nonnegative companion matrices and star height of n rational series abstract we prove a new result on n rational series in one variable this result gives under an appropriate hypothesis a necessary and sufficient condition for an n rational series to be of star height 1 the proof uses a theorem of handelman on integral companion matrices

scheduling with monotonous earliness and tardiness penalties abstract we discuss the one machine model with deterministic processing times in the first part we restrict the model to the common due date case in the second part an equivalence between this model and the equal slack due date model is shown as a penalty function f we use the sum of identical functions f of the lateness both earliness and tardiness the function f must be monotonous with respect to the absolute lateness no other restrictions are necessary several special cases are known in the literature and summarized here to show the generality of our approach this idea of penalizing jobs whose completion times deviate from their due date arises in some scheduling models for just in time production we give two structural results for an optimal schedule an optimal schedule works without idle times except eventually one at time 0 and is v shaped using these two structural results we construct an optimal schedule with a pseudopolynomial algorithm this algorithm has a complexity bound of o np where p denotes the sum of the given processing times for a subclass of penalty functions we extend the pseudopolynomial algorithm to a fully polynomial approximation scheme the complexity bound for this approximation scheme is of the order o n 3 1 e where e denotes the relative precision of the approximate solution as mentioned above we show the equivalence of the common due date problem and the equal slack due date problem mathematically these two problems can be expressed as common due date rule d i d for all jobs i and equal slack rule d i d p i for all jobs i where p i denotess the given processing time of job i and d is a constant value

two step estimation of functional linear models with applications to longitudinal data functional linear models are useful in longitudinal data analysis they include many classical and recently proposed statistical models for longitudinal data and other functional data recently smoothing spline and kernel methods have been proposed for estimating their coefficient functions nonparametrically but these methods are either intensive in computation or inefficient in performance to overcome these drawbacks in this paper a simple and powerful two step alternative is proposed in particular the implementation of the proposed approach via local polynomial smoothing is discussed methods for estimating standard deviations of estimated coefficient functions are also proposed some asymptotic results for the local polynomial estimators are established two longitudinal data sets one of which involves time dependent covariates are used to demonstrate the approach proposed simulation studies show that our two step approach improves the kernel method proposed by hoover and co workers in several aspects such as accuracy computational time and visual appeal of the estimators

punctuality and idleness in just in time scheduling abstract in scheduling problems with irregular cost functions such as deviation functions in earliness tardiness scheduling problems optimal solutions usually contain some idleness periods during which no activity is processed then minimizing the penalties for not delivering on time and minimizing the idleness cost are two complementary criteria for a schedule a dynamic programming procedure in which the states are represented by continuous two dimensional piecewise linear functions is proposed to compute the cost of the pareto optimal schedules

a fixed interval due date scheduling problem with earliness and due date costs in this paper we consider a problem where n jobs are to be scheduled on a single machine and assigned to one of the two due dates which are given at equal intervals tardy jobs are not allowed thus the due dates are deadlines there is a linear due date penalty and linear earliness penalty and the sum of these penalties is to be minimized this problem is shown to be np hard one case of the problem the unrestricted case is shown to be easy to solve for the restricted case lower and upper bounds are developed computational experience is reported which suggests that the bounds are quite effective

a recovering beam search algorithm for the single machine just in time scheduling problem abstract we consider the just in time scheduling problem where the just in time notion is captured by means of multiple conflicting criteria the calculation of any non dominated solution for these criteria is achieved by solving an extension of the single machine problem of minimising the mean weighted deviation from distinct due dates in the extended problem each job to schedule is also constrained by a release date and a deadline this problem is np hard in the strong sense and we propose heuristic algorithms to solve it computational experiments show that among those algorithms the most effective heuristic in terms of quality is a recovering beam search algorithm

minimizing maximum promptness and maximum lateness on a single machine we consider the following single machine bicriteria scheduling problem a set of n independent jobs has to be scheduled on a single machine that can handle only one job at a time and that is available from time zero onwards each job jj requires processing during a given positive uninterrupted time pj and has a given target start time sj and due date dj with a dj sj a pj for some constant a for each job jjj 1 n its promptness pj is defined as the difference between the target start time and the actual start time and its lateness lj as the difference between the completion time and the due date we consider the problem of finding a schedule that minimizes a function f of maximum promptness pmax max1 j npj and maximum lateness lmax max1 j nlj we assume that f is nondecreasing in both arguments we present an on2 algorithm for the variant in which idle time is not allowed and an on2 log n algorithm for the special case in which the objective function is linear we prove that the problem is np hard if neither of these restrictions is imposed as a side result we prove that the special case of minimizing maximum lateness subject to release dates that lie in the interval dj pj a dj a for all j 1 n and for some constant a is solvable in on log n time if no machine idle time is allowed and in on2 log n time if machine idle time is allowed

