parameter estimation of delay dynamical system from a scalar time series under external noise we introduce an adaptive learning rules for estimating all unknown parameters of delay dynamical system using a scalar time series sufficient condition for synchronization is derived using krasovskii lyapunov theory this scheme is highly applicable in secure communication since multiple messages can be transmitted through multiple parameter modulations one of the advantage of this method is that parameter estimation is also possible even when only one time series of the transmitter is available we present numerical examples for mackey glass system with periodic delay time which are used to illustrate the validity of this scheme the corresponding numerical results and the effect of external noise are also studied

chaotic component obscured by strong periodicity in voice production system the effect of glottal aerodynamics in producing the nonlinear characteristics of voice is investigated by comparing the outputs of the asymmetric composite model and the two mass model the two mass model assumes the glottal airflow to be laminar nonviscous and incompressible in this model when the asymmetric factor is decreased from 0 65 to 0 35 only 1 1 and 1 2 modes are detectable however with the same parameters four vibratory modes 1 1 1 2 2 4 2 6 are found in the asymmetric composite model using the navier stokes equations to describe the complex aerodynamics in the glottis moreover the amplitude of the waveform is modulated by a small amplitude noiselike series the nonlinear detection method reveals that this noiselike modulation is not random but rather it is deterministic chaos this result agrees with the phenomenon often seen in voice in which the voice signal is strongly periodic but modulated by a small amplitude chaotic component the only difference between the two mass model and the composite model is in their descriptions of glottal airflow therefore the complex aerodynamic characteristics of glottal airflow could be important in generating the nonlinear dynamic behavior of voice production including bifurcation and a small amplitude chaotic component obscured by strong periodicity

adaptive approximation method for joint parameter estimation and identical synchronization of chaotic systems we introduce a numerical approximation method for estimating an unknown parameter of a primary chaotic system which is partially observed through a scalar time series specifically we show that the recursive minimization of a suitably designed cost function that involves the dynamic state of a fully observed secondary system and the observed time series can lead to the identical synchronization of the two systems and the accurate estimation of the unknown parameter the salient feature of the proposed technique is that the only external input to the secondary system is the unknown parameter which needs to be adjusted we present numerical examples for the lorenz system which show how our algorithm can be considerably faster than some previously proposed methods

approximation algorithms for scheduling unrelated parallel machines we consider the following scheduling problem there arem parallel machines andn independent jobs each job is to be assigned to one of the machines the processing of jobj on machinei requires timep ij the objective is to find a schedule that minimizes the makespan our main result is a polynomial algorithm which constructs a schedule that is guaranteed to be no longer than twice the optimum we also present a polynomial approximation scheme for the case that the number of machines is fixed both approximation results are corollaries of a theorem about the relationship of a class of integer programming problems and their linear programming relaxations in particular we give a polynomial method to round the fractional extreme points of the linear program to integral points that nearly satisfy the constraints in contrast to our main result we prove that no polynomial algorithm can achieve a worst case ratio less than 3 2 unlessp np we finally obtain a complexity classification for all special cases with a fixed number of processing times

approximation schemes for the restricted shortest path problem this note contains two fully polynomial approximation schemes for the shortest path problem with an additional constraint the main difficulty in constructing such algorithms arises since no trivial lower and upper bounds on the solution value whose ratio is polynomially bounded are known in spite of this difficulty one of the algorithms presented here is strongly polynomial applications to other problems are also discussed

approximation algorithms for single source unsplittable flow in the single source unsplittable flow problem we are given a network g a source vertex s and k commodities with sinks ti and real valued demands rho i 1 leq i leq k we seek to route the demand rho i of each commodity i along a single s ti flow path so that the total flow routed across any edge e is bounded by the edge capacity ue the conceptual difficulty of this np hard problem arises from combining packing constraints due to the existence of capacities with path selection in a graph of arbitrary topology in this paper we give a generic framework which yields approximation algorithms that are simpler than those previously known and achieve significant improvements upon the approximation ratios our framework with appropriate subroutines applies to all optimization versions previously considered and unlike previous work treats in a unified manner directed and undirected graphs we provide extensions of our algorithms which yield the best possible approximation guarantees for restricted sets of demand values and an associated scheduling problem

