a polynomial time approximation scheme for the two stage multiprocessor flow shop problem in this paper we investigate the two stage multiprocessor flow shop scheduling problem f2 p cmax where the numbers m1 and m2 of machines available in the two stages are part of the input we demonstrate the existence of a polynomial time approximation scheme for this problem this result solves the simplest case of an open problem that has been posed by leslie hall in a recent paper hall 1995 an extension of our algorithm yields an approximation scheme for the closely related two stage multiprocessor job shop problem

criteria for quasi convexity and pseudo convexity relationships and comparisons a first order criterion for pseudo convexity and second order criteria for quasi convexity and pseudo convexity are given for twice differentiable functions on open convex sets the relationships between these second order criteria and other known criteria are also analysed finally the numbers of operations required to verify these criteria are calculated and compared

rank of a hadamard product abstract we provide a new proof of a sharp lower bound for the rank of the hadamard product of positive semidefinite matrices our proof uses standard matrix analysis tools and involves the rank of one factor and the kruskal rank of the other it leads to a new understanding of when the hadamard exponential of a positive semidefinite matrix can be singular

job shop scheduling with unit processing times we consider randomized algorithms for the preemptive job shop problem or equivalently the case in which all operations have unit length we give an approximation for the case of two machines where 1 45 an improved approximation ratio of o log m log log m for an arbitrary number m of machines and the first 2 e approximation for a constant number of machines the first result is via an approximation algorithm for a string matching problem that is of independent interest

short shop schedules we consider the open shop job shop and flow shop scheduling problems with integral processing times we give polynomial time algorithms to determine if an instance has a schedule of length at most 3 and show that deciding if there is a schedule of length at most 4 is x1d4a9 x1d4ab complete the latter result implies that unless x1d4ab x1d4a9 x1d4ab there does not exist a polynomial time approximation algorithm for any of these problems that constructs a schedule with length guaranteed to be strictly less than 5 4 times the optimal length this work constitutes the first nontrivial theoretical evidence that shop scheduling problems are hard to solve even approximately

on gcd lcm and hilbert matrices and their applications we give upper bounds for the p norm of the hilbert matrix h 1 i j 1 i j 1 n and its hadamard square furthermore determine lower bounds for the frobenius norms of gcd and lcm matrices

matrix theoretic criteria for the quasiconvexity of twice continuously differentiable functions abstract the author examines matrices and bordered matrices having exactly one or at most one negative eigenvalue these results are then used to state matrix theoretic criteria for the quasiconvexity of twice continuously differentiable functions for quadratic functions a new criterion for quasiconvexity is established and its equivalence to the already known criterion 11 23 is also shown

bayesian state estimation on finite horizons the case of linear state space model abstract the finite impulse response fir filter and infinite impulse response filter including the kalman filter kf are generally considered as two different types of state estimation methods in this paper the sequential bayesian philosophy is extended to a filter design using a fixed amount of most recent measurements with the aim of exploiting the fir structure and unifying some basic fir filters with the kf specifically the conditional mean and covariance of the posterior probability density functions are first derived to show the fir counterpart of the kf to remove the dependence on initial states the corresponding likelihood is further maximized and realized iteratively it shows that the maximum likelihood modification unifies the existing unbiased fir filters by tuning a weighting matrix moreover it converges to the kalman estimate with the increase of horizon length and can thus be considered as a link between the fir filtering and the kf several important properties including stability and robustness against errors of noise statistics are illustrated finally a moving target tracking example and an experiment with a three degrees of freedom helicopter system are introduced to demonstrate effectiveness

subdivision direction selection in interval methods for global optimization the role of the interval subdivision selection rule is investigated in branch and bound algorithms for global optimization the class of rules that allows convergence for the model algorithm is characterized and it is shown that the four rules investigated satisfy the conditions of convergence a numerical study with a wide spectrum of test problems indicates that there are substantial differences between the rules in terms of the required cpu time the number of function and derivative evaluations and space complexity and two rules can provide substantial improvements in efficiency

