minimizing total weighted completion time in a two machine flow shop scheduling under simple linear deterioration abstract in this paper we address a two machine flow shop scheduling problem under simple linear deterioration by a simple linear deterioration function we mean that the processing time of a job is a simple linear function of its execution start time the objective is to find a sequence that minimizes total weighted completion time optimal schedules are obtained for some special cases for the general case several dominance properties and two lower bounds are derived to speed up the elimination process of a branch and bound algorithm a heuristic algorithm is also proposed to overcome the inefficiency of the branch and bound algorithm computational analysis on randomly generated problems is conducted to evaluate the branch and bound algorithm and heuristic algorithm

symmetry and phase locking in a ring of pulse coupled oscillators with distributed delays abstract phase locking in a ring of pulse coupled integrate and fire oscillators with distributed delays is analysed using group theory the period of oscillation of a solution and those related by symmetry is determined self consistently numerical continuation of maximally symmetric solutions in characteristic system length and timescales yields bifurcation diagrams with spontaneous symmetry breaking the stability of phase locked solutions is determined via a linearisation of the oscillator firing map in the weak coupling regime averaging leads to an effective phase coupled model with distributed phase shifts and the analysis of the system is considerably simplified in particular the collective period of a solution is now slaved to the relative phases for odd numbered rings spontaneous symmetry breaking can lead to a change of stability of a travelling wave state via a simple hopf bifurcation the resulting non phase locked solutions are constructed via numerical continuation at these bifurcation points the corresponding behaviour in the integrate and fire system is explored with simulations showing bifurcations to quasiperiodic firing patterns

a time indexed formulation of non preemptive single machine scheduling problems we consider the formulation of non preemptive single machine scheduling problems using time indexed variables this approach leads to very large models but gives better lower bounds than other mixed integer programming formulations we derive a variety of valid inequalities and show the role of constraint aggregation and the knapsack problem with generalised upper bound constraints as a way of generating such inequalities a cutting plane branch and bound algorithm based on these inequalities has been implemented computational experience on small problems with 20 30 jobs and various constraints and objective functions is presented

neural activity measures and their dynamics we provide an asymptotically justified derivation of activity measure evolution equations amees for a finite size neural network the approach takes into account the dynamics for each isolated neuron in the network being modeled by a biophysical model i e hodgkin huxley equations or their reductions by representing the interacting network as self and pairwise interactions we propose a general definition of spatial projections of the network called activity measures that quantify the activity of a network we show that the evolution equations that govern the dynamics of the activity measure shadow the activity measure of the network i e the two quantities stay close to each other for all times for general interactions and various asymptotic dynamics the amees effectively serve as a dimensionality reduction technique for the complex network when spatial synchrony and coherence are present and allow us to a priori predict network dynamics that would not be guessed from individual neuron behav

partial isometries and pseudoinverses in semi hilbertian spaces abstract in this article the concepts of partial isometries normal partial isometries and generalized projections in the context of operators defined on a semi hilbertian space are developed in particular we analyze the relationship between these operators and different notions of pseudoinverses in semi hilbertian spaces finally we apply the results obtained to describe the set of weighted projections into closed subspaces

generalized and hypergeneralized projectors abstract generalizations of the class of projectors are considered within the classes of normal and ep matrices some properties are derived and results on the sum difference and product of generalized and hypergeneralized projectors are given

the two machine flowshop total completion time problem improved lower bounds and a branch and bound algorithm abstract this paper presents a branch and bound algorithm for the two machine flowshop scheduling problem with the objective of minimizing the sum of completion times the main feature of the branch and bound algorithm is a new lower bounding scheme that is based on a network formulation of the problem with extensive computational tests we demonstrate that the branch and bound algorithm can solve problems with up to 60 45 jobs where processing times are uniformly distributed in the 1 10 1 100 range