truthful generalized assignments via stable matching in the generalized assignment problem gap a set of jobs seek to be assigned to a set of machines for every job machine pair there are a specific value and an accommodated capacity for the assignment the objective is to find an assignment that maximizes the total sum of values given that the capacity constraint of every machine is satisfied the gap is a classic optimization problem and has been studied extensively from the algorithmic perspective dughmi and ghosh dughmi s ghosh a 2010 truthful assignment without money acm conf electronic commerce acm new york 325 334 proposed the game theoretical framework in which every job is owned by a selfish agent who aims to maximize the value of his own assignment they gave a logarithmic approximation truthful in expectation mechanism and left open the problem whether there exists a truthful mechanism with a constant approximation factor in this paper we give an affirmative answer to this question and provide a constant approximation mechanism

coupled and k sided placements generalizing generalized assignment in modern data centers and cloud computing systems jobs often require resources distributed across nodes providing a wide variety of services motivated by this we study the coupled placement problem in which we place jobs into computation and storage nodes with capacity constraints so as to optimize some costs or profits associated with the placement the coupled placement problem is a natural generalization of the widely studied generalized assignment problem which concerns the placement of jobs into single nodes providing one kind of service we also study a further generalization the k sided placement problem in which we place jobs into k tuples of nodes each node in a tuple offering one of k services for both the coupled and k sided placement problems we consider minimization and maximization versions in the minimization versions mincpand min k ksp the goal is to achieve minimum placement cost while incurring a minimum blowup in the capacity of the individual nodes our first main result is an algorithm for min k ksp that achieves optimal cost while increasing capacities by at most a factor of k 1 k 1 also yielding the first constant factor approximation for mincp in the maximization versions maxcp and max k ksp the goal is to maximize the total weight of the jobs that are placed under hard capacity constraints max k ksp can be expressed as a k column sparse integer program and can be approximated to within a factor of o k factor using randomized rounding of a linear program relaxation we consider alternative combinatorial algorithms that are much more efficient in practice our second main result is a local search based combinatorial algorithm that yields a 15 approximation and o k 2 o k2 approximation for maxcp and max k ksp respectively finally we consider an online version of max k ksp and present algorithms that achieve logarithmic competitive ratio under certain necessary technical assumptions

estimating model parameters by chaos synchronization using chaos synchronization and a proposed iterative method of parameter adaptation we precisely estimate the model parameters of chaotic systems and synchronize two chaotic systems with originally mismatching model parameters this parameter adaptation method can be applied to a spatiotemporal chaotic system with a one way coupled map lattice as a biomedical application this method is capable of estimating the asymmetric tension parameter of a vocal fold model

theoretical explanation of observed decreasing failure rate pooled data on the times of successive failures of the air conditioning system of a fleet of jet airplanes seemed to indicate that the life distribution had a decreasing failure rate more refined analysis showed that the failure distribution for each airplane separately was exponential but with a different failure rate using the theorem that a mixture of distributions each having a non increasing failure rate e g a mixture of exponential distributions itself has a non increasing failure rate the apparent decreasing failure rate of the pooled air conditioning life distribution was satisfactorily explained the present study has implications in other areas where an observed decreasing failure rate may well be the result of mixing exponential distributions having different parameters

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

mixtures of exponential distributions arbitrary nonparametric mixtures of exponential and weibull fixed shape distributions are considered as possible models for a lifetime distribution a characterization of such distributions is given by the well known characterization of laplace transforms the maximum likelihood estimate of the mixing distribution is investigated and found to be supported on a finite number of points it is shown to be unique and weakly convergent to the true mixing measure with probability one a practical algorithm for computing the maximum likelihood estimate is described its performance is briefly discussed and some illustrative examples given

recovering unknown model parameters contained in a class of time variant chaotic dynamical systems abstract this work deals mainly with the problem of recovering all unknown parameters for a class of time variant chaotic dynamical systems from given time sequence based on synchronization between a chaotic sender system and an additional receiver system a procedure which combines a linear feedback technique with updated feedback gain and an adapted control strategy associated with the law of estimated parameters is developed to dynamically determine the values of unknown parameters contained in the sender system to promote widespread applications the structure of the receiver system can be independent of that of the sender system the effectiveness of this procedure is guaranteed by the periodic version of the classical lasalle invariance principle of differential equations illustrations are presented for a harmonically excited duffing oscillator and a four dimensional chaotic oscillator the numerical results reveal the present procedure not only can precisely recover unknown model parameters but also can rapidly response to sudden changes in unknown parameters in addition it has great robustness against the disturbance of noise

