efficient algorithms for the inverse spanning tree problem the inverse spanning tree problem is to modify edge weights in a graph so that a given treet is a minimum spanning tree the objective is to minimize the cost of the deviation the cost of deviation is typically a convex function we propose algorithms here that are faster than all known algorithms for the problem our algorithm s run time for any convex inverse spanning tree problem iso nm log 2n for a graph onn nodes andm edges plus the time required to find the minima of then convex deviation functions this not only improves on the complexity of previously known algorithms for the general problem but also for algorithms devised for special cases for the case when the objective is weighted absolute deviation sokkalingam et al 1999 devised an algorithm with run timeo n2m log nc forc the maximum edge weight for the sum of absolute deviations our algorithm runs in timeo n2 logn matching the run time of a recent ahuja and orlin 2000 improvement for this case a new algorithm for bipartite matching in path graphs is reported here with complexity ofo n1 5 logn this leads to a second algorithm for the sum of absolute deviations running ino n1 5 logn logc steps

an evaluation of some methods for fitting dose response models to quantal response developmental toxicology data the analysis of quantal response developmental toxicology data by dose response modeling is discussed with emphasis on methods that avoid exact distributional assumptions these methods quasi likelihood bootstrapping and jackknifing are contrasted with analyses based on the beta binomial distribution for the resampling procedures dose response models are fit under a binomial likelihood a justification for this choice of estimator in resampling plans is given based on an extension of the standard results for asymptotic normality and consistency of maximum likelihood estimators this justification depends only on the true distribution of the data having the usual binomial expectation a quasi likelihood approach is also considered in which simple assumptions about the intralitter correlation structure are made quasi likelihood methods are in theory asymptotically robust to misspecification of the intralitter correlation structure the practical implications of these asymptotic results are evaluated in a simulation study

beta binomial poisson regression models for repeated bivariate counts we analyze data obtained from a study designed to evaluate training effects on the performance of certain motor activities of parkinson s disease patients maximum likelihood methods were used to fit beta binomial poisson regression models tailored to evaluate the effects of training on the numbers of attempted and successful specified manual movements in 1 min periods controlling for disease stage and use of the preferred hand we extend models previously considered by other authors in univariate settings to account for the repeated measures nature of the data the results suggest that the expected number of attempts and successes increase with training except for patients with advanced stages of the disease using the non preferred hand

dose response models for teratological experiments in a recent paper hereinafter referred to as rvr rai and van ryzin 1985 propose a dose response model for use in low dose extrapolation from teratological experiments involving quantal responses suppose n litters are divided into m 1 dose groups the ith group consisting of ni litters exposed to dose di o do di dn the group i 0 being a zero dose control let sij denote the size of the jth litter in the ith group j 1 ni and let rij denote the number of foetuses or pups in the litter exhibiting the toxic response of interest the model proposed by rvr assumes that the conditional distribution of rij given sij sij is binomial sij p1j where

bivariate latent variable models for clustered discrete and continuous outcomes abstract we use the concept of a latent variable to derive the joint distribution of a continuous and a discrete outcome and then extend the model to allow for clustered data the model can be parameterized in a way that allows one to write the joint distribution as a product of a standard random effects model for the continuous variable and a correlated probit model for the discrete variable this factorization suggests a convenient approach to parameter estimation using quasi likelihood techniques our approach is motivated by the analysis of developmental toxicity experiments for which a number of discrete and continuous outcomes are measured on offspring clustered within litters fetal weight and malformation data illustrate the results

quantitative risk assessment for teratological effects abstract this article presents a quantitative procedure for using a benchmark dose to obtain low dose risk estimates for reproductive and developmental toxic effects this procedure combines the best features of the previously proposed methods for handling litter effects for teratology data and the currently used methods for quantitative risk assessment the beta binomial distribution is used to account for litter effects and the weibull dose response model is used for modeling teratogenic effects a benchmark dose defined to be the lowest dose at which the excess risk does not exceed 1 with 95 confidence is proposed to replace the no observed effect level noel the noel is generally the highest experimental dose that is not statistically different from the control the noel approach does not use experimental data effectively for quantitative risk estimation in this article a lower limit on the safe dose is estimated by linearly extrapolating downward from the benchmark dose this procedure is

fast algorithms for bipartite network flow we discuss network flow in a bipartite graph g with node sets s and t we show that karzanov s algorithm runs in time o s 2 t on g and that the mpm algorithm can be modified to run in the same bound for the common case that the degree of each node in t is bounded by a constant we show that a modified version of the mpm algorithm runs in time o s 3 s t on g the importance of these results comes from the common occurrence of problems that can be modeled and solved using network flow on bipartite graphs where s ll t in many applications involving bounded degree on the nodes in t t theta s 2 and our results reduce the best bounds on bipartite flow from o s 6 to o s 3 we use our results on bipartite flow to obtain the fastest known bounds on several combinatorial problems and mention several additional problems involving bipartite flow where s is much smaller than t

