improvement and comparison of heuristics for solving the uncapacitated multisource weber problem the multisource weber problem is to locate simultaneouslym facilities in the euclidean plane to minimize the total transportation cost for satisfying the demand ofn fixed users each supplied from its closest facility many heuristics have been proposed for this problem as well as a few exact algorithms heuristics are needed to solve quickly large problems and to provide good initial solutions for exact algorithms we compare various heuristics i e alternative location allocation cooper 1964 projection bongartz et al 1994 tabu search brimberg and mladenovic 1996a p median plus weber hansen et al 1996 genetic search and several versions of variable neighbourhood search based on empirical tests that are reported it is found that most traditional and some recent heuristics give poor results when the number of facilities to locate is large and that variable neighbourhood search gives consistently best results on average in moderate computing time

ergodicity of the 2d navier stokes equations with degenerate stochastic forcing the stochastic 2d navier stokes equations on the torus driven by degenerate noise are studied we characterize the smallest closed invariant subspace for this model and show that the dynamics restricted to that subspace is ergodic in particular our results yield a purely geometric characterization of a class of noises for which the equation is ergodic in l 2 0 t 2 unlike previous works this class is independent of the viscosity and the strength of the noise the two main tools of our analysis are the asymptotic strong feller property introduced in this work and an approximate integration by parts formula the first when combined with a weak type of irreducibility is shown to ensure that the dynamics is ergodic the second is used to show that the first holds un

a clustering technique for the identification of piecewise affine systems we propose a new technique for the identification of discrete time hybrid systems in the piecewise affine pwa form this problem can be formulated as the reconstruction of a possibly discontinuous pwa map with a multi dimensional domain in order to achieve our goal we provide an algorithm that exploits the combined use of clustering linear identification and pattern recognition techniques this allows to identify both the affine submodels and the polyhedral partition of the domain on which each submodel is valid avoiding gridding procedures moreover the clustering step used for classifying the datapoints is performed in a suitably defined feature space which allows also to reconstruct different submodels that share the same coefficients but are defined on different regions measures of confidence on the samples are introduced and exploited in order to improve the performance of both the clustering and the final linear regression procedure

entropy formula for random transformations we exhibit random strange attractors with random sinai bowen ruelle measures for the composition of independent random diffeomorphisms

srb measures for a class of partially hyperbolic attractors in hilbert spaces abstract in this paper we study the existence of srb measures and their properties for infinite dimensional dynamical systems in a hilbert space we show several results including i if the system has a partially hyperbolic attractor with nontrivial finite dimensional unstable directions then it has at least one srb measure ii if the attractor is uniformly hyperbolic and the system is topological mixing and the splitting is holder continuous then there exists a unique srb measure which is mixing iii if the attractor is uniformly hyperbolic and the system is non wondering and the splitting is holder continuous then there exist at most finitely many srb measures iv for a given hyperbolic measure there exist at most countably many ergodic components whose basin contains an observable set

tight error bounds for space time orthogonal block codes under slow rayleigh flat fading the performance of space time orthogonal block stob codes over slow rayleigh fading channels and maximum likelihood ml decoding is investigated two bonferroni type bounds one upper bound and one lower bound for the symbol error rate ser and bit error rate ber of the system are obtained the bounds are expressed in terms of the pairwise error probabilities peps and the two dimensional pairwise error probabilities 2 d peps of the transmitted symbols furthermore the bounds can be efficiently evaluated and they hold for arbitrary nonstandard signaling schemes and mappings numerical results demonstrate that the bounds are very accurate in estimating the performance of stob codes in particular the upper and lower bounds often coincide even at low channel signal to noise ratios large constellation sizes and large diversity orders

k means type algorithms a generalized convergence theorem and characterization of local optimality the k means algorithm is a commonly used technique in cluster analysis in this paper several questions about the algorithm are addressed the clustering problem is first cast as a nonconvex mathematical program then a rigorous proof of the finite convergence of the k means type algorithm is given for any metric it is shown that under certain conditions the algorithm may fail to converge to a local minimum and that it converges under differentiability conditions to a kuhn tucker point finally a method for obtaining a local minimum solution is given

existence of periodic orbits and horseshoes for mappings in a separable banach space abstract for a smooth map in a separable banach space with a hyperbolic invariant measure we mainly prove that positivity of the measure theoretic entropy of the hyperbolic measure implies the existence of periodic orbits and horseshoes this is an extension of lian and young s work on maps in a hilbert space to the case of systems on a banach space