maximum likelihood estimation for multivariate observations of markov sources parameter estimation for multivariate functions of markov chains a class of versatile statistical models for vector random processes is discussed the model regards an ordered sequence of vectors as noisy multivariate observations of a markov chain mixture distributions are a special case the foundations of the theory presented here were established by baum petrie soules and weiss a powerful representation theorem by fan is employed to generalize the analysis of baum em et al to a larger class of distributions

improved approximation algorithms for shop scheduling problems in the job shop scheduling problem there are m machines and n jobs a job consists of a sequence of operations each of which must be processed on a specified machine and the aim is to complete all jobs as quickly as possible this problem is strongly cal np hard even for very restrictive special cases the authors give the first randomized and deterministic polynomial time algorithms that yield polylogarithmic approximations to the optimal length schedule these algorithms also extend to the more general case where a job is given not by a linear ordering of the machines on which it must be processed but by an arbitrary partial order comparable bounds can also be obtained when there are m types of machines a specified number of machines of each type and each operation must be processed on one of the machines of a specified type as well as for the problem of scheduling unrelated parallel machines subject to chain precedence constraints

hadamard inverses square roots and products of almost semidefinite matrices abstract let a aij be an n n symmetric matrix with all positive entries and just one positive eigenvalue bapat proved then that the hadamard inverse of a given by a 1 1 a ij is positive semidefinite we show that if moreover a is invertible then a 1 is positive definite we use this result to obtain a simple proof that with the same hypotheses on a except that all the diagonal entries of a are zero the hadamard square root of a given by a 1 2 a ij 1 2 has just one positive eigenvalue and is invertible finally we show that if a is any positive semidefinite matrix and b is almost positive definite and invertible then a b 1 e t b 1 e a

approximation schemes for job shop scheduling problems with controllable processing times in this paper we study the job shop scheduling problem under the assumption that the jobs have controllable processing times the fact that the jobs have controllable processing times means that it is possible to reduce the processing time of the jobs by paying a certain cost we consider two models of controllable processing times continuous and discrete for both models we present polynomial time approximation schemes when the number of machines and the number of operations per job are fixed

brief paper box particle filtering for nonlinear state estimation using interval analysis in recent years particle filters have been applied to a variety of state estimation problems a particle filter is a sequential monte carlo bayesian estimator of the posterior density of the state using weighted particles the efficiency and accuracy of the filter depend mostly on the number of particles used in the estimation and on the propagation function used to re allocate weights to these particles at each iteration if the imprecision i e bias and noise in the available information is high the number of particles needs to be very large in order to obtain good performances this may give rise to complexity problems for a real time implementation this kind of imprecision can easily be represented by interval data if the maximum error is known handling interval data is a new approach successfully applied to different real applications in this paper we propose an extension of the particle filter algorithm able to handle interval data and using interval analysis and constraint satisfaction techniques in standard particle filtering particles are punctual states associated with weights whose likelihoods are defined by a statistical model of the observation error in the box particle filter particles are boxes associated with weights whose likelihood is defined by a bounded model of the observation error experiments using actual data for global localization of a vehicle show the usefulness and the efficiency of the proposed approach

bernoulli particle box particle filters for detection and tracking in the presence of triple measurement uncertainty this work presents sequential bayesian detection and estimation methods for nonlinear dynamic stochastic systems using measurements affected by three sources of uncertainty stochastic set theoretic and data association uncertainty following mahler s framework for information fusion the paper develops the optimal bayes filter for this problem in the form of the bernoulli filter for interval measurements two numerical implementations of the optimal filter are developed the first is the bernoulli particle filter pf which turns out to require a large number of particles in order to achieve a satisfactory performance for the sake of reduction in the number of particles the paper also develops an implementation based on box particles referred to as the bernoulli box pf a box particle is a random sample that occupies a small and controllable rectangular region of nonzero volume in the target state space manipulation of boxes utilizes the methods of interval analysis the two implementations are compared numerically and found to perform remarkably well the target is reliably detected and the posterior probability density function of the target state is estimated accurately the bernoulli box pf however when designed carefully is computationally more efficient