a uniform type inverse spectrum theorem for entrywise nonnegative matrices abstract influenced by earlier results of fiedler m fiedler eigenvalues of nonnegative symmetric matrices linear algebra appl 9 1974 119 142 wuven guo wuven eigenvalues of nonnegative matrices linear algebra appl 266 1997 261 270 established interesting theorems and posed several natural questions in the inverse spectrum problem for entrywise nonnegative matrices we answer some of these of a uniform character obtaining the sharpest possible results

algebraic shift equivalence and primitive matrices motivated by symbolic dynamics we study the problem given a unital subring s of the reals when is a matrix a algebraically shift equivalent over s to a primitive matrix we conjecture that simple necessary conditions on the nonzero spectrum of a are sufficient and establish the conjecture in many cases if s is the integers we give some lower bounds on sizes of realizing primitive matrices for dedekind domains we prove that algebraic shift equivalence implies algebraic strong shift equivalence

on the distribution of dominance in populations of social organisms bumble bees may possess a scalar character called dominance which changes according to certain rules as a result of encounters between pairs of organisms an equation for the distribution of dominance in a population is derived based on a set of plausible axioms the resulting boltzmann like integrodifferential equation is analyzed analytically and or numerically for certain important special cases

joint modelling of paired sparse functional data using principal components we propose a modelling framework to study the relationship between two paired longitudinally observed variables the data for each variable are viewed as smooth curves measured at discrete time points plus random errors while the curves for each variable are summarized using a few important principal components the association of the two longitudinal variables is modelled through the association of the principal component scores we use penalized splines to model the mean curves and the principal component curves and cast the proposed model into a mixed effects model framework for model fitting prediction and inference the proposed method can be applied in the difficult case in which the measurement times are irregular and sparse and may differ widely across individuals use of functional principal components enhances model interpretation and improves statistical and numerical stability of the parameter estimates

growth type invariants for ℤ d subshifts of finite type and arithmetical classes of real numbers we discuss some numerical invariants of multidimensional shifts of finite type sfts which are associated with the growth rates of the number of admissible finite configurations extending an unpublished example of tsirelson a strange two dimensional symbolic system 1992 we show that growth complexities of the form exp n o 1 are possible for non integer s in terminology of de carvalho port math 54 1 19 40 1997 such subshifts have entropy dimension the class of possible s are identified in terms of arithmetical classes of real numbers of weihrauch and zheng math log q 47 1 51 65 2001

a hybrid multi objective immune algorithm for a flow shop scheduling problem with bi objectives weighted mean completion time and weighted mean tardiness this paper investigates a novel multi objective model for a no wait flow shop scheduling problem that minimizes both the weighted mean completion time c w and weighted mean tardiness t w obtaining an optimal solution for this type of complex large sized problem in reasonable computational time by using traditional approaches and optimization tools is extremely difficult this paper presents a new hybrid multi objective algorithm based on the features of a biological immune system is and bacterial optimization bo to find pareto optimal solutions for the given problem to validate the performance of the proposed hybrid multi objective immune algorithm hmoia in terms of solution quality and diversity level various test problems are examined further the efficiency of the proposed algorithm based on various metrics is compared against five prominent multi objective evolutionary algorithms ps nc ga nsga ii spea ii moia and misa our computational results suggest that our proposed hmoia outperforms the five foregoing algorithms especially for large sized problems

stronger lagrangian bounds by use of slack variables applications to machine scheduling problems lagrangian relaxation is a powerful bounding technique that has been applied successfully to manynp hard combinatorial optimization problems the basic idea is to see annp hard problem as an easy to solve problem complicated by a number of nasty side constraints we show that reformulating nasty inequality constraints as equalities by using slack variables leads to stronger lower bounds the trick is widely applicable but we focus on a broad class of machine scheduling problems for which it is particularly useful we provide promising computational results for three problems belonging to this class for which lagrangian bounds have appeared in the literature the single machine problem of minimizing total weighted completion time subject to precedence constraints the two machine flow shop problem of minimizing total completion time and the single machine problem of minimizing total weighted tardiness

the classification of some generalised bunce deddens algebras abstract we use k theory to prove an isomorphism theorem for a large class of generalised bunce deddens algebras constructed by kribs and solel from a directed graph e and a sequence of positive integers in particular we compute the torsion free component of the k 0 group for a class of generalised bunce deddens algebras to show that supernatural numbers are a complete invariant for this class

an algorithm for the multiple objective integer linear programming problem abstract a technique is presented for solving the multiple objective integer linear programming problem the technique can be used to identify some or all efficient solutions while the technique is applicable with any integer programming algorithm it is well suited for implementation using integer postoptimality techniques such an implementation based on balas additive algorithm is described for problems with zero one variables

dynamic programming approach to the single machine sequencing problem with different due dates abstract given a set of n jobs each of which is assigned a due date and all jobs are simultaneously available to be processed on a single machine the problem is to find the optimal job processing order that minimizes the sum of absolute deviation of job completion times about their respective due dates since this problem has been shown to be np complete we present a dp dynamic programming formulation of the problem and apply the principle of optimality of dp to find the optimal solution by implicit enumeration