truthful mechanism design via correlated tree rounding a powerful algorithmic technique for truthful mechanism design is the maximal in distributional range midr paradigm unfortunately many such algorithms use heavy algorithmic machinery e g the ellipsoid method and approximate solution of convex programs in this paper we present a correlated rounding technique for designing mechanisms that are truthful in expectation it is elementary and can be implemented quickly the main property we rely on is that the domain offers fractional optimum solutions with a tree structure in auctions based on the generalized assignment problem each bidder has a publicly known knapsack constraint that captures the subsets of items that are of value to him he has a private valuation for each item and strives to maximize the value of assigned items minus payment for this domain we design a truthful 2 approximate midr mechanism for social welfare maximization it avoids using the ellipsoid method or convex programming in contrast to some previous work our mechanism achieves exact truthfulness in restricted related scheduling with selfish machines each job comes with a public weight and it must be assigned to a machine from a public job specific subset each machine has a private speed and strives to maximize payments minus workload of jobs assigned to it here we design a mechanism for makespan minimization this is a single parameter domain but the approximation status of the optimization problem is similar to unrelated machine scheduling the best known algorithm obtains a non truthful 2 approximation for unrelated machines and there is 1 5 hardness our mechanism matches this bound with a truthful 2 approximation

the constrained minimum weighted sum of job completion times problem we consider the problem of minimizing the weighted sum of job completion times on a single machine subject to certain job weights with an additional side constraint on the weighted sum of job completion times with respect to different job weights this problem is np hard and we provide a polynomial time approximation scheme for this problem our method is based on lagrangian relaxation mixed with carefully guessing the positions of certain jobs in the schedule

approximation algorithms for data placement problems we develop approximation algorithms for the problem of placing replicated data in arbitrary networks where the nodes may both issue requests for data objects and have capacity for storing data objects so as to minimize the average data access cost we introduce the data placement problem to model this problem we have a set of caches mathcal f a set of clients mathcal d and a set of data objects mathcal o each cache i can store at most u i data objects each client j in mathcal d has demand d j for a specific data object o j in mathcal o and has to be assigned to a cache that stores that object storing an object o in cache i incurs a storage cost of f i o and assigning client j to cache i incurs an access cost of d jc ij the goal is to find a placement of the data objects to caches respecting the capacity constraints and an assignment of clients to caches so as to minimize the total storage and client access costs we present a 10 approximation algorithm for this problem our algorithm is based on rounding an optimal solution to a natural linear programming relaxation of the problem one of the main technical challenges encountered during rounding is to preserve the cache capacities while incurring only a constant factor increase in the solution cost we also introduce the connected data placement problem to capture settings where write requests are also issued for data objects so that one requires a mechanism to maintain consistency of data we model this by requiring that all caches containing a given object be connected by a steiner tree to a root for that object which issues a multicast message upon a write to any copy of that object the total cost now includes the cost of these steiner trees we devise a 14 approximation algorithm for this problem we show that our algorithms can be adapted to handle two variants of the problem a a k median variant where there is a specified bound on the number of caches that may contain a given object and b a generalization where objects have lengths and the total length of the objects stored in any cache must not exceed its capacity

on a recursive method for the estimation of unknown parameters of partially observed chaotic systems we investigate a recently proposed method for on line parameter estimation and synchronization in chaotic systems this novel technique has been shown effective to estimate a single unknown parameter of a primary chaotic system with known functional form that is only partially observed through a scalar time series it works by periodically updating the parameter of interest in a secondary system with the same functional form as the primary one but no explicit coupling between their dynamic variables in order to minimize a suitably defined cost function in this paper we review the basics of the method and investigate its robustness and new extensions in particular we study the performance of the novel technique in the presence of noise either observational i e an additive contamination of the observed time series or dynamical i e a random perturbation of the system dynamics and when there is a mismatch between the primary and secondary systems numerical results including comparisons with other techniques are presented finally we investigate the extension of the original method to perform the estimation of two unknown parameters and illustrate its effectiveness by means of computer simulations