turbo segmentation of textured images we consider the problem of semi supervised segmentation of textured images existing model based approaches model the intensity field of textured images as a gauss markov random field to take into account the local spatial dependencies between the pixels classical bayesian segmentation consists of also modeling the label field as a markov random field to ensure that neighboring pixels correspond to the same texture class with high probability well known relaxation techniques are available which find the optimal label field with respect to the maximum a posteriori or the maximum posterior mode criterion but these techniques are usually computationally intensive because they require a large number of iterations to converge in this paper we propose a new bayesian framework by modeling two dimensional textured images as the concatenation of two one dimensional hidden markov autoregressive models for the lines and the columns respectively a segmentation algorithm which is similar to turbo decoding in the context of error correcting codes is obtained based on a factor graph approach the proposed method estimates the unknown parameters using the expectation maximization algorithm

the computation of the square roots of circulant matrices abstract in the first part of this paper we investigate the reduced forms of circulant matrices and quasi skew circulant matrices by using their properties we present two efficient algorithms to compute the square roots of circulant matrices and quasi skew circulant matrices respectively those methods are faster than the traditional algorithm which is based on the schur decomposition in the second part we further consider circulant h matrices with positive diagonal entries and develop two algorithms for computing their principal square roots those two algorithms have the common advantage that is they only need matrix matrix multiplications in their iterative sequences an operation which can be done very efficiently on modern high performance computers

generalized schur complements and p complementable operators abstract let a be a selfadjoint operator and p be an orthogonal projection both operating on a hilbert space h we say that a is p complementable if a p 0 holds for some r in this case we define i p a max r a p 0 as a tool for computing ip a we introduce a natural generalization of the schur complement or shorted operator of a to s r p denoted by a p we give expressions and a characterization for ip a that generalize some known results for particular choices of p we also study some aspects of the shorted operator a p for p complementable a under the hypothesis of compatibility of the pair a s we give some applications in the finite dimensional context

makespan minimization in open shops a polynomial time approximation scheme in this paper we demonstrate the existence of a polynomial time approximation scheme for makespan minimization in the open shop scheduling problem with an arbitrary fixed numberm of machines for the variant of the problem where the number of machines is part of the input it is known that the existence of an approximation scheme would implyp np hence our result draws a precise separating line between approximable cases i e withm fixed and non approximable cases i e withm part of the input of this shop problem 1998 the mathematical programming society inc published by elsevier science b v

optimisation and adaptation of synchronisation controllers for networked second order infinite dimensional systems abstractthe adaptation and optimisation of synchronisation control for networked second order distributed parameter systems are considered the objective is to design output feedback controllers guaranteeing agreement between the states of the n systems that individually track a reference model the controller structure involves feedback terms consisting of the pairwise difference of the measurements of the second order systems as well as coupling terms that enforce consensus placing the closed loop networked systems in aggregate form allows for further optimisation of the synchronisation gains using the aggregate systems closed loop energy as a suitable optimisation measure the search for the synchronisation gains reduces to the minimisation of the optimisation index which eventually is described by the trace of the solution to a parameterised lyapunov operator equation considering the adaptation of the synchronisation gains offers an alternative to optimisation the adaptation is based on lyapuno

regime switching for dynamic correlations we propose a new model for the variance between multiple time series the regime switching dynamic correlation we decompose the covariances into correlations and standard deviations and the correlation matrix follows a regime switching model it is constant within a regime but different across regimes the transitions between the regimes are governed by a markov chain this model does not suffer from a curse of dimensionality and it allows analytic computation of multi step ahead conditional expectations of the variance matrix when combined with the armach model taylor modelling financial time series wiley new york and schwert j finance 44 5 1989 1115 for the standard deviations we also present an empirical application which illustrates that our model can have a better fit of the data than the dynamic conditional correlation model proposed by engle j business econ statist 20 3 2002 339