a dose response model for teratological experiments involving quantal responses this paper introduces a dose response model for teratological quantal response data where the probability of response for an offspring from a female at a given dose varies with the litter size the maximum likelihood estimators for the parameters of the model are given as the solution of a nonlinear iterative algorithm two methods of low dose extrapolation are presented one based on the litter size distribution and the other a conservative method the resulting procedures are then applied to a teratological data set from the literature

optimal flows in networks with multiple sources and sinks with applications to oil and gas lease investment programs in the classical maximal flow problem the objective is to maximize the supply to a single sink in a capacitated network in this paper we consider general capacitated networks with multiple sinks the objective is to optimize a general concave preference relation on the set of feasible supply vectors we show that an optimal solution can be obtained by a marginal allocation procedure an efficient implementation results in an adaptation of the augmenting path algorithm we also discuss an application of the procedure for an investment company that deals in oil and gas ventures

optimal power of two replenishment strategies in capacitated general production distribution networks in this paper we develop a model for a capacitated production distribution network of general but acyclic topology with a general bill of materials as considered in mrp material requirement planning or drp distribution requirement planning systems this model assumes stationary deterministic demand rates and a standard stationary cost structure it is a generalization of the uncapacitated model treated in the seminal papers of maxwell and muckstadt 1985 and roundy 1986 the capacity constraints consist of bounds on the frequency with which individual items can or need to be replenished we derive a pair of simple and efficient algorithms capable of determining an optimal power of two policy these algorithms consist of a limited number of maximum flow computations in networks closely related to the production distribution network the complexity of these algorithms even when applied to the uncapacitated model compares favorably with that of the existing alternative solution methods

low dose rate extrapolation using the multistage model the distribution of the maximum likelihood estimates of virtually safe levels of exposure to environmental chemicals is derived by using large sample theory and monte carlo simulation according to the armitage doll multistage model using historical dose response we develop a set of 33 two stage models upon which we base our conclusions the large sample distributions of the virtually safe dose are normal for cases in which the multistage model parameters have nonzero expectation and are skewed in other cases the large sample theory does not provide a good approximation of the distribution observed for small bioassays when monte carlo simulation is used the constrained nature of the multistage model parameters leads to bimodal distributions for small bioassays the two modes are the direct result of estimating the linear parameter in the multistage model the lower mode results from estimating this parameter to be nonzero and the upper mode from estimating it to be zero the results of this research emphasize the need for incorporation of the biological theory in the model selection process

effective dynamics in hamiltonian systems with mixed phase space an adequate characterization of the dynamics of hamiltonian systems at physically relevant scales has been largely lacking here we investigate this fundamental problem and we show that the finite scale hamiltonian dynamics is governed by effective dynamical invariants which are significantly different from the dynamical invariants that describe the asymptotic hamiltonian dynamics the effective invariants depend both on the scale of resolution and the region of the phase space under consideration and they are naturally interpreted within a framework in which the nonhyperbolic dynamics of the hamiltonian system is modeled as a chain of hyperbolic systems

modeling the dependence between number of trials and success probability in beta binomial poisson mixture distributions des modeles beta binomiaux sont frequemment utilises pour des donnees binomiales avec sur dispersion avec une probabilite binomiale de succes suivant une distribution beta on suppose que le nombre d essais binomiaux dans chaque binomiale est non aleatoire et non liee a la probabilite de succes dans de nombreuses etudes sur le comportement neanmoins les observations binomiales ont des structures plus complexes dans cet article nous developpons un modele de melange beta binomial poisson pour autoriser une relation entre le nombre d essais et la probabilite de succes pour des donnees binomiales avec sur dispersion nous mettons en oeuvre un algorithme em pour calculer simultanement des estimations du maximum de vraisemblance des parametres du modele et de leur ecart type correspondant a titre d illustration nous appliquons cette methodologie a l etude du comportement alimentaire de herons a dos vert dans deux ruisseaux du sud ouest du missouri

a generalized multihit dose response model for low dose extrapolation a quantal dose response model based on a multihit theory of toxic response is presented when spontaneous background toxic response is included the model involves three unknown parameters the maximum likelihood estimators for these three parameters are given as the solution of a nonlinear iterative algorithm the resulting three dimensional vector of estimators is shown to be asymptotically strongly consistent asymptotically unique with probability one and when suitably normalized it has asymptotically a trivariate normal distribution on the basis of these results a large sample goodness of fit test is given the use of this model for low dose extrapolation is indicated application of the results is illustrated using three sets of toxicity data

efficient algorithms for finding optimal power of two policies for production distribution systems with general joint setup costs we consider a production distribution system represented by a general directed acyclic network each node is associated with a specific product at a given location and or production stage an arc i j indicates that item i is used to produce item j external demands may occur at any of the network s nodes these demands occur continuously at item specific constant rates components may be assembled in any given proportions the cost structure consists of inventory carrying variable and fixed production distribution costs the latter depend at any given replenishment epoch on the specific set of items being replenished according to an arbitrary set function merely assumed to be monotone and submodular it has been shown that a simply structured so called power of two policy is guaranteed to come within 2 of a lower bound for the minimum cost in this paper we derive efficient algorithms for the computation of an optimal power of two policy possibly in combination with this lower bound these consist of a limited number of polymatroidal maximum flow calculations in networks closely associated with the original production distribution network