single machine scheduling polyhedra with precedence constraints we consider nonpreemptive single machine scheduling subject to precedence constraints we define feasible schedules by the vector of the job completion times and study the structure of the convex hull of all feasible schedules called the scheduling polyhedron p we derive classes of valid inequalities for p and necessary and sufficient conditions under which they are facet inducing our main result is a complete description of the minimal linear system defining p when the precedence constraints are series parallel moreover this system consists of two classes of facet inducing inequalities associated with series and parallel compositions respectively if the precedence constraints are not series parallel we present another class of facet inducing inequalities for p associated with induced z subgraphs we also show that the convex hull of all preemptive feasible schedules is identical to p if and only if the precedence constraints form an out forest

renewal sums under mixtures of exponentials abstract we start with applying two methods to derive formulas of a mixture of exponential process i e a renewal process whose inter arrival time follows a mixture of exponentials further stochastic order properties are discussed when comparing this process to a poisson process with the same expectation of inter arrival times based on these properties formulas and ordering properties are given for the non discounted compound process as well as the discounted one explicit formulas for the density functions are also provided for both cases under the discounted compound case several new results are derived for heavy tailed distributions finally the laguerre series approximation is proposed and tested for various common actuarial indices e g var cte and stop loss premium

structure of a simple scheduling polyhedron in a one machine nonpreemptive scheduling problem the feasible schedules may be defined by the vector of the corresponding job completion times for given positive processing times the associated simple scheduling polyhedronp is the convex hull of these feasible completion time vectors the main result of this paper is a complete description of the minimal linear system definingp we also give a complete combinatorial description of the face lattice ofp and a simple o n logn separation algorithm this algorithm has potential usefulness in cutting plane type algorithms for more difficult scheduling problems

structure identification based on steady state control experimental results and applications we report experimental results on structure identification of nonlinear systems by a steady state control method the idea underlying the method is to drive the nonlinear system to steady state by applying a suitable feedback control input it turns out experimentally that this control based structure identification method can be used for some applications such as estimation of initial conditions and state variables of nonlinear systems and structure identification of some special elements two attractors of the chua oscillator are presented to illustrate the reliability of the suggested techniques under the hypotheses of measurable state variables and physical access to the system for implementing the proportional feedback

parameter and state estimation of experimental chaotic systems using synchronization we examine the use of synchronization as a mechanism for extracting parameter and state information from experimental systems we focus on important aspects of this problem that have received little attention previously and we explore them using experiments and simulations with the chaotic colpitts oscillator as an example system we explore the impact of model imperfection on the ability to extract valid information from an experimental system we compare two optimization methods an initial value method and a constrained method each of these involves coupling the model equations to the experimental data in order to regularize the chaotic motions on the synchronization manifold we explore both time dependent and time independent coupling and discuss the use of periodic impulse coupling we also examine both optimized and fixed or manually adjusted coupling for the case of an optimized time dependent coupling function u t we find a robust structure which includes sharp peaks and intervals where it is zero this structure shows a strong correlation with the location in phase space and appears to depend on noise imperfections of the model and the lyapunov direction vectors for time independent coupling we find the counterintuitive result that often the optimal rms error in fitting the model to the data initially increases with coupling strength comparison of this result with that obtained using simulated data may provide one measure of model imperfection the constrained method with time dependent coupling appears to have benefits in synchronizing long data sets with minimal impact while the initial value method with time independent coupling tends to be substantially faster more flexible and easier to use we also describe a method of coupling which is useful for sparse experimental data sets our use of the colpitts oscillator allows us to explore in detail the case of a system with one positive lyapunov exponent the methods we explored are easily extended to driven systems such as neurons with time dependent injected current they are expected to be of value in nonchaotic systems as well software is available on request

scheduling multiple variable speed machines we examine scheduling problems where we control not only the assignment of jobs to machines but also the time used by the job on the machine for instance many tooling machines allow control of the speed at which a job is run increasing the speed incurs costs due to machine wear but also increases throughput we discuss some fundamental scheduling problems in this environment and give algorithms for some interesting cases some cases are inherently difficult so for these we give heuristics our approach illustrates the exploitation of underlying network structure in combinatorial optimization problems we create heuristics that optimally schedule a large portion of the jobs and then attempt to fit in the remainder this also gives a method for quickly finding valid inequalities violated by the linear relaxation solution for the problem of minimizing the sum of makespan and production costs a rounding heuristic is within a constant factor of optimal our heuristics are compared to other classical heu