the two machine flowshop scheduling problem with sequence independent setup times new lower bounding strategies abstract the two machine flowshop environment with sequence independent setup times has been intensely investigated both from theoretical and practical perspectives in the scheduling literature nevertheless very scant attention has been devoted to deriving effective lower bounding strategies in this paper we propose new lower bounds for the total completion time minimization criterion these bounds are based on three relaxation schemes namely the waiting time based relaxation scheme the single machine based relaxation scheme and the lagrangian relaxation scheme extensive computational study carried on instances with up to 500 jobs reveals that embedding the waiting time based bounding strategy within the lagrangian relaxation framework yields the best performance while requiring negligible cpu time

phase locked patterns and amplitude death in a ring of delay coupled limit cycle oscillators we study the existence and stability of phase locked patterns and amplitude death states in a closed chain of delay coupled identical limit cycle oscillators that are near a supercritical hopf bifurcation the coupling is limited to nearest neighbors and is linear we analyze a model set of discrete dynamical equations using the method of plane waves the resultant dispersion relation which is valid for any arbitrary number of oscillators displays important differences from similar relations obtained from continuum models we discuss the general characteristics of the equilibrium states including their dependencies on various system parameters we next carry out a detailed linear stability investigation of these states in order to delineate their actual existence regions and to determine their parametric dependence on time delay time delay is found to expand the range of possible phase locked patterns and to contribute favorably toward their stability the amplitude death state is studied in the parameter space of time delay and coupling strength it is shown that death island regions can exist for any number of oscillators n in the presence of finite time delay a particularly interesting result is that the size of an island is independent of n when n is even but is a decreasing function of n when n is odd

travelling waves in chains of pulse coupled integrate and fire oscillators with distributed delays abstract we analyse travelling waves in a chain of pulse coupled integrate and fire oscillators with nearest neighbour coupling and delayed interactions this is achieved by approximating the equations for phase locking in terms of a singularly perturbed two point continuum boundary value problem the latter has a solution provided that a self consistent value for the collective frequency of oscillations can be found we investigate how the qualitative behaviour of travelling waves depends on the distribution of natural frequencies across the chain and the form of delayed interactions a linear stability analysis of phase locked solutions is carried out in terms of perturbations of the firing times of the oscillators it is shown how travelling waves destabilize when the detuning between oscillators or the strength of the coupling becomes too large

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

generalized pairwise interchanges and machine scheduling abstract in this paper a generalization of pairwise interchanges is considered and applied to machine scheduling problems it is shown how these swap operators can be used to compute bounds for branch and bound procedures to prove dominance properties and to define a high performance neighborhood for local search methods

antiphase synchronization of phase reduced oscillators using open loop control in this report we present an elegant method to build and maintain an antiphase configuration of two nonlinear oscillators with different natural frequencies and dynamics described by the sinusoidal phase reduced model the antiphase synchronization is achieved using a common input that couples the oscillators and consists of a sequence of square pulses of appropriate amplitude and duration this example provides a proof of principle that open loop control can be used to create desired synchronization patterns for nonlinear oscillators when feedback is expensive or impossible to obtain

the two machine flowshop total completion time problem branch and bound algorithms based on network flow formulation abstract we consider the flowshop problem on two machines with sequence independent setup times to minimize total completion time large scale network flow formulations of the problem are suggested together with strong lagrangian bounds based on these formulations to cope with their size filtering procedures are developed to solve the problem to optimality we embed the lagrangian bounds into two branch and bound algorithms the best algorithm is able to solve all 100 job instances of our testbed with setup times and all 140 job instances without setup times thus significantly outperforming the best algorithms in the literature

phase transition to frequency entrainment in a long chain of pulse coupled oscillators a long chain of pulse coupled oscillators was studied the oscillators interacted via a phase response curve similar to those obtained from pacemaker cells in the heart the natural frequencies were random numbers from a distribution with finite bandwidth stable frequency entrained states were shown always to exist above a critical coupling strength below the critical coupling the probability to have such states was shown to be zero if the number of oscillators is infinite this discontinuity establishes the existence of a phase transition in the thermodynamic limit for weak coupling clusters of frequency entrained oscillators emerged the cluster sizes were exponentially distributed even when the critical coupling was approached at this coupling the mean cluster size diverged to infinity according to a power law the standard deviation of the distribution of mean frequencies in the chain converged to zero also according to a power law

