numerical methods for optimum experimental design in dae systems subject of this paper is the design of optimal experiments for chemical processes described by nonlinear dae models the optimization aims at maximizing the statistical quality of a parameter estimate from experimental data this leads to optimal control problems with an unusual and intricate objective function which depends implicitly on first derivatives of the solution of the underlying dae we treat these problems by the direct approach and solve them using a structured sqp method the required first and second derivatives of the solution of the dae are computed very efficiently by a special coupling of the techniques of internal numerical differentiation and automatic differentiation the performance of our approach is demonstrated for an application to chemical reaction kinetics

semi infinite programming theory methods and applications starting from a number of motivating and abundant applications in 2 including control of robots eigenvalue computations mechanical stress of materials and statistical design the authors describe a class of optimization problems which are referred to as semi infinite because their constraints bound functions of a finite number of variables on a whole region in 3 5 first and second order optimality conditions are derived for general nonlinear problems as well as a procedure for reducing the problem locally to one with only finitely many constraints another main effort for achieving simplification is through duality in 6 there algebraic properties of finite linear programming are brought to bear on duality theory in semi infinite programming section 7 treats numerical methods based on either discretization or local reduction with the emphasis on the design of superlinearly convergent sqp type methods taking this differentiable point of view this paper can be considered to be complementar

modelling balanced longitudinal data maximum likelihood estimation and analysis of variance for linear models assuming a within experimental units covariance structure that incorporates errors of measurement serial correlation and variation between units results on explicit estimation of regression parameters are used to simplify maximum likelihood estimation of covariance parameters the use of an analysis of variance table as a simpler alternative to likelihood inference is illustrated with two examples

the number of maximal torsion cosets in subvarieties of tori we present sharp bounds on the number of maximal torsion cosets in a subvariety of the complex algebraic torus gm n our first main result gives a bound in terms of the degree of the defining polynomials a second result gives a bound in terms of the toric degree of the subvariety as a consequence we prove the conjectures of ruppert and of aliev and smyth on the number of isolated torsion points of a hypersurface these conjectures bound this number in terms of the multidegree and the volume of the newton polytope of a polynomial defining the hypersurface respectively

quantifier elimination for the reals with a predicate for the powers of two in 1985 van den dries showed that the theory of the reals with a predicate for the integer powers of two admits quantifier elimination in an expanded language and is hence decidable he gave a model theoretical argument which provides no apparent bounds on the complexity of a decision procedure we provide a syntactical argument that yields a procedure that is primitive recursive although not elementary in particular we show that it is possible to eliminate a single block of existential quantifiers in time 2 o n 0 where n is the length of the input formula and 2 k x denotes k fold iterated exponentiation

arma covariance structures with time heteroscedasticity for repeated measures experiments abstract rochon and helms 1989 presented a model for analyzing repeated measures experiments the general linear model was used to assess the influence of covariate information and arma time series models were put forward to characterize the covariance matrix among the repeated measures practical experience has suggested however that the arma assumption of constant variances and autocovariances over time is too restrictive for many applications for example observations may be relatively stable toward the beginning of the study but become more variable toward the end this article presents a modification to this structure which provides for heteroscedasticity over time maximum likelihood ml estimation procedures are considered and the estimators are found to enjoy optimal large sample properties a scoring algorithm is described for iterating to a solution of the ml equations the model is illustrated with data from a clinical trial investigating human erythropoietin for treating anemia in end

periodic subvarieties of semiabelian varieties and annihilators of irreducible representations abstract let g be a semiabelian variety defined over a field of characteristic 0 endowed with an endomorphism we prove there is no proper subvariety y g which intersects the orbit of each periodic point of g under the action of as an application we are able to give a topological characterization of the annihilator ideals of irreducible representations in certain skew polynomial algebras

best linear recursive estimation for mixed linear models abstract recursive estimation techniques for fixed and completely random models are extended to mixed linear models the kalman filter is used to obtain recursive estimators for a two part random model where the second random factor obeys a generalized autoregressive process by passing to the limit in an appropriate way recursions for the mixed model are derived

a robust optimization approach to experimental design for model discrimination of dynamical systems a high ranking goal of interdisciplinary modeling approaches in science and engineering are quantitative prediction of system dynamics and model based optimization quantitative modeling has to be closely related to experimental investigations if the model is supposed to be used for mechanistic analysis and model predictions typically before an appropriate model of an experimental system is found different hypothetical models might be reasonable and consistent with previous knowledge and available data the parameters of the models up to an estimated confidence region are generally not known a priori therefore one has to incorporate possible parameter configurations of different models into a model discrimination algorithm which leads to the need for robustification in this article we present a numerical algorithm which calculates a design of experiments allowing optimal discrimination of different hypothetic candidate models of a given dynamical system for the most inappropriate worst case parameter configurations within a parameter range the design comprises initial values system perturbations and the optimal placement of measurement time points the number of measurements as well as the time points are subject to design the statistical discrimination criterion is worked out rigorously for these settings a derivation from the kullback leibler divergence as optimization objective is presented for the case of discontinuous heaviside functions modeling the measurement decision which are replaced by continuous approximations during the optimization procedure the resulting problem can be classified as a semi infinite optimization problem which we solve in an outer approximations approach stabilized by a suggested homotopy strategy whose efficiency is demonstrated we present the theoretical framework algorithmic realization and numerical results