an approximation algorithm for the generalized assignment problem the generalized assignment problem can be viewed as the following problem of scheduling parallel machines with costs each job is to be processed by exactly one machine processing jobj on machinei requires timep ij and incurs a cost ofc ij each machinei is available fort i time units and the objective is to minimize the total cost incurred our main result is as follows there is a polynomial time algorithm that given a valuec either proves that no feasible schedule of costc exists or else finds a schedule of cost at mostc where each machinei is used for at most 2t i time units we also extend this result to a variant of the problem where instead of a fixed processing timep ij there is a range of possible processing times for each machine job pair and the cost linearly increases as the processing time decreases we show that these results imply a polynomial time 2 approximation algorithm to minimize a weighted sum of the cost and the makespan i e the maximum job completion time we also consider the objective of minimizing the mean job completion time we show that there is a polynomial time algorithm that given valuesm andt either proves that no schedule of mean job completion timem and makespant exists or else finds a schedule of mean job completion time at mostm and makespan at most 2t

tight approximation algorithms for maximum separable assignment problems a separable assignment problem sap is defined by a set of bins and a set of items to pack in each bin a value fij for assigning item j to bin i and a separate packing constraint for each bin i e for each bin a family of subsets of items that fit in to that bin the goal is to pack items into bins to maximize the aggregate value this class of problems includes the maximum generalized assignment problem gap 1 and a distributed caching problem dcp described in this paper given a approximation algorithm for finding the highest value packing of a single bin we give a polynomial time lp rounding based 1 1 e approximation algorithm a simple polynomial time local search 1 e approximation algorithm for any e 0 therefore for all examples of sap that admit an approximation scheme for the single bin problem we obtain an lp based algorithm with 1 1 e e approximation and a local search algorithm with e approximation guarantee furthermore for cases in which the subproblem admits a fully polynomial approximation scheme such as for gap the lp based algorithm analysis can be strengthened to give a guarantee of 1 1 e the best previously known approximation algorithm for gap is a approximation by shmoys and tardos and chekuri and khanna our lp algorithm is based on rounding a new linear programming relaxation with a provably better integrality gap to complement these results we show that sap and dcp cannot be approximated within a factor better than 1 1 e unless np dtime no log log n even if there exists a polynomial time exact algorithm for the single bin problem we extend the 1 1 e approximation algorithm to a constant factor approximation algorithms for a nonseparable assignment problem with applications in maximizing revenue for budget constrained combinatorial auctions and the adwords assignment problem we generalize the local search algorithm to yield a e approximation algorithm for the maximum k median problem with hard capacities

monotone covering problems with an additional covering constraint we provide preliminary results regarding the existence of a polynomial time approximation scheme ptas for minimizing a linear function over a 0 1 covering polytope which is integral with one additional covering constraint our algorithm is based on extending the methods of goemans and ravi for the constrained minimum spanning tree problem and in particular implies the existence of a ptas for several covering integer programming problems with a totally unimodular constraint matrix these include the cases when the columns of the constraint matrix either have at most two nonzero elements are incidence vectors of a laminar family or have consecutive ones and no column is contained in another

a unified approach to scheduling on unrelated parallel machines we develop a single rounding algorithm for scheduling on unrelated parallel machines this algorithm works well with the known linear programming quadratic programming and convex programming relaxations for scheduling to minimize completion time makespan and other well studied objective functions this algorithm leads to the following applications for the general setting of unrelated parallel machines i a bicriteria algorithm for a schedule whose weighted completion time and makespan simultaneously exhibit the current best individual approximations for these criteria ii better than two approximation guarantees for scheduling to minimize the lp norm of the vector of machine loads for all 1

parameter estimations of parametrically excited pendulums based on chaos feedback synchronization in this paper an iterate parameter estimation scheme based on chaos feedback synchronization is applied for parametrically excited pendulums the response pendulum can exactly reproduce the system parameters and bifurcation diagram of the drive pendulum thus allowing two chaotic pendulums to be synchronized even though their initial parameter values are quite different the effects of feedback function and feedback weight are investigated feedback and parameter controls suppress the perturbations resulting from noise and parameter mismatches this parameter estimation method based on feedback synchronization is robust to large parameter mismatches