further results on generalized and hypergeneralized projectors abstract the notions of generalized and hypergeneralized projectors introduced by gros and trenkler j gro s j trenkler generalized and hypergeneralized projectors linear algebra appl 264 1997 463 474 are revisited on the one hand the present paper provides several new characterizations of these sets and on the other the properties of generalized and hypergeneralized projectors related to various matrix partial orderings are considered moreover the paper demonstrates the usefulness in studying the properties of generalized and hypergeneralized projectors of the representation of complex matrices given in corollary 6 by hartwig and spindelbock r e hartwig k spindelbock matrices for which a and a commute linear and multilinear algebra 14 1984 241 256

phase locking in chains of multiple coupled oscillators phase locking in chains of weakly coupled oscillators with coupling beyond nearest neighbors is studied starting with a piecewise linear coupling function a homotopy method is applied to prove the existence of phase locked solutions numerical examples are provided to illustrate the existence and the properties of the solutions differences between multiple coupling and nearest neighbor coupling are also discussed 2000 elsevier science b v all rights reserved

stable rotating waves in two dimensional discrete active media the existence and stability of stable rotating solutions spiral waves in a discrete system of coupled phase models is proven monotone methods are used to obtain existence and qualitative features of the solutions an application of fenichel s results for singular perturbation implies the existence for a one variable model for excitability numerical comparisons with the phase model and a realistic membrane model are made a numerically computed hopf bifurcation shows the existence of the wobbling core observed in spatially continuous models

on a matrix decomposition of hartwig and spindelbock abstract the main task of the paper is to demonstrate that corollary 6 in r e hartwig k spindelbock matrices for which a and a commute linear and multilinear algebra 14 1984 241 256 provides a powerful tool to investigate square matrices with complex entries this aim is achieved on the one hand by obtaining several original results involving square matrices and on the other hand by reestablishing some of the facts already known in the literature often in extended and or generalized forms the particular attention is paid to the usefulness of the aforementioned corollary to characterize various classes of matrices and to explore matrix partial orderings

the two machine total completion time flow shop problem in this paper we study the np hard scheduling problem of minimizing total completion time in a two machine flow shop five known lower bounds are discussed and two new ones are presented a new dominance criterion is also proposed several versions of a branch and bound method are derived by applying both individually and combined these lower bounds a heuristic procedure is also presented that uses a constructive o n2 time method which computes a good starting solution together with a neighborhood search based on pairwise interchanges computational results show that the exact method can handle problems of up to 30 jobs in size within a reasonable amount of time and that the heuristic procedure has an average error of less than 0 5 from the optimal value and less than 2 7 from the lower bound

a lagrangean based branch and bound algorithm for single machine sequencing with precedence constraints to minimize total weighted completion time the single machine sequencing problem is considered in which there are precedence constraints on the jobs the objective is to minimize the sum of weighted completion times a lower bound is obtained by successively performing a lagrangean relaxation of appropriate constraints each lagrange multiplier is chosen to provide the maximum increment to the lower bound subject to retaining the nonnegativity of the coefficients of the variables when no further suitable constraints can be introduced into the lagrangean function the variables having zero cost coefficient are used to obtain a feasible sequence which provides an upper bound the gap between the lower and upper bound is reduced by removing some constraints from the lagrangean function and replacing them with others this lower bounding procedure is used in a branch and bound algorithm computational results indicate that the algorithm can satisfactorily solve problems with up to 100 jobs

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

spatial noise stabilizes periodic wave patterns in oscillatory systems on finite domains invasions in oscillatory systems generate in their wake spatiotemporal oscillations consisting of either periodic wavetrains or irregular oscillations that appear to be spatiotemporal chaos we have shown previously that when a finite domain with zero flux boundary conditions has been fully invaded the spatiotemporal oscillations persist in the irregular case but die out in a systematic way for periodic traveling waves in this paper we consider the effect of environmental inhomogeneities on this persistence we use numerical simulations of several predator prey systems to study the effect of random spatial variation of the kinetic parameters on the die out of regular oscillations and the long time persistence of irregular oscillations we find no effect on the latter but remarkably a moderate spatial variation in parameters leads to the persistence of regular oscillations via the formation of target patterns in order to study this target pattern production analytically we turn to systems numerical simulations confirm analagous behavior in this generic oscillatory system we then repeat this numerical study using piecewise linear spatial variation of parameters rather than random variation which also gives formation of target patterns under certain circum stances which we discuss we study this in detail by deriving an analytical approximation to the targets formed when the parameter 0 varies in a simple piecewise linear manner across the do main using perturbation theory we end by discussing the applications of our results in ecology and chemistry