scheduling around a small common due date a set of n jobs has to be scheduled on a single machine which can handle only one job at a time each job requires a given positive uninterrupted processing time and has a positive weight the problem is to find a schedule that minimizes the sum of weighted deviations of the job completion times from a given common due date d which is smaller than the sum of the processing times we prove that this problem is np hard even if all job weights are equal in addition we present a pseudopolynomial algorithm that requires o n2d time and o nd space

minimizing variation of production rates in just in time systems a survey abstract in the past several years there has been growing interest in scheduling problems where jobs are penalized both for being early and for being tardy this notable deviation from previous work in which finishing early is generally regarded as being at least as desirable as finishing on time is perceived to be the one that well captures the scheduling dimension of jit production systems a number of excellent surveys on these problems has appeared over the last four years there is however another important scheduling objective in jit production systems which is to minimize variation of rates at which processes supply their outputs these scheduling problems are for example of primary concern in the toyota jit system thus far most research efforts in this area have been focused on minimizing variation of the rate at which different products are being produced on the final multi model assembly line which itself is a supplying process we shall review the results of this research and relate them to the due date based scheduling problems extensions and open problems will also be reviewed schedules that minimize variation of the rate at which different products are being produced on the line do not necessarily minimize variation in the line demand for outputs of processes that supply it few heuristics for the problem of minimizing the variation are available and hardly anything is known on its complexity as wel as exact algorithms to tackle it we shall review a mathematical programming model of the problem and open questions that result from it

earliness tardiness scheduling problems ii derivation of completion times about a restrictive common due date a companion paper part i considers the problem of minimizing the weighted earliness and tardiness of jobs scheduled on a single machine around a common due date d which is unrestrictively late this paper part ii considers the problem of minimizing the unweighted earliness and tardiness of jobs allowing the possibility that d is early enough to constrain the scheduling decision we describe several optimality conditions the recognition version of the problem is shown to be np complete in the ordinary sense confirming a well known conjecture moreover this complexity definition is precise since we describe a dynamic programming algorithm which runs in pseudopolynomial time this algorithm is also extremely efficient computationally providing an improvement over earlier procedures of almost two orders of magnitude in the size of instance that can be solved finally we describe a special case of the problem which is polynomially solvable

analytical and numerical aspects of certain nonlinear evolution equations ii numerical nonlinear schrodinger equation abstract various numerical methods are employed in order to approximate the nonlinear schrodinger equation namely i the classical explicit method ii hopscotch method iii implicit explicit method iv crank nicolson implicit scheme v the ablowitz ladik scheme vi the split step fourier method f tappert and vii pseudospectral fourier method fornberg and whitham comparisons between the ablowitz ladik scheme which was developed using notions of the inverse scattering transform and the other utilized schemes are obtained

recovery of the absorption coefficient from diffused reflected light using a discrete diffusive model an algorithm based on a discrete model for photon migration is proposed for recovering the absorption coefficient in a semi infinite slab a pulsed light source is modeled and only reflected signals are used in the reconstruction the diffusion coefficient and speed of light are assumed constant and known the algorithm is based on the result that the earliest reflected signals obtained from a particular voxel depend either in a linear or in a quadratical fashion on the square of the absorption coefficient in that voxel by solving the discrete model in the forward direction in a region where the absorption coefficient has been calculated already the absorption coefficients in the voxels on the boundary of the region are calculated using interpolation results show that simple absorptive regions can be accurately recovered

elgenvalues of nonnegative matrices abstract in a partial continuation of work by fiedler some spectral properties of symmetric nonnegative matrices are extended to general nonnegative matrices

new solution methods for single machine bicriteria scheduling problem minimization of average flowtime and number of tardy jobs we consider the bicriteria scheduling problem of minimizing the number of tardy jobs and average flowtime on a single machine this problem which is known to be np hard is important in practice as the former criterion conveys the customer s position and the latter reflects the manufacturer s perspective in the supply chain we propose four new heuristics to solve this multiobjective scheduling problem two of these heuristics are constructive algorithms based on beam search methodology the other two are metaheuristic approaches using a genetic algorithm and tabu search our computational experiments indicate that the proposed beam search heuristics find efficient schedules optimally in most cases and perform better than the existing heuristics in the literature

the spectra of nonnegative integer matrices via formal power series an old problem in matrix theory is to determine the n tuples of complex numbers which can occur as the spectrum of a matrix with nonnegative entries see bp94 chapter 4 or min88 chapter vii authors have studied the case where the ntuple is comprised of real numbers bor95 cia68 fri78 kel71 per53 sal72 sou83 sul49 the case where the matrices under consideration are symmetric fie74 jll96 and the general problem joh81 lm99 ll79 rea94 rea96 wuw97 various necessary conditions and sufficient conditions have been provided but a complete characterization is known for real n tuples only for n 4 kel71 sul49 and for complex n tuples only for n 3 ll79 motivated by symbolic dynamics boyle and handelman refocused attention on the nonzero part of the spectrum by making the following spectral conjecture bh91 bh93 see also boy93 8 and lm95 chapter 11 below a matrix a is primitive if all entries of a are nonnegative and for some n all entries of a are strictly positive also