dimension formula for random transformations we consider compositions of random diffeomorphisms and show that the dimension of sample measures equals lyapunov dimension as conjectured in the nonrandom case by yorke et al

moving horizon estimation for hybrid systems we propose a state smoothing algorithm for hybrid systems based on moving horizon estimation mhe by exploiting the equivalence between hybrid systems modeled in the mixed logic dynamical form and piecewise affine systems we provide sufficient conditions on the time horizon and the penalties on the state at the beginning of the estimation horizon to guarantee asymptotic convergence of the mhe scheme moreover we propose two practical algorithms for the computation of penalties that allow us to implement mhe by solving a mixed integer quadratic program

toward a theory of rank one attractors introduction 1 statement of results part i preparation 2 relevant results from one dimension 3 tools for analyzing rank one maps part ii phase space dynamics 4 critical structure and orbits 5 properties of orbits controlled by critical set 6 identification of hyperbolic behavior formal inductive procedure 7 global geometry via monotone branches 8 completion of induction 9 construction of srb measures part iii parameter issues 10 dependence of dynamical structures on parameter 11 dynamics of curves of critical points 12 derivative growth via statistics 13 positive measure sets of good parameters appendices

spectral bayesian estimation for general stochastic hybrid systems abstract general stochastic hybrid systems gshs have been formulated to represent various types of uncertainties in hybrid dynamical systems in this paper we propose computational techniques for bayesian estimation of gshs in particular the fokker planck equation that describes the evolution of uncertainty distributions along gshs is solved by spectral techniques where an arbitrary form of probability density of the hybrid state is represented by a mixture of fourier series the method is based on splitting the fokker planck equation represented by an integro partial differential equation into the partial differentiation part for continuous diffusion and the integral part for discrete transition and integrating the solution of each part the propagated density function is used with a likelihood function in the bayes formula to estimate the hybrid state for given sensor measurements the unique feature of the proposed technique is that the probability density describing complete stochastic properties of the hybrid state is constructed without relying on the common gaussian assumption in contrast to other methods that compute certain expected values such as mean or variance we apply the proposed method to the estimation of two examples the bouncing ball model and the dubins vehicle model we show that the proposed technique yields propagated densities consistent with monte carlo simulations more accurate estimates over the gaussian based approach and some computational benefits over a particle filter

observability and controllability of piecewise affine and hybrid systems we prove in a constructive way the equivalence between piecewise affine systems and a broad class of hybrid systems described by interacting linear dynamics automata and propositional logic by focusing our investigation on the former class we show through counterexamples that observability and controllability properties cannot be easily deduced from those of the component linear subsystems instead we propose practical numerical tests based on mixed integer linear programming

a tree structured piecewise linear adaptive filter the authors propose and analyze a novel architecture for nonlinear adaptive filters these nonlinear filters are piecewise linear filters obtained by arranging linear filters and thresholds in a tree structure a training algorithm is used to adaptively update the filter coefficients and thresholds at the nodes of the tree and to prune the tree the resulting tree structured piecewise linear adaptive filter inherits the robust estimation and fast adaptation of linear adaptive filters along with the approximation and model fitting properties of tree structured regression models a rigorous analysis of the training algorithm for the tree structured filter is performed some techniques are developed for analyzing hierarchically organized stochastic gradient algorithms with fixed gains and nonstationary dependent data simulation results show the significant advantages of the tree structured piecewise linear filter over linear and polynomial filters for adaptive echo cancellation

attractors for random dynamical systems a criterion for existence of global random attractors for rds is established existence of invariant markov measures supported by the random attractor is proved for spde this yields invariant measures for the associated markov semigroup the results are applied to reation diffusion equations with additive white noise and to navier stokes equations with multiplicative and with additive white noise

independence in topological and c dynamics we develop a systematic approach to the study of independence in topological dynamics with an emphasis on combinatorial methods one of our principal aims is to combinatorialize the local analysis of topological entropy and related mixing properties we also reframe our theory of dynamical independence in terms of tensor products and thereby expand its scope to c dynamics

entropy chaos and weak horseshoe for infinite dimensional random dynamical systems in this paper we study the complicated dynamics of infinite dimensional random dynamical systems that include deterministic dynamical systems as their special cases in a polish space without assuming any hyperbolicity we prove if a continuous random map has a positive topological entropy then it contains a topological horseshoe we also show that the positive topological entropy implies the chaos in the sense of li yorke the complicated behavior exhibited here is induced by the positive entropy but not the randomness of the system 2017 wiley periodicals inc