an optimal experimental design criterion for discriminating between non normal models summary typically t optimality is used to obtain optimal designs to discriminate between homoscedastic models with normally distributed observations some extensions of this criterion have been made for the heteroscedastic case and binary response models in the literature in this paper a new criterion based on the kullback leibler distance is proposed to discriminate between rival models with non normally distributed observations the criterion is coherent with the approaches mentioned above an equivalence theorem is provided for this criterion and an algorithm to compute optimal designs is developed the criterion is applied to discriminate between the popular michaelis menten model and a typical extension of it under the log normal and the gamma distributions

screening and diagnosis when within individual observations are markov dependent the statistical model currently used for determining the amount of regression to the mean that will occur in a screening study includes an assumption that repeat observations within the same subject are mutually independent this assumption has been used in the determination of the number of repeat observations within an individual that is required to reduce the amount of regression to the mean or the probability of misclassification to a given value in this paper the model is extended to the case in which repeat observations within an individual are markov dependent new expressions are given for the regression to the mean based on the time delay between screening and re examination and on the use of an average of several measurements for both screening and re examination the extended model is used to describe the conditional distribution of the long term mean of an individual given several measurements and this distribution is suggested as a diagnostic tool a method is presented for estimation of the autocorrelation coefficient in very short time series observed in several individuals the autocorrelation in diastolic blood pressure is estimated from a set of repeat observations one day apart on a group of subjects

on the use of consistent approximations in the solution of semi infinite optimization and optimal control problems we consider a pair consisting of an optimization problem and its optimality function p and define consistency of approximating problem optimality function pairs p n n to p in terms of the epigraphical convergence of the p n to p and the hypographical convergence of the optimality functions n to we then show that standard discretization techniques decompose semi infinite optimization and optimal control problems into families of finite dimensional problems which together with associated optimality functions are consistent discretizations to the original problems we then present two types of techniques for using consistent approximations in obtaining an approximate solution of the original problems the first is a filter type technique similar to that used in conjunction with penalty functions the second one is an adaptive discretization technique that can be viewed as an implementation of a conceptual algorithm for solving the original problems

stable polynomials and crystalline measures explicit examples of positive crystalline measures and fourier quasicrystals are constructed using pairs of stable polynomials answering several open questions in the area

the deligne mumford compactification of the real multiplication locus and teichmuller curves in genus 3 in the moduli space mathcal m g of genus g riemann surfaces consider the locus mathcal r mathcal m mathcal o of riemann surfaces whose jacobians have real multiplication by the order mathcal o in a totally real number field f of degree g if g 3 we compute the closure of mathcal r mathcal m mathcal o in the deligne mumford compactification of mathcal m g and the closure of the locus of eigenforms over mathcal r mathcal m mathcal o in the deligne mumford compactification of the moduli space of holomorphic 1 forms for higher genera we give strong necessary conditions for a stable curve to be in the boundary of mathcal r mathcal m mathcal o boundary strata of mathcal r mathcal m mathcal o are parameterized by configurations of elements of the field f satisfying a strong geometry of numbers type restriction

a note on modelling the covariance structure of repeated measurements geary 1989 biometrics 45 1183 1195 generalized the repeated measurements models used by wilson hebel and sherwin 1981 biometrics 37 553 565 and mansour nordheim and rutledge 1985 biometrics 41 287 294 in this note it is shown analytically that geary s generalization is not suitable because of difficulties in estimating the generalizing parameter this verifies the simulation based results of geary

maximum likelihood estimation of variance components in repeated measures designs assuming autoregressive errors summary linear models used for estimation of variance components are generally formulated under the assumption of independent errors herein we consider a two way mixed model with errors assumed to follow a first order nonstationary autoregressive process maximum likelihood techniques are employed to estimate the variance components and also a parameter for the autoregression an example using lactational yield of cows is given along with some monte carlo results

on the mathematical foundations of nondifferentiable optimization in engineering design it is shown by example that a large class of engineering design problems can be transcribed into the form of a canonical optimization problem with inequality constraints involving mar functions such problems are commonly referred to as semi infinite optimization problems the bulk of this paper is devoted to the development of a mathematical theory for the construction of first order nondifferentiable optimization algorithms related to phase i phase ii methods of feasible directions which solve these semi infinite optimization problems the applicability of the theory is illustrated with examples that are relevant to engineering design

the fields of real and complex numbers with a small multiplicative group we consider the model theory of the real and complex fields with a multiplicative group having the mann property among these groups are the finitely generated multiplicative groups in these fields as a by product we obtain some results on groups with the mann property in rings of witt vectors and in fields of positive characteristic k