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

design of charge balanced time optimal stimuli for spiking neuron oscillators in this letter we investigate the fundamental limits on how the interspike time of a neuron oscillator can be perturbed by the application of a bounded external control input a current stimulus with zero net electric charge accumulation we use phase models to study the dynamics of neurons and derive charge balanced controls that achieve the minimum and maximum interspike times for a given bound on the control amplitude our derivation is valid for any arbitrary shape of the phase response curve and for any value of the given control amplitude bound in addition we characterize the change in the structures of the charge balanced time optimal controls with the allowable control amplitude we demonstrate the applicability of the derived optimal control laws by applying them to mathematically ideal and experimentally observed neuron phase models including the widely studied hodgkin huxley phase model and by verifying them with the corresponding original full state space models this work addresses a fundamental problem in the field of neural control and provides a theoretical investigation to the optimal control of oscillatory systems

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

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

a branch and bound algorithm for three machine flowshop scheduling problem to minimize total completion time with separate setup times in this paper we address the three machine flowshop scheduling problem setup times are considered separate from processing times and the objective is to minimize total completion time we show that the three site distributed database scheduling problem can be modeled as a three machine flowshop scheduling problem a lower bound is developed and a dominance relation is established moreover an upper bound is developed by using a three phase hybrid heuristic algorithm furthermore a branch and bound algorithm incorporating the developed lower bound dominance relation and the upper bound is presented computational analysis on randomly generated problems is conducted to evaluate the lower and upper bounds the dominance relation and the branch and bound algorithm the analysis shows the efficiency of the upper bound and hence it can be used for larger size problems as a heuristic algorithm

an effective differential evolution algorithm for permutation flow shop scheduling problem the permutation flow shop problem pfssp is an np hard problem of wide engineering and theoretical background in this paper a hybrid differential evolution de called l hde is proposed to solve the flow shop scheduling problem which combines the de with the individual improving scheme iis and greedy based local search first to make de suitable for pfssp a new largest rank rule lrv based on a random key is introduced to convert the continuous position in de to the discrete job permutation so that the de can be used for solving pfssp second the neh heuristic was combined with the random initialization to initialize the population with certain quality and diversity third the iis based local search is used for improving the diversity of population and enhancing the quality of the solution with a certain probability fourth the greedy based local search is designed to help the algorithm to escape from local minimum additionally simulations and comparisons based on pfssp benchmarks are carried out which show that our algorithm is both effective and efficient

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

multifrequency synthesis using two coupled nonlinear oscillator arrays we illustrate a scheme that exploits the theory of symmetry breaking bifurcations for generating a spatio temporal pattern in which one of two interconnected arrays each with n van der pol oscillators oscillates at n times the frequency of the other a bifurcation analysis demonstrates that this type of frequency generation cannot be realized without the mutual interaction between the two arrays it is also demonstrated that the mechanism for generating these frequencies between the two arrays is different from that of a master slave interaction a synchronization effect or that of subharmonic and ultraharmonic solutions generated by forced systems this kind of frequency generation scheme can find applications in the developed field of nonlinear antenna and radar systems

further properties of generalized and hypergeneralized projectors generalized and hypergeneralized projectors introduced by gros and trenkler linear algebra appl 264 1997 463 are revisited several properties of such matrices are established some of the results obtained extend and or generalize those given in the reference above and some others are solutions to new problems

improved lower bounds for minimizing the sum of completion times of n jobs over m machines in a flow shop abstract the paper considers the classic n job m machine scheduling problem where the objective is to minimize the sum of completion times a procedure is presented for obtaining m 1 new machine based lower bounds the result is an improved overall lower bound