analysis of time series subject to changes in regime abstract this paper introduces an em algorithm for obtaining maximum likelihood estimates of parameters for processes subject to discrete shifts in autoregressive parameters with the shifts themselves modeled as the outcome of a discrete valued markov process the simplicity of the em algorithm permits potential application of the approach to large vector systems

circum euclidean distance matrices and faces abstract we study the structure of circum euclidean distance matrices those euclidean distance matrices generated by points lying on a hypersphere we show for example that such euclidean distance matrices are characterized as having constant row sums and they constitute the interior of the cone of all euclidean distance matrices also we provide a formula for computing the radius of a representing configuration in the smallest embedding dimension r and show that rk d r 1 finally we obtain a geometric characterization of the faces of this cone given a configuration of points and its euclidean distance matrix d any matrix in the minimal face containing d comes from a configuration that is a linear perturbation of the points that generate d

sequential imputations and bayesian missing data problems abstract for missing data problems tanner and wong have described a data augmentation procedure that approximates the actual posterior distribution of the parameter vector by a mixture of complete data posteriors their method of constructing the complete data sets is closely related to the gibbs sampler both required iterations and similar to the em algorithm convergence can be slow we introduce in this article an alternative procedure that involves imputing the missing data sequentially and computing appropriate importance sampling weights in many applications this new procedure works very well without the need for iterations sensitivity analysis influence analysis and updating with new data can be performed cheaply bayesian prediction and model selection can also be incorporated examples taken from a wide range of applications are used for illustration

serial correlation in latent discrete variable models abstract we consider the problems of estimation and testing in models with serially correlated discrete latent variables a particular case of this is the time series regression model in which a discrete explanatory variable is measured with error test statistics are derived for detecting serial correlation in such a model we then show that the likelihood function can be evaluated by a recurrence relation and thus maximum likelihood estimation is computationally feasible an illustrative example of these methods is given followed by a brief discussion of their applicability to a markov model of switching regressions

hardness of approximating flow and job shop scheduling problems we consider several variants of the job shop problem that is a fundamental and classical problem in scheduling the currently best approximation algorithms have worse than logarithmic performance guarantee but the only previously known inapproximability result says that it is np hard to approximate job shops within a factor less than 5 4 closing this big approximability gap is a well known and long standing open problem this article closes many gaps in our understanding of the hardness of this problem and answers several open questions in the literature it is shown the first nonconstant inapproximability result that almost matches the best known approximation algorithm for acyclic job shops the same bounds hold for the general version of flow shops where jobs are not required to be processed on each machine similar inapproximability results are obtained when the objective is to minimize the sum of completion times it is also shown that the problem with two machines and the preemptive variant with three machines have no ptas

a series form solution for pricing variance and volatility swaps with stochastic volatility and stochastic interest rate abstract in this paper we present analytical pricing formulae for variance and volatility swaps when both of the volatility and interest rate are assumed to be stochastic and follow a cir cox ingersoll ross process forming a heston cir hybrid model the solutions are written in a series form with a theoretical proof of their convergence ensuring the accuracy of the determined swap prices the application of the formulae in practice is also demonstrated through the designed numerical experiments

alternative algorithms for the estimation of dynamic factor mimic and varying coefficient regression models this paper provides a general approach to the formulation and estimation of dynamic unobserved component models after introducing the general model two methods for estimating the unknown parameters are presented both are algorithms for maximizing the likelihood function the first is based on the method of scoring the second is the em algorithm a derivative free method each iteration of em requires a kalman filter and smoother followed by straightforward regression calculations the paper suggests using the em methods to quickly locate a neighborhood of the maximum scoring can then be used to pinpoint the maximum and calculate the information matrix

minimizing average completion time in the presence of release dates a natural and basic problem in scheduling theory is to provide good average quality of service to a stream of jobs that arrive over time in this paper we consider the problem of schedulingn jobs that are released over time in order to minimize the average completion time of the set of jobs in contrast to the problem of minimizing average completion time when all jobs are available at time 0 all the problems that we consider are np hard and essentially nothing was known about constructing good approximations in polynomial time we give the first constant factor approximation algorithms for several variants of the single and parallel machine models many of the algorithms are based on interesting algorithmic and structural relationships between preemptive and nonpreemptive schedules and linear programming relaxations of both many of the algorithms generalize to the minimization of averageweighted completion time as well 1998 the mathematical programming society inc published by elsevier science b v