nonparametric estimation of conditional distributions and rank tracking probabilities with time varying transformation models in longitudinal studies an objective of longitudinal analysis is to estimate the conditional distributions of an outcome variable through a regression model the approaches based on modeling the conditional means are not appropriate for this task when the conditional distributions are skewed or cannot be approximated by a normal distribution through a known transformation we study a class of time varying transformation models and a two step smoothing method for the estimation of the conditional distribution functions based on our models we propose a rank tracking probability and a rank tracking probability ratio to measure the strength of tracking ability of an outcome variable at two different time points our models and estimation method can be applied to a wide range of scientific objectives that cannot be evaluated by the conditional mean based models we derive the asymptotic properties for the two step local polynomial estimators of the conditional distribution functions finite sample properties of our procedures are i

inverse chromatic number problems in interval and permutation graphs abstract given a graph g and a positive integer k the inverse chromatic number problem consists in modifying the graph as little as possible so that it admits a chromatic number not greater than k in this paper we focus on the inverse chromatic number problem for certain classes of graphs first we discuss diverse possible versions and then focus on two application frameworks which motivate this problem in interval and permutation graphs the inverse booking problem and the inverse track assignment problem the inverse booking problem is closely related to some previously known scheduling problems we propose new hardness results and polynomial cases the inverse track assignment problem motivates our study of the inverse chromatic number problem in permutation graphs we show how to solve in polynomial time a generalization of the problem with a bounded number of colors

minmax scheduling with job classes and earliness tardiness costs abstract we address scheduling problems with job dependent due dates and general possibly nonlinear and asymmetric earliness and tardiness costs the number of distinct due dates is substantially smaller than the number of jobs thus jobs are partitioned to classes where all jobs of a given class share a common due date we consider the settings of a single machine and parallel identical machines our objective is of a minmax type i e we seek a schedule that minimizes the maximum earliness tardiness cost among all jobs we introduce a nonlinear program that needs to be solved in order to obtain an optimal solution for the single machine case the case of parallel identical machines is np hard even for two machines linear costs and a single common due date we introduce an lpt based largest processing time first heuristic and a simple lower bound on the optimal cost both the heuristic and the lower bound are asymptotically accurate under very general conditions our numerical tests indicate that the heuristic produces very close to optimal schedules in all settings

power series with positive coefficients arising from the characteristic polynomials of positive matrices let a be an n times n entrywise positive matrix and let f t det i t a we prove the surprising result that there always exists a positive integer n such that the formal power series expansion of 1 f t 1 n around t 0 has positive coefficients

strong shift equivalence and shear adjacency of nonnegative square integer matrices abstract for two square matrices a b of possibly different sizes with nonnegative integer entries write a 1 b if a rs and b sr for some two nonnegative integer matrices r s the transitive closure of this relation is called strong shift equivalence and is important in symbolic dynamics where it has been shown by r f williams to characterize the isomorphism of two topological markov chains with transition matrices a and b one invariant is the characteristic polynomial up to factors of however no procedure for deciding strong shift equivalence is known even for 2 2 matrices a b in fact for n n matrices with n 2 no nontrivial sufficient condition is known this paper presents such a sufficient condition that a and b are in the same component of a directed graph whose vertices are all n n nonnegative integer matrices sharing a fixed characteristic polynomial and whose edges correspond to certain elementary similarities for n 2 this result gives confirmation of strong shift equivalences that previously could not be verified for n 2 previous results are strengthened and the structure of the directed graph is determined

a characterization of trace zero nonnegative 5 5 matrices let 1 2 3 4 5 be a list of complex numbers with 1 2 3 4 5 0 necessary and sufficient conditions for the existence of an entry wise nonnegative 5 5 matrix a with spectrum are presented

entropy at a weight per symbol and embeddings of markov chains in 11 krieger gave a remarkable embedding result for shifts of finite type he proved that two simple necessary conditions strict inequality of the topological entropies of the shifts and the existence of an embedding for their periodic points are in fact sufficient for markov chains when the appropriate definitions of embedding and subsystem were supplied in 10 analogous necessary conditions strict inequality of functions and the existence of a weight preserving embedding for periodic points became apparent however an example in 10 also revealed these conditions to not be sufficient in this paper we bring to bear on embeddings of markov chains the ideas we introduced in 16 in fact we work in the closely related setting of triples z a a a f where 2 a aa is a shift of finite type and f is a function assigning weights to the edges of the graph associated with sa aa the func t ionf takes values in ir or more generally in n q for some qen the weight of a periodic orbit which corresponds to a cycle in the graph is then the sum of the weights of the edges lying on the cycle division by the length of the cycle gives the weight per symbol in 16 we continued the rational linear span of the set wps i of weights per symbol is a finite dimensional vector space vs the convex hull of wps i in v i is a polytope wpsi called the weight per symbol polytope consideration of the faces of wps i gives subsystems of r a aa f which are ordered according to the ordering of the faces the resulting nesting of subsystems is the scaffold of a o a f an embedding of a triple i a a a f in another 2 b ab g is a continuous shift commuting injection q 2 a 12 which preserves weights of periodic orbits the two necessary conditions mentioned above imply w p s i c w when the boundary c wpsi meets wpsg that is when a face f of wps i meets a face g of wpsg any embedding must carry the subsystem corresponding to f into that corresponding to g and this gives rise to further necessary conditons a discussion of these complications and a description of the example of 10 in these terms will be given in sect 7 before that the main embedding