identification of non linear system structure and parameters using regime decomposition abstract an off line algorithm for empirical modeling and identification of non linear dynamic systems is presented the minimal input to the algorithm is a sequence of empirical data and the model order using this information the algorithm searches for an optimal model structure and parameters within a rich non linear model set the model representation is based on the interpolation of a number of simple local models where each local model has a limited range of validity but the local models yield a complete global model when interpolated the method is illustrated using simulated data

constructive neural networks with piecewise interpolation capabilities for function approximations this paper proposes a constructive neural network with a piecewise linear or nonlinear local interpolation capability to approximate arbitrary continuous functions this neural network is devised by introducing a space tessellation which is a covering of the euclidean space by nonoverlapping hyperpolyhedral convex cells in the proposed neural network a number of neural network granules nng s are processed in parallel and repeated regularly with the same structures each nng does a local mapping with an interpolation capability for a corresponding hyperpolyhedral convex cell in a tessellation the plastic weights of the nng can be calculated to implement the mapping for training data consequently this reduces training time and alleviates the difficulties of local minima in training in addition the interpolation capability of the nng improves the generalization for the new data within the convex cell the proposed network requires additional neurons for tessellation over the standard multilayer neural networks this increases the network size but does not slow the retrieval response when implemented by parallel architecture

the metric entropy of diffeomorphisms part i characterization of measures satisfying pesin s entropy formula soit m une variete de riemann compacte soit f m m un diffeomorphisme et soit m une mesure de probabilite de borel f invariante sur m on identifie les mesures pour lesquelles l inegalite de margulis et ruelle qui relie l entropie aux exposants de lyapunov atteint l egalite on demontre une formule valable pour toutes les mesures invariantes

on li yorke pairs the li yorke definition of chaos proved its value for interval maps in this paper it is considered in the setting of general topological dynamics we adopt two opposite points of view on the one hand sufficient conditions for li yorke chaos in a topological dynamical system are given we solve a long standing open question by proving that positive entropy implies li yorke chaos on the other hand properties of dynamical systems without li yorke pairs are investigated in addition to having entropy 0 they are minimal when transitive and the property is stable under factor maps arbitrary products and inverse limits finally it is proved that minimal systems without li yorke pairs are disjoint from scattering systems

j means a new local search heuristic for minimum sum of squares clustering abstract a new local search heuristic called j m eans is proposed for solving the minimum sum of squares clustering problem the neighborhood of the current solution is defined by all possible centroid to entity relocations followed by corresponding changes of assignments moves are made in such neighborhoods until a local optimum is reached the new heuristic is compared with two other well known local search heuristics k and h m eans as well as with h m eans an improved version of the latter in which degeneracy is removed moreover another heuristic which fits into the variable neighborhood search metaheuristic framework and uses j m eans in its local search step is proposed too results on standard test problems from the literature are reported it appears that j m eans outperforms the other local search methods quite substantially when many entities and clusters are considered

absolutely continuous invariant measures for one parameter families of one dimensional maps given a one parameter familyf x of maps of the interval 0 1 we consider the set of parameter values for whichf has an invariant measure absolutely continuous with respect to lebesgue measure we show that this set has positive measure for two classes of maps i f x f x where 0 4 andf x is a functionc3 near the quadratic mapx 1 x and ii f x f x mod 1 wheref isc3 f 0 f 1 0 andf has a unique nondegenerate critical point in 0 1

characteristic exponents and invariant manifolds in hilbert space the multiplicative ergodic theorem and the construction almost everywhere of stable and unstable manifolds pesin theory are extended to differentiable dynamical systems on hilbert manifolds under some compactness assumptions the results apply to partial differential equations of evolution and also to non invertible maps of compact manifolds

the stable manifold theorem for stochastic differential equations type equations are treated starting with the existence of a stochastic flow for a sde we introduce the notion of a hyperbolic stationary trajectory we prove the existence of invariant random stable and unstable manifolds in the neighborhood of the hyperbolic stationary solution for stratonovich sdes the stable and unstable manifolds are dynamically characterized using forward and backward solutions of the anticipating sde the proof of the stable manifold theorem is based on ruelle oseledec multiplicative ergodic theory