approximability of flow shop scheduling shop scheduling problems are notorious for their intractability both in theory and practice in this paper we construct a polynomial approximation scheme for the flow shop scheduling problem with an arbitrary fixed number of machines for the three common shop models open flow and job this result is the only known approximation scheme since none of the three models can be approximated arbitrarily closely in the general case unless p np the result demonstrates the approximability gap between the models in which the number of machines is fixed and those in which it is part of the input of the instance the result can be extended to flow shops with job release dates and delivery times and to flow shops with a fixed number of stages where the number of machines at any stage is fixed 1998 the mathematical programming society inc published by elsevier science b v

a study on several combination problems of classic shop scheduling and shortest path in this paper we study several combinatorial optimization problems which combine the classic open shop or job shop scheduling problem and the shortest path problem our goal is to select a subset of jobs that constitutes a feasible solution of the shortest path problem and then execute the selected jobs on the shop machines to minimize the makespan i e the last completion time of all the jobs we prove that these problems are np hard even if there are two machines if the number of machines is an input we show that it is unlikely to find approximation algorithms with performance ratios better than 2 unless p np we present an intuitive approximation algorithm when the number of machines is an input and an improved approximation algorithm when the number of machines is fixed in addition we propose a polynomial time approximation scheme for the open shop case when the number of machines is fixed

a tutorial on particle filters for online nonlinear non gaussian bayesian tracking increasingly for many application areas it is becoming important to include elements of nonlinearity and non gaussianity in order to model accurately the underlying dynamics of a physical system moreover it is typically crucial to process data on line as it arrives both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics in this paper we review both optimal and suboptimal bayesian algorithms for nonlinear non gaussian tracking problems with a focus on particle filters particle filters are sequential monte carlo methods based on point mass or particle representations of probability densities which can be applied to any state space model and which generalize the traditional kalman filtering methods several variants of the particle filter such as sir asir and rpf are introduced within a generic framework of the sequential importance sampling sis algorithm these are discussed and compared with the standard ekf through an illustrative example

tight bounds for permutation flow shop scheduling in flow shop scheduling there are m machines and n jobs such that every job has to be processed on the machines in the fixed order 1 m in the permutation flow shop problem it is also required that each machine process the set of all jobs in the same order formally given n jobs along with their processing times on each machine the goal is to compute a single permutation of the jobs n n that minimizes the maximum job completion time makespan of the schedule resulting from the previously best known approximation guarantee for this problem was o m log m 1 2 sviridenko m 2004 a note on permutation flow shop problem ann oper res 129 247 252 in this paper we obtain an improved o min m1 2 n1 2 approximation algorithm for the permutation flow shop scheduling problem by finding a connection between the scheduling problem and the longest increasing subsequence problem our approximation ratio is relative to the lower bounds of maximum job length and maximum machine load and is the best possible such result this also resolves an open question from potts et al potts c d shmoys d williamson 1991 permutation vs nonpermutation flow shop schedules oper res lett 10 281 284 by algorithmically matching the gap between permutation and nonpermutation schedules we also consider the weighted completion time objective for the permutation flow shop scheduling problem using a natural linear programming relaxation and our algorithm for the makespan objective we obtain an o min m1 2 n1 2 approximation algorithm for minimizing the total weighted completion time improving on the previously best known guarantee of em for any constant e 0 smutnicki c 1998 some results of the worst case analysis for flow shop scheduling eur j oper res 109 66 87 we give a matching lower bound on the integrality gap of our linear programming relaxation