quantile regression methods for reference growth charts estimation of reference growth curves for children s height and weight has traditionally relied on normal theory to construct families of quantile curves based on samples from the reference population age specific parametric transformation has been used to significantly broaden the applicability of these normal theory methods non parametric quantile regression methods offer a complementary strategy for estimating conditional quantile functions we compare estimated reference curves for height using the penalized likelihood approach of cole and green statistics in medicine 1992 11 1305 1319 with quantile regression curves based on data used for modern finnish reference charts an advantage of the quantile regression approach is that it is relatively easy to incorporate prior growth and other covariates into the analysis of longitudinal growth data quantile specific autoregressive models for unequally spaced measurements are introduced and their application to diagnostic screening is illustrated copyright 2005 john wiley sons ltd

two machine flow shop scheduling with two criteria maximum earliness and makespan abstract in this study we address the problem of minimizing makespan and maximum earliness simultaneously in a two machine flow shop environment we develop a branch and bound procedure that generates all efficient solutions with respect to two criteria we propose several lower and upper bounding schemes to enhance the efficiency of the algorithm we also propose a heuristic procedure that generates approximate efficient solutions our computational results reveal that the branch and bound procedure is capable of solving problems with up to 25 jobs and the heuristic procedure produces approximate efficient solutions that are very close to exact efficient solutions in very small computation times

predicting survival probabilities with semiparametric transformation models abstract prediction of survival probabilities for future patients is one of the main goals of fitting survival data with regression models in this article we consider a large class of semiparametric transformation models which includes the well known proportional hazards and proportional odds models for the analysis of failure time data specifically we propose pointwise and simultaneous confidence interval procedures for the survival probability of future patients with specific covariates these procedures can be easily implemented through simulation and are illustrated with the data from two well known clinical studies

efficient neighborhood search for the one machine earliness tardiness scheduling problem abstract this paper addresses the one machine scheduling problem where the objective is to minimize a sum of costs such as earliness tardiness costs since the sequencing problem is np hard local search is very useful for finding good solutions unlike scheduling problems with regular cost functions the scheduling or timing problem is not trivial when the sequence is fixed therefore the local search approaches must deal with both job interchanges in the sequence and the timing of the sequenced jobs we present a new approach that efficiently searches in a large neighborhood and always returns a solution for which the timing is optimal

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

realizable lists on a class of nonnegative matrices abstract a square matrix of order n with n 2 is called permutative matrix when all its rows are permutations of the first row in this paper recalling spectral results for partitioned into 2 by 2 symmetric blocks matrices sufficient conditions on a given complex list to be the list of the eigenvalues of a nonnegative permutative matrix are given in particular we study niep and pniep when some complex elements in the lists under consideration have non zero imaginary part realizability regions for nonnegative permutative matrices are obtained a guo s realizability preserving perturbations result is obtained

on the existence and nonexistence of finitary codings for a class of random fields we study the existence of finitary codings also called finitary homomorphisms or finitary factor maps from a finite valued i i d process to certain random fields for markov random fields we show using ideas of marton and shields that the presence of a phase transition is an obstruction for the existence of the above coding this yields a large class of bernoulli shifts for which no such coding exists conversely we show that for the stationary distribution of a monotone exponentially ergodic probabilistic cellular automaton such a coding does exist the construction of the coding is partially inspired by the propp wilson algorithm for exact simulation in particular combining our results with a theorem of martinelli and olivieri we obtain the fact that for the plus state for the ferromagnetic ising model on mathbf z d d geq 2 there is such a coding when the interaction parameter is below its critical value and there is no such coding when the interaction parameter is above its critical value

single machine scheduling of unit time jobs with earliness and tardiness penalties the problem of determining a schedule of jobs with unit time lengths on a single machine that minimizes the total weighted earliness and tardiness penalties with respect to arbitrary rational due dates is formulated as an integer programming problem we show that if the penalties meet a certain criterion called the dominance condition then there exists an extremal optimal solution to the lp relaxation that is integral leading to a polynomial time solution procedure the general weighted symmetric penalty structure is one cost structure that satisfies the dominance condition we point out other commonly found penalty structures that also fall into this category