tests of independence treatment heterogeneity dose related trend with exchangeable binary data abstract existing methods of testing for treatment effects for clustered binary data include the beta binomial quasilikelihood gee procedures all of these methods revolve around the mean response and the second order correlation however these two parameters alone do not fully determine the effect of treatment this article develops nonparametric likelihood ratio procedures to test for independence heterogeneity dose related trend in dose response studies involving exchangeable binary data the hypotheses of independence heterogeneity trend are expressed in terms of joint probabilities of similar responses among cluster mates constrained maximum likelihood estimates of these probabilities are computed and used to construct test statistics unlike the test statistics for independence and heterogeneity the asymptotic distribution of the likelihood ratio test for trend is not exactly a chi square however an upper bound of its p value is obtained by using a chi squared distribution a set of clustere

a full likelihood procedure for analysing exchangeable binary data a full likelihood procedure is proposed for analyzing correlated binary data under the assumption of exchangeability the binomial and beta binomial models are shown to occur as special cases correspondingly respectively to the choice of degenerate and beta mixing distributions for a finite exchangeable binary sequence of random variables expressions for the joint distribution moments and correlations of all orders are derived maximum likelihood estimates of the moments of all orders are computed and used to estimate correlations and the distribution of the number of responses in a cluster in an application to developmental toxicology data analysis the procedure introduced is compared with a beta binomial and a generalized estimating equation procedure in which mean response and intralitter correlation are linked to dose

cluster sampling techniques in quantal response teratology and developmental toxicity studies summary this paper presents a model free approach for evaluating teratology and developmental toxicity data involving clustered binary responses in teratology studies a major statistical problem arises from the effect of intralitter correlation or the potential for littermates to respond similarly some statistical methods impose strict distributional assumptions to account for extra binomial variation while others rely on nonparametric resampling and empirical variance estimation techniques quasi likelihood methods and generalized estimating equations gee which model the marginal mean variance relationship also avoid strict distributional assumptions the proposed approach often used to analyze complex sample survey data is based on a first order taylor series approximation and a between cluster variance estimation procedure yielding consistent variance estimates for binomial based proportions and regression coefficients from dose response models the cluster sample technique presented here in the context of a logistic dose response model incorporates many of the advantages of quasi likelihood methods are valid for any underlying nested correlation structure and are adaptable to a variety of analytical settings the results of a simulation study show the cluster sample technique to be a viable competitor to gee methods currently receiving attention

a parametric maximum flow algorithm for bipartite graphs with applications abstract suppose we are given a capacitated bipartite network g with node sets s and t in network g the arc capacities are not fixed values but are functions of a single parameter where is a continuous real variable our problem is to determine the minimum value of such that the maximum flow value in the corresponding network equals a given threshold for this problem an algorithm of time complexity o nm 2 log m n is presented where n is the number of nodes in s m is the number of nodes in t and n m examples are then given to show how to use this parametric algorithm to solve practical problems

the geometric maximum traveling salesman problem we consider the traveling salesman problem when the cities are points in n x211d d for some fixed d and distances are computed according to geometric distances determined by some norm we show that for any polyhedral norm the problem of finding a tour of maximum length can be solved in polynomial time if arithmetic operations are assumed to take unit time our algorithms run in time o nf 2 log n where f is the number of facets of the polyhedron determining the polyhedral norm thus for example we have o n2 log n algorithms for the cases of points in the plane under the rectilinear and sup norms this is in contrast to the fact that finding a minimum length tour in each case is np hard our approach can be extended to the more general case of quasi norms with a not necessarily symmetric unit ball where we get a complexity of o n2f 2 log n for the special case of two dimensional metrics with f 4 which includes the rectilinear and sup norms we present a simple algorithm with o n running time the algorithm does not use any indirect addressing so its running time remains valid even in comparison based models in which sorting requires n log n time the basic mechanism of the algorithm provides some intuition on why polyhedral norms allow fast algorithms complementing the results on simplicity for polyhedral norms we prove that for the case of euclidean distances in n x211d d for d 3 the maximum tsp is np hard this sheds new light on the well studied difficulties of euclidean distances

a fast parametric maximum flow algorithm and applications the classical maximum flow problem sometimes occurs in settings in which the arc capacities are not fixed but are functions of a single parameter and the goal is to find the value of the parameter such that the corresponding maximum flow or minimum cut satisfies some side condition finding the desired parameter value requires solving a sequence of related maximum flow problems in this paper it is shown that the recent maximum flow algorithm of goldberg and tarjan can be extended to solve an important class of such parametric maximum flow problems at the cost of only a constant factor in its worst case time bound faster algorithms for a variety of combinatorial optimization problems follow from the result