computing minimal volume credible sets using interval analysis application to bayesian estimation given a random vector p with a probability density function pdf pi p a credible set pi p with level alpha is a set that contains p with a probability alpha the problem of characterizing minimal volume credible sets which correspond to level sets for pi is considered it is only assumed that the expression of pi p results from a combination of elementary operators and elementary functions sin cos abs etc this paper provides an algorithm able to compute accurate inner and outer approximations of minimal volume credible sets in a guaranteed way the approach is based on interval analysis and an application to nonlinear parameter estimation in a bayesian context is treated a windows solver associated with the presented algorithm is made available at http www ensieta fr e3i2 jaulin bayes zip

nonlinearities and regimes in conditional correlations with different dynamics abstract new parameterizations of the dynamic conditional correlation dcc model and of the regime switching dynamic correlation rsdc model are introduced such that these models provide a specific dynamics for each correlation they imply a nonlinear autoregressive form of dependence on lagged correlations and are based on properties of the hadamard exponential matrix the new models are applied to a data set of twenty stock market indices and a data set of the thirty dow jones components comparing them to the classical dcc and rsdc models the empirical results show that the new models improve their classical versions in terms of several criteria

loop detection of mobile robots using interval analysis this paper proposes an original set membership approach for loop detection of mobile robots in the situation where proprioceptive sensors only are available to detect loops the new concepts of thet plane which is a two dimensional space with time coordinates are introduced intervals of functions or tubes are then used to represent uncertain trajectories and tests are provided in order to eliminate parts of the t plane that do not correspond to any loop an experiment with an actual underwater robot is proposed in order to illustrate the principle and the efficiency of the approach

an observation on the hadamard product of hermitian matrices abstract we give the best possible bound from below in the lowener ordering for the hadamard product a b in terms of a multiple of a when a is positive semidefinite nonzero and b is positive definite

guaranteed nonlinear estimation using constraint propagation on sets bounded error estimation is the estimation of the parameter or state vector of a model from experimental data under the assumption that some suitably de ned errors should belong to some prior feasible sets when the model outputs are linear in the vector to be estimated a number of methods are available to enclose all estimates that are consistent with the data into simple sets such as ellipsoids orthotopes or parallelotopes thereby providing guaranteed set estimates in the nonlinear case the situation is much less developed and there are very few methods that produce such guaranteed estimates in this paper the discrete time problem is cast into the more general framework of constraint satisfaction problems algorithms rather classical in the area of interval constraint propagation are extended by replacing intervals by more general subsets of real vector spaces this makes it possible to propose a new algorithm that contracts the feasible domains for each uncertain variable optimally i e no smaller domain could be obtained and e ciently the resulting methodology is illustrated on discrete time nonlinear state estimation the state at time k is estimated either from past measurement only or from all measurements assumed to be available from the start even in the causal case prior information on the future value of the state and output vectors due for instance to physical constraints is readily taken into account

approximating disjoint path problems using packing integer programs in a packing integer program we are given a matrix a and column vectors b c with nonnegative entries we seek a vector x of nonnegative integers which maximizes c t x subject to ax leq b the edge and vertex disjoint path problems together with their unsplittable flow generalization are np hard problems with a multitude of applications in areas such as routing scheduling and bin packing these two categories of problems are known to be conceptually related but this connection has largely been ignored in terms of approximation algorithms we explore the topic of approximating disjoint path problems using polynomial size packing integer programs motivated by the disjoint paths applications we introduce the study of a class of packing integer programs called column restricted we develop improved approximation algorithms for column restricted programs a result that we believe is of independent interest additional approximation algorithms for disjoint paths are presented that are simple to implement and achieve good performance when the input has a special structure

specification testing when score test statistics are identically zero we investigate the problem of previous specification testing when the score vector evaluated at the restricted mle is identically zero several econometric examples are provided a general test procedure which generalizes the geometric principle of the score test is proposed the wald and the likelihood ratio tests are also analyzed even under such irregularities the usual asymptotic distribution of the likelihood ratio statistics is still valid however the wald type statistics need to be modified the generalized score the likelihood ratio and the modified wald tests are shown to be asymptotically equivalent the asymptotic efficiency of the tests is derived