a branch and bound approach for single machine scheduling with earliness and tardiness penalties abstract an n job single machine scheduling problem in which each job has a distinct due date d i is studied in this paper the objective is to determine an optimal schedule 0 s for a set of jobs s such that the total absolute deviation of the schedule is minimized this objective function is based on the due date value and on the earliness or tardiness of each job in the selected sequence this paper presents a bounding scheme for the calculation of different lower bounds based on the overlap elimination procedure on a just in time schedule properties and theorems of the overlap elimination procedure are also provided finally a numerical example is illustrated and some extensions of the approach are also discussed

williams s conjecture is false for reducible subshifts we show that for two subshifts of finite type having exactly two irreducible components strong shift equivalence is not the same as shift equiv alence this refutes the williams conjecture w in the reducible case the irreducible case remains an open problem mathematics research group alabama state university montgomery alabama 36101 this content downloaded from 207 46 13 180 on thu 08 sep 2016 04 22 09 utc all use subject to http about jstor org terms

on the nonnegative eigenvalue problem abstract 1 1 n is the spectrum of a stochastic matrix of order n 1 if and only if there exists some real matrix b of order n with spectrum 1 n and some n simplex s r n containing the origin such that bs s this result appears implicitly in ciarlet s work and it provides us with a geometrical tool to obtain sufficient conditions for the nonnegative eigenvalue problem we employ it here to generalize the sufficient conditions given by kellogg

minimizing total completion time in a two machine we consider the problem of minimizing total completion time in a two machine owshop we present a heuristic with worst case bound 2 where and denote the minimum and maximum processing time of all operations furthermore we analyze four special cases equal processing times on the first machine equal processing times on the second machine processing a job on the first machine takes time no less than its processing on the second machine and processing a job on the first machine takes time no more than its processing on the second machine we prove that the rst special case is np hard in the strong sense and present an o n log n approximation algorithm for it with worst case bound 4 3 we repeat the easy polynomial algorithms for the cases two and three and show that problem four is solvable in polynomial time as well

nonparametric smoothing estimates of time varying coefficient models with longitudinal data this paper considers nonparametric estimation in a varying coefficient model with repeated measurements y ij x ij t ij for i 1 n and j 1 n i where x ij x ij x ijk t and y ij x ij t ij denote the jth outcome covariate and time design points respectively of the ith subject the model considered here is y ij x ij t t ij e i t ij where t 0 t k t t for k 0 are smooth nonparametric functions of interest and e i t is a zero mean stochastic process the measurements are assumed to be independent for different subjects but can be correlated at different time points within each subject two nonparametric estimators of t namely a smoothing spline and a locally weighted polynomial are derived for such repeatedly measured data a crossvalidation criterion is proposed for the selection of the corresponding smoothing parameters asymptotic properties such as consistency rates of convergence and asymptotic mean squared errors are established for kernel estimators a special case of the local polynomials these asymptotic results give useful insights into the reliability of our general estimation methods an example of predicting the growth of children born to hiv infected mothers based on gender hiv status and maternal vitamin a levels shows that this model and the corresponding nonparametric estimators are useful in epidemiological studies

strong shift equivalence and the generalized spectral conjecture for nonnegative matrices abstract given matrices a and b shift equivalent over a dense subring r of r with a primitive we show that b is strong shift equivalent over r to a primitive matrix this result shows that the weak form of the generalized spectral conjecture for primitive matrices implies the strong form the foundation of this work is the recent result that for any ring r the group nk 1 r of algebraic k theory classifies the refinement of shift equivalence by strong shift equivalence for matrices over r

theory and methodology a bicriteria approach to the two machine flow shop scheduling problem in this paper we address the problem of minimizing makespan and sum of completion times simultaneously in a two machine flow shop environment we formulate the problem as a bicriteria scheduling problem and develop a branch and bound procedure that iteratively solves restricted single objective scheduling problems until the set of efficient solutions is completely enumerated we report computational results and explore certain properties of the set of efficient solutions we then discuss their implications for the decision maker

an extension theorem for closing maps of shifts of finite type if there exists some rightclosing factor map a b between aperiodic shifts of finite type then any right closing map x b from any shift of finite type x contained in a can be extended to a right closing factor map from all of a onto b we prove this and give some consequences

the real nonnegative inverse eigenvalue problem is np hard abstract a list of complex numbers is realizable if it is the spectrum of a nonnegative matrix in 1949 suleimanova posed the nonnegative inverse eigenvalue problem niep the problem of determining which lists of complex numbers are realizable the version for reals of the niep rniep asks for realizable lists of real numbers in the literature there are many sufficient conditions or criteria for lists of real numbers to be realizable we will present an unified account of these criteria then we will see that the decision problem associated to the rniep is np hard and we will study the complexity for the decision problems associated to known criteria

rice s theorem for the limit sets of cellular automata abstract rice s theorem is a well known result in the theory of recursive functions a corresponding theorem for cellular automata limit sets is proved all nontrivial properties of limit sets of cellular automata cas are shown undecidable the theorem remains valid even if only one dimensional cas are considered