invariant manifolds for stochastic partial differential equations invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems the theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems and for stochastic ordinary differential equations is relatively mature in this paper we present a unified theory of invariant manifolds for infinite dimensional random dynamical systems generated by stochastic partial differential equations we first introduce a random graph transform and a fixed point theorem for nonautonomous systems then we show the existence of generalized fixed points which give the desired invariant manifolds

the p median problem a survey of metaheuristic approaches the p median problem is one of the basic models in discrete location theory as with most location problems it is classified as np hard and so heuristic methods are usually used to solve it metaheuristics are frameworks for building heuristics in this survey we examine the p median with the aim of providing an overview on advances in solving it using recent procedures based on metaheuristic rules

packing and partitioning orbitopes we introduce orbitopes as the convex hulls of 0 1 matrices that are lexicographically maximal subject to a group acting on the columns special cases are packing and partitioning orbitopes which arise from restrictions to matrices with at most or exactly one 1 entry in each row respectively the goal of investigating these polytopes is to gain insight into ways of breaking certain symmetries in integer programs by adding constraints e g for a well known formulation of the graph coloring problem we provide a thorough polyhedral investigation of packing and partitioning orbitopes for the cases in which the group acting on the columns is the cyclic group or the symmetric group our main results are complete linear inequality descriptions of these polytopes by facet defining inequalities for the cyclic group case the descriptions turn out to be totally unimodular while for the symmetric group case both the description and the proof are more involved the associated separation problems can be solved in linear time

control of systems integrating logic dynamics and constraints this paper proposes a framework for modeling and controlling systems described by interdependent physical laws logic rules and operating constraints denoted as mixed logical dynamical mld systems these are described by linear dynamic equations subject to linear inequalities involving real and integer variables mld systems include linear hybrid systems finite state machines some classes of discrete event systems constrained linear systems and nonlinear systems which can be approximated by piecewise linear functions a predictive control scheme is proposed which is able to stabilize mld systems on desired reference trajectories while fulfilling operating constraints and possibly take into account previous qualitative knowledge in the form of heuristic rules due to the presence of integer variables the resulting on line optimization procedures are solved through mixed integer quadratic programming miqp for which efficient solvers have been recently developed some examples and a simulation case study on a complex gas supply system are reported

lyapunov exponents periodic orbits and horseshoes for semiflows on hilbert spaces two settings are considered flows on finite dimensional riemann ian manifolds and semiflows on hilbert spaces with conditions consistent with those in systems defined by dissipative parabolic pdes under certain assump tions on lyapunov exponents and entropy we prove the existence of geometric structures called horseshoes this implies in particular the presence of infinitely many periodic solutions for diffeomorphisms of compact manifolds analogous results are due to a katok here we extend katok s results to i continuous time and ii infinite dimensions courant institute of mathematical sciences new york university 251 mercer street new york new york 10012 e mail address lian cims nyu edu courant institute of mathematical sciences new york university 251 mercer street new york new york 10012 e mail address lsy cims nyu edu

lower bounds on the error probability of block codes based on improvements on de caen s inequality new lower bounds on the error probability of block codes with maximum likelihood decoding are proposed the bounds are obtained by applying a new lower bound on the probability of a union of events derived by improving on de caen s lower bound the new bound includes an arbitrary function to be optimized in order to achieve the tightest results since the optimal choice of this function is known but leads to a trivial and useless identity we find several useful approximations for it each resulting in a new lower bound for the additive white gaussian noise awgn channel and the binary symmetric channel bsc the optimal choice of the optimization function is stated and several approximations are proposed when the bounds are further specialized to linear codes the only knowledge on the code used is its weight enumeration the results are shown to be tighter than the latest bounds in the current literature such as those by seguin 1998 and by keren and litsyn 2001 moreover for the bsc the new bounds widen the range of rates for which the union bound analysis applies thus improving on the bound to the error exponent compared with the de caen based bounds

dissipative homoclinic loops of two dimensional maps and strange attractors with one direction of instability we prove that when subjected to periodic forcing of the form p t d h x y c sin t certain two dimensional vector fields with dissipative homoclinic loops generate strange attractors with sinai ruelle bowen measures for a set of forcing parameters of positive lebesgue measure the proof extends ideas of afraimovich and shilnikov and applies the recent theory of rank 1 maps developed by wang and young we prove a general theorem and then apply this theorem to an explicit model a forced duffing equation of the form d 2 q