an improved branch and bound algorithm for the two machine total completion time flow shop problem we consider the two machine total completion time flow shop scheduling problem this problem is known to be np hard in the strong sense an improved lagrangean relaxation approach is proposed two new dominance criteria are introduced to curtail the enumeration tree a branch and bound algorithm capable of solving to optimality medium size problem instances is presented

the two and m machine flowshop scheduling problems with bicriteria of makespan and mean flowtime abstract this paper considers the flowshop scheduling problem with the objective of minimizing the weighted sum of makespan and mean flowtime even though the two machine problem has been addressed and several heuristics have been established in the literature these heuristics have not been compared in this paper a comparison of these available heuristics in the literature is conducted moreover three new heuristic algorithms are proposed which can be utilized for both the two machine and m machine problems computational experiments indicate that the proposed heuristics are superior to all the existing heuristics in the literature including a genetic algorithm two dominance relations are also developed one for the two machine and the other for the three machine problem experimental results show that both relations are efficient

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

phase transition and other phenomena in chains of coupled oscilators a very broad framework is given for the investigation of long chains of n weakly coupled oscillators the framework allows nonmonotonic changes of natural frequency along the chain differences in coupling strengths anisotropy in the two directions of coupling and very general local coupling functions it is shown that the phase locked solutions of all the systems of oscillators within this framework converge for large n to solutions of a class of nonlinear singularly perturbed two point boundary value problems using the latter continuum equations it is also shown that there are parameter regimes in which the solutions have qualitatively different behavior with a phase transition like change in behavior across the boundary between parameter regimes in the limit n to infty special important cases are discussed including the effects of local changes in frequencies local changes in coupling strengths and different kinds of anisotropy

heteroclinic cycles in rings of coupled cells abstract symmetry is used to investigate the existence and stability of heteroclinic cycles involving steady state and periodic solutions in coupled cell systems with d n symmetry using the lattice of isotropy subgroups we study the normal form equations restricted to invariant fixed point subspaces and prove that it is possible for the normal form equations to have robust asymptotically stable heteroclinic cycles connecting periodic solutions with steady states and periodic solutions with periodic solutions a center manifold reduction from the ring of cells to the normal form equations is then performed using this reduction we find parameter values of the cell system where asymptotically stable cycles exist simulations of the cycles show trajectories visiting steady states and periodic solutions and reveal interesting spatio temporal patterns in the dynamics of individual cells we discuss how these patterns are forced by normal form symmetries

interaction of chaotic rotating waves in coupled rings of chaotic cells abstract the interaction of two chaotic rotating waves of the type recently reported by matias et al europhys lett 37 1997 379 is studied experimentally with arrays of non linear electronic circuits arranged in ring geometries unidirectional coupling is assumed for the cell to cell coupling within the same ring but between rings cells are coupled diffusively depending on the relative sense of driving competition between a rotating chaotic wave and a global synchronized state has been observed the results are rationalized by means of a linear stability analysis around the uniform synchronized behavior where the circulant symmetry of the system allows to express the problem as a superposition of a series of fourier modes

minimizing total completion time in a two machine flow shop with deteriorating jobs this paper considers a two machine flow shop scheduling problem with deteriorating jobs by a deteriorating job we mean that the processing time of a job is an increasing function of its execution start time a simple linear deterioration function is assumed the objective is to find a sequence that minimizes total completion time optimal solutions are obtained for some special cases for the general case several dominance properties and two lower bounds are derived to speed up the elimination process of a branch and bound algorithm a heuristic algorithm is also proposed to overcome the inefficiency of the branch and bound algorithm computational results show that the proposed heuristic algorithm performs effectively and efficiently

an alternative characterization of generalized projectors abstract one of the results of gros and trenkler linear algebra appl 264 1997 463 asserts that a square complex matrix k is a generalized projector if and only if it is i quadripotent ii normal and iii partial isometry the authors supplemented this statement by proving that condition iii in the above characterization can actually be deleted the purpose of the present note is to show that also an alternative reduction of the set of conditions i iii is possible as a consequence of establishing the redundancy of ii under the presence of i and iii