one processor scheduling with symmetric earliness and tardiness penalties we consider one processor scheduling problems having the following form tasks t1 t2 tn are given with each ti having a specified length li and a preferred starting time ai or equivalently a preferred completion time bi the tasks are to be scheduled nonpreemptively i e a task cannot be split on a single processor to begin as close to their preferred starting times as possible we examine two different cost measures for such schedules the sum of the absolute discrepancies from the preferred starting times and the maximum such discrepancy for the first of these we show that the problem of finding minimum cost schedules is np complete however we give an efficient algorithm that finds minimum cost schedules whenever the tasks either all have the same length or are required to be executed in a given fixed sequence for the second cost measure we give an efficient algorithm that finds minimum cost schedules in general with no constraints on the ordering or lengths of the tasks

pert scheduling with convex cost functions this paper deals with the problem of finding a minimum cost schedule for a set of dependent activities when a convex cost function is attached to the starting time of each activity a first optimality necessary and sufficient condition bearing on the head and tail blocks of a schedule is first established a second such condition that uses the spanning active equality trees of a schedule leads to design a generic algorithm for the general case when the cost function is the usual earliness tardiness linear function with assymetric and independent penalty coefficients the problem is shown to be solved in o n max n m finally the special cases when the precedence graph is an intree or a family of chains are then also shown to be solved by efficient polynomial algorithms

small polynomial matrix presentations of nonnegative matrices we investigate the use of polynomial matrices to give efficient presentations of nonnegative matrices exhibiting prescribed spectral and algebraic behavior

minmax earliness tardiness costs with unit processing time jobs the problem addressed in this paper is defined by m parallel identical machines n jobs with identical unit processing time job dependent weights and a common due date for all jobs the objective is of a minmax type i e we are interested in minimizing the cost of the worst scheduled job in the case of a non restrictive i e sufficiently large common due date the problem is shown to have a solution that is polynomial in the number of jobs the solution in the case of a restrictive due date remains polynomial in the number of jobs but is exponential in the number of machines we introduce a lower bound on the optimal cost and an efficient heuristic we show that the worst case relative error of the heuristic is bounded by 2 and that this bound is tight we also prove that the heuristic is asymptotically optimal under very general assumptions finally we provide an extensive numerical study demonstrating that in most cases the heuristic performs extremely well

level schedules for mixed model just in time processes a mixed model manufacturing facility running under a just in time jit production system is controlled by setting the production sequence of the final assembly process this sequence is set to achieve the primary goal of an organization operating under a jit system which is to maintain a constant rate of part usage in this paper a graph theoretic approach is used to determine an optimal solution for this goal for a new nonconvex objective function furthermore it is shown that a schedule always exists such that at all times the deviation of actual production from the desired level of production for every product is never more than one unit

a bicriteria two machine permutation flowshop problem the problem attacked in this paper is the scheduling of n jobs on two machines which are assumed to be continuously available all jobs are available at the beginning of the scheduling period setup times are included in the processing times no preemption of jobs is allowed the objective is the minimization of a weighted combination of the average job flowtime and the schedule makespan three branch and bound bb and each one of these problems is solved for five different levels of the weighting factor an analysis into the resulting efficient points is also included an improved version of fsh1 called fsh2 is developed and both heuristics are subjected to extensive numerical experimentation

the automorphism group of a shift of finite type let xt at be a shift of finite type and g aut vt denote the group of homeomorphisms of xt commuting with t we investigate the algebraic properties of the countable group g and the dynamics of its action on xt and associated spaces using marker constructions we show g contains many groups such as the free group on two generators however g is residually finite so does not contain divisible groups or the infinite symmetric group the doubly exponential growth rate of the number of automorphisms depending on n coordinates leads to a new and nontrivial topological invariant of crt whose exact value is not known we prove that modulo a few points of low period g acts transitively on the set of points with least at period n using padic analysis we generalize to most finite type shifts a result of boyle and krieger that the gyration function of a full shift has infinite order the action of g on the dimension group of at is investigated we show there are no proper infinite compact g invariant sets we give a complete characterization of the g orbit closure of a continuous probability measure and deduce that the only continuous g invariant measure is that of maximal entropy examples questions and problems complement our analysis and we conclude with a brief survey of some remaining open problems

on positive matrices abstract we relate several results on positive matrices due to soittola 1976 handelman 1981 1987 and lind 1984 giving conditions for the existence of some positive matrix to represent a linear map the result of soittola concerns finite automata and those of handelman and lind concern symbolic dynamics

an adaptive ts approach to jit sequencing with variable processing times and sequence dependent setups this paper addresses a single machine sequencing problem with variable processing times and sequence dependent setups the objective is to find the best trade off between the jit goal and the processing time compression and extension costs by simultaneously determining the job sequence and processing times for concerned jobs due to the combinatorial nature of the problem it cannot be optimally solved in polynomial time a tabu search approach is used to provide good and quick solutions to improve the computational efficiency an adaptive neighbourhood generation method is proposed and used in the tabu search algorithm a total of 100 problems of different sizes have been solved to test the proposed approach our computational experience shows that the adaptive approach outperforms several other neighbourhood generation methods in terms of both convergence rate and solution quality the effects of the search parameters are also discussed