invariant manifolds for stochastic wave equations abstract in this paper we consider a class of stochastic wave equations with nonlinear multiplicative noise we first show that these stochastic wave equations generate random dynamical systems or stochastic flows by transforming the stochastic wave equations to random wave equations through a stationary random homeomorphism then we establish the existence of random invariant manifolds for the random wave equations due to the temperedness of the nonlinearity we obtain only local invariant manifolds no matter how large the spectral gap is unlike the deterministic cases based on these random dynamical systems we prove the existence of random invariant manifolds in a tempered neighborhood of an equilibrium finally we show that the images of these invariant manifolds under the inverse stationary transformation give invariant manifolds for the stochastic wave equations

tight error bounds for nonuniform signaling over awgn channels we consider a bonferroni type lower bound due to kounias 1968 on the probability of a finite union the bound is expressed in terms of only the individual and pairwise event probabilities however it suffers from requiring an exponentially complex search for its direct implementation we address this problem by presenting a practical algorithm for its evaluation this bound is applied together with two other bounds a recent lower bound the kat bound and a greedy algorithm implementation of an upper bound due to hunter 1976 to examine the symbol error p sub a and bit error p sub b probabilities of an uncoded communication system used in conjunction with m ary phase shift keying psk quadrature amplitude qam psk qam modulations and maximum a posteriori map decoding over additive white gaussian noise awgn channels it is shown that the bounds which can be efficiently computed provide an excellent estimate of the error probabilities over the entire range of the signal to noise ratio snr e sub b n sub 0 the new algorithmic bound and the greedy bound are particularly impressive as they agree with the simulation results even during very severe channel conditions

a distance based point reassignment heuristic for the k hyperplane clustering problem abstract we consider the k hyperplane clustering problem where given a set of m points in r n we have to partition the set into k subsets clusters and determine a hyperplane for each of them so as to minimize the sum of the squares of the euclidean distances between the points and the hyperplane of the corresponding clusters we give a nonconvex mixed integer quadratically constrained quadratic programming formulation for the problem since even very small size instances are challenging for state of the art spatial branch and bound solvers like couenne we propose a heuristic in which many critical points are reassigned at each iteration such points which are likely to be ill assigned in the current solution are identified using a distance based criterion and their number is progressively decreased to zero our algorithm outperforms the best available one proposed by bradley and mangasarian on a set of real world and structured randomly generated instances for the largest instances we obtain an average improvement in the solution quality of 54

hinging hyperplanes for regression classification and function approximation a hinge function y h x consists of two hyperplanes continuously joined together at a hinge in regression prediction classification pattern recognition and noiseless function approximation use of sums of hinge functions gives a powerful and efficient alternative to neural networks with computation times several orders of magnitude less than is obtained by fitting neural networks with a comparable number of parameters a simple and effective method for finding good hinges is presented

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

random perturbations of axiom a basic sets in this paper we study small random diffeomorphism type perturbations of an axiom a basic set by means of the structural stability of such a basic set with respect to time dependent perturbations and by means of the markov partition of the basic set we apply the thermodynamic formalism of random subshifts of finite type to this situation obtaining some ergodic theoretic results concerning equilibrium states

an efficient algorithmic lower bound for the error rate of linear block codes we present an efficient algorithmic lower bound for the block error rate of linear binary block codes under soft maximum likelihood decoding over binary phase shift keying modulated additive white gaussian noise channels we cast the problem of finding a lower bound on the probability of a union as an optimization problem that seeks to find the subset that maximizes a recent lower bound due to kuai alajaji and takahara that we will refer to as the kat bound the improved bound which is denoted by lb s is asymptotically tight as the signal to noise ratio snr grows to infinity and depends only on the code s weight enumeration function for its calculation the use of a subset of the codebook to evaluate the lb s lower bound not only significantly reduces computational complexity but also tightens the bound specially at low snrs numerical results for binary block codes indicate that at high snrs the lb s bound is tighter than other recent lower bounds in the literature which comprise the lower bound due to seguin the kat bound evaluated on the entire codebook and the dot product and norm bounds due to cohen and merhav

