4 4 5 for a given integer 1

an exact algorithm to minimize mean squared deviation of job completion times about a common due date abstract we consider a deterministic n job single machine scheduling problem with the objective of minimizing the mean squared deviation msd of job completion times about a common due date d the msd measure is non regular and its value can decrease when one or more completion times increases msd problem is connected with the completion time variance ctv problem and has been proved to be np hard this problem finds application in situations where uniformity of service is important we present an exact algorithm of pseudo polynomial complexity using ideas from branch and bound and dynamic programming we propose a dominance rule and also develop a lower bound on msd the dominance rule and lower bound are effectively combined and used in the development of the proposed algorithm the search space is explored using the breadth first branching strategy the asymptotic space complexity of the algorithm is o nd irrespective of the version of the problem tightly constrained constrained or unconstrained the proposed algorithm provides optimal solutions for problem instances up to 1000 jobs size under different due date settings

an effective and sharp lower bound on seshadri constants on surfaces with picard number 1 abstract on an algebraic surface with picard number 1 we compute in terms of the generator of the ample ray a lower bound for seshadri constant valid at every point of the surface we show that this bound cannot be improved in general

a bayesian approach to nonlinear random effects models nonlinear random effects models are considered from the bayesian point of view the method of analysis follows closely that of lindley and smith 1972 journal of the royal statistical society series b 34 1 42 the numerical method is related to the em algorithm

semi nonparametric maximum likelihood estimation on developpe une approche basee sur une innovation due a phillips 1983 sur les approximations des fonctions de densite

note a note on the minimization of mean squared deviation of completion times about a common due date this paper points out a conceptual flaw present in a recent publication it shows how the methodology can be modified to correct this flaw it also presents improved bounds to determine the nature of a given problem

positivity of line bundles on general blow ups of abelian surfaces abstract let s l s be a polarized abelian surface and let m c l s i 1 r e i be a line bundle on bl r s where bl r s s is the blow up of s at r general points with exceptional divisors e 1 e r in this paper we provide a criterion for k very ampleness of m also we deal with the case when s is an arbitrary surface of picard number one with a numerically trivial canonical divisor

nonlinear mixed effects models for repeated measures data we propose a general nonlinear mixed effects model for repeated measures data and define estimators for its parameters the proposed estimators are a natural combination of least squares estimators for nonlinear fixed effects models and maximum likelihood or restricted maximum likelihood estimators for linear mixed effects models we implement newton raphson estimation using previously developed computational methods for nonlinear fixed effects models and for linear mixed effects models two examples are presented and the connections between this work and recent work on generalized linear mixed effects models are discussed

fay s trisecant identity and conformal field theory we study the correlation functions of a system of free chiral fermions on a compact riemann surface using techniques of algebraic geometry fay s trisecant identity arises as a consequence of the proof of the uniqueness of correlation functions