modelling the covariance structure of repeated measurements models for repeated measurements used by wilson hebel and sherwin 1981 biometrics 37 553565 and mansour nordheim and rutledge 1985 biometrics 41 287 294 are considered these two models are generalized by the a p e k model obtained by introducing an extra parameter k a more general class of models described by kenward unpublished ph d thesis university of reading 1981 is briefly discussed simulation results are presented in which model parameters are estimated by maximum likelihood and likelihood ratios are used as criteria for choosing between models a set of blood pressure data is used to illustrate model fitting

o minimality and the andre oort conjecture for mathbb c n we give an unconditional proof of the andre oort conjecture for arbitrary products of modular curves we establish two generalizations the first includes the manin mumford conjecture for arbitrary products of elliptic curves defined over q as well as lang s conjecture for torsion points in powers of the multiplicative group the second includes the manin mumford conjecture for abelian varieties defined over q our approach uses the theory of o minimal structures a part of model theory and follows a strategy proposed by zannier and implemented in three recent papers a new proof of the manin mumford conjecture by pila zannier a proof of a special but new case of pink s relative manin mumford conjecture by masser zannier and new proofs of certain known results of andre oort manin mumford type by pila 2010 mathematics subject classification 11g18 03c64

small points on subvarieties of a torus let v be a subvariety of a torus de ned over the algebraic numbers we give a qualitative and quantitative description of the set of points of v of height bounded by invariants associated to any variety containing v especially we determine whether such a set is or is not dense in v we then prove that these sets can always be written as the intersection of v with a nite union of translates of tori of which we control the sum of the degrees as a consequence we prove a conjecture by the rst author and david up to a logarithmic factor

the number of solutions of decomposable form equations has only finitely many solutions the diophantine approximation techniques of thue and mahler and improvements by siegel dyson roth and bombieri made it possible to derive good explicit upper bounds for the number of solutions of 1 1 the best such upper bound to date due to bombieri 1 is 2 12r bombieri assumed that f is irreducible and r 6 which was not essential in his proof for t 0 i e f x y 1 in x y z bombieri and schmidt 2 derived the upper bound constant r which is best possible in terms of r

arithmetic group symmetry and finiteness properties of torelli groups we examine groups whose resonance varieties characteristic varieties and sigma invariants have a natural arithmetic group symmetry and we explore implications on various niteness properties of subgroups we compute resonance varieties characteristic varieties and alexander polynomials of torelli groups and we show that all subgroups containing the johnson kernel have nite rst betti number when the genus is at least 4 we also prove that in this range the i adic completion of the alexander invariant is nite dimensional and the kahler property for the torelli group implies the nite generation of the johnson kernel

dynamical anomalous subvarieties structure and bounded height theorems abstract according to medvedev and scanlon 14 a polynomial f x q x of degree d 2 is called disintegrated if it is not conjugate to x d or to c d x where c d is the chebyshev polynomial of degree d let n n let f 1 f n q x be disintegrated polynomials of degrees at least 2 and let f 1 f n be the corresponding coordinate wise self map of p 1 n let x be an irreducible subvariety of p 1 n of dimension r defined over q we define the anomalous locus of x which is related to the periodic subvarieties of p 1 n we prove that the anomalous locus of x is zariski closed this is a dynamical analogue of a theorem of bombieri masser and zannier 4 we also prove that the points in the intersection of x with the union of all irreducible periodic subvarieties of p 1 n of codimension r have bounded height outside the anomalous locus of x this is a dynamical analogue of habegger s theorem 8 which was previously conjectured in 4 the slightly more general self maps f 1 f n where each f i q x is a disintegrated rational function are also treated at the end of the paper

a criterion for weak convergence on berkovich projective space we give a criterion for the weak convergence of unit borel measures on the n dimensional berkovich projective space bf p n k over a complete non archimedean field k as an application we give a sufficient condition for a certain type of equidistribution on bf p n k in terms of a weak zariski density property on the scheme theoretic projective space mathbb p n tilde k vphantom 0 over the residue field tilde k as a second application in the case of residue characteristic zero we give an ergodic theoretic equidistribution result for the powers of a point a in the n dimensional unit torus mathbb t n k over k this is a non archimedean analogue of a well known result of weyl over mathbb c and its proof makes essential use of a theorem of mordell lang type for mathbb g m n due to laurent

intersections of polynomial orbits and a dynamical mordell lang conjecture we prove that if nonlinear complex polynomials of the same degree have orbits with infinite intersection then the polynomials have a common iterate we also prove a special case of a conjectured dynamical analogue of the mordell lang conjecture

local systems on analytic germ complements abstract we prove that the cohomology jump loci of rank one local systems on the complement in a small ball of a germ of a complex analytic set are finite unions of torsion translates of subtori this is a generalization of the classical monodromy theorem stating that the eigenvalues of the monodromy on the cohomology of the milnor fiber of a germ of a holomorphic function are roots of unity