scheduling to minimize the total resource consumption with a constraint on the sum of completion times abstract we consider the problem of scheduling a set of jobs on a single machine where the release time of a job is related to the amount of resource consumed the objective is to minimize the total amount of resource consumed subject to a constraint on the sum of completion times of the jobs we show that the problem is np hard in general and can be solved efficiently when the resource consumption function is linear the parallel machine case is also discussed

random walk and the area below its path a simple random walk with reflected origin is considered the walk starts at the origin and it must return to the origin at time 2n we show that the expected area below the path of this walk is n22n 1 cn2n if however the walk is required to return to the origin for the first time at time 2n then the expected area below the path of this bernoulli excursion is 2n 1 22n 1 cn2n we also show that if v1 vn is the order statistics based on a sample of size n from a uniform distribution over 0 1 and that if u1 un is another independent set of order statistics from the same distribution then e i 1n vi ui n22n 1 2n 1 cn2n we use this result to find an average case performance of the earliest due date edd heuristic for one machine scheduling problem with earliness and tardiness penalties we also apply some of the results to larson s queue inference engine 1990

methods for estimating a conditional distribution function abstract motivated by the problem of setting prediction intervals in time series analysis we suggest two new methods for conditional distribution estimation the first method is based on locally fitting a logistic model and is in the spirit of recent work on locally parametric techniques in density estimation it produces distribution estimators that may be of arbitrarily high order but nevertheless always lie between 0 and 1 the second method involves an adjusted form of the nadaraya watson estimator it preserves the bias and variance properties of a class of second order estimators introduced by yu and jones but has the added advantage of always being a distribution itself our methods also have application outside the time series setting for example to quantile estimation for independent data this problem motivated the work of yu and jones

analysis of transformation models with censored data summary in this paper we consider a class of semi parametric transformation models under which an unknown transformation of the survival time is linearly related to the covariates with various completely specified error distributions this class of regression models includes the proportional hazards and proportional odds models inference procedures derived from a class of generalised estimating equations are proposed to examine the covariate effects with censored observations numerical studies are conducted to investigate the properties of our proposals for practical sample sizes these transformation models coupled with the new simple inference procedures provide many useful alternatives to the cox regression model in survival analysis

regular languages and their generating functions the inverse problem the technique of determining a generating function for an unambiguous context free language is known as the schutzenberger methodology for regular languages elena barcucci et al proposed an approach for inverting this methodology based on soittola s theorem this idea allows a combinatorial interpretation by means of a regular language of certain positive integer sequences that are defined by c finite recurrences in this paper we present a maple implementation of this inverse methodology and describe various applications we give a short introduction to the underlying theory i e the question of deciding n rationality in addition some aspects and problems concerning the implementation are discussed some examples from combinatorics illustrate its applicability

quantile regression in partially linear varying coefficient models semiparametric models are often considered for analyzing longitudinal data for a good balance between flexibility and parsimony in this paper we study a class of marginal partially linear quantile models with possibly varying coefficients the functional coefficients are estimated by basis function approximations the estimation procedure is easy to implement and it requires no specification of the error distributions the asymptotic properties of the proposed estimators are established for the varying coefficients as well as for the constant coefficients we develop rank score tests for hypotheses on the coefficients including the hypotheses on the constancy of a subset of the varying coefficients hypothesis testing of this type is theoretically challenging as the dimensions of the parameter spaces under both the null and the alternative hypotheses are growing with the sample size we assess the finite sample performance of the proposed method by monte carlo simulation studies and demonstrate its value by the analysis of an aids data set where the modeling of quantiles provides more comprehensive information than the usual least squares approach

another proof of soittola s theorem soittola s theorem characterizes r or n rational formal power series in one variable among the rational formal power series with nonnegative coefficients we present here a new proof of the theorem based on soittola s and perrin s proofs together with some new ideas that allows us to separate algebraic and analytic arguments

single machine scheduling with symmetric earliness and tardiness penalties abstract this research focuses on scheduling jobs with varying processing times and distinct due dates on a single machine subject to earliness and tardiness penalties hence this work will find application in a just in time jit production environment the scheduling problem is formulated as a 0 1 linear integer program with three sets of constraints where the objective is to minimize the sum of the absolute deviations between job completion times and their respective due dates the first two sets of constraints are equivalent to the supply and demand constraints of an assignment problem the third set which represents the process time non overlap constraints is relaxed to form the lagrangian dual problem the dual problem is then solved using the subgradient algorithm efficient heuristics have also been developed in this work to yield initial primal feasible solutions and to convert primal infeasible solutions to feasibility the computational results show that the relative deviation from optimality obtained by the subgradient algorithm is less than 3 for problem sizes varying from 10 to 100 jobs