nonlinear filters based on combinations of piecewise polynomials with compact support when nonlinear filters are designed based on input output observations the descriptive nonlinear transformation between the input and the output signals is often unknown filters with generalized models are therefore required for a good characterization of these cases in this paper we introduce a class of filters obtained from the additive combination of multiple kernels each kernel constitutes a localized model for the desired nonlinear mapping and is defined as a multivariate continuous piecewise polynomial cpp function with compact support by bringing together the efficiency of piecewise polynomial approximations and the flexibility of kernel combinations we end up with models able to represent effectively a broad variety of nonlinearities a localized threshold decomposition operator ltd is introduced to provide closed form expressions for continuous nonsmooth kernels whereas the method of splines is used to derive smooth functionals simple equalization problems involving nonlinear nonminimum phase and non gaussian channels are used to examine the advantages of the proposed methods and compare them with other conventional alternatives

data based identification and control of nonlinear systems via piecewise affine approximation the piecewise affine pwa model represents an attractive model structure for approximating nonlinear systems in this paper a procedure for obtaining the pwa autoregressive exogenous arx autoregressive systems with exogenous inputs models of nonlinear systems is proposed two key parameters defining a pwarx model namely the parameters of locally affine subsystems and the partition of the regressor space are estimated the former through a least squares based identification method using multiple models and the latter using standard procedures such as neural network classifier or support vector machine classifier having obtained the pwarx model of the nonlinear system a controller is then derived to control the system for reference tracking both simulation and experimental studies show that the proposed algorithm can indeed provide accurate pwa approximation of nonlinear systems and the designed controller provides good tracking performance

random attractors for stochastic reaction diffusion equations on unbounded domains the existence of a pullback attractor is established for a stochastic reaction diffusion equation on all n dimensional space the nonlinearity is dissipative for large values of the state and the stochastic nature of the equation appears as spatially distributed temporal white noise the reaction diffusion equation is recast as a random dynamical system and asymptotic compactness for this is demonstrated by using uniform a priori estimates for far field values of solutions

mean li yorke chaos for random dynamical systems abstract in this paper we studied the complexity of some random dynamical systems with positive topological entropy the random dynamical systems are usually generated by stochastic partial differential equations spdes and contain randomness in many ways we proved that there exists mean li yorke chaotic phenomenon in some random dynamical systems with positive entropy

a lower bound on the error probability for signals in white gaussian noise in this correspondence we apply a recent inequality by de caen 1997 to derive a lower bound on the probability of error for m ary signals derived from a binary linear code and used on the additive white gaussian noise channel with a maximum likelihood decoder this bound depends only on the weight enumerator of the code and the signal to noise ratio e sub b n sub 0 we show that this bound converges to the union upper bound as e sub b n sub 0 goes to infinity finally by means of examples we compare our lower bound with those of shannon and swaszek and with poltyrev s upper bound

a comparison of heuristic procedures for minimum within cluster sums of squares partitioning perhaps the most common criterion for partitioning a data set is the minimization of the within cluster sums of squared deviation from cluster centroids although optimal solution procedures for within cluster sums of squares wcss partitioning are computationally feasible for small data sets heuristic procedures are required for most practical applications in the behavioral sciences we compared the performances of nine prominent heuristic procedures for wcss partitioning across 324 simulated data sets representative of a broad spectrum of test conditions performance comparisons focused on both percentage deviation from the best found wcss values as well as recovery of true cluster structure a real coded genetic algorithm and variable neighborhood search heuristic were the most effective methods however a straightforward two stage heuristic algorithm hk means also yielded exceptional performance a follow up experiment using 13 empirical data sets from the clustering literature generally supported the results of the experiment using simulated data our findings have important implications for behavioral science researchers whose theoretical conclusions could be adversely affected by poor algorithmic performances

a tabu search approach for the minimum sum of squares clustering problem in this paper a tabu search based clustering approach called ts clustering is proposed to deal with the minimum sum of squares clustering problem in the ts clustering algorithm five improvement operations and three neighborhood modes are given the improvement operation is used to enhance the clustering solution obtained in the process of iterations and the neighborhood mode is used to create the neighborhood of tabu search the superiority of the proposed method over some known clustering techniques is demonstrated for artificial and real life data sets

characteristic exponents for a viscous fluid subjected to time dependent forces we consider a viscous incompressible fluid enclosed in a bounded region of 2 or 3 and subjected to time dependent forces using bound state estimates for the schrodinger operator we obtain rigorous bounds for the characteristic exponents entropy kolmogorov sinai invariant and hausdorff dimension of attracting sets our methods are of potential use for more general time evolutions described by nonlinear partial differential equations

brief analysis of discrete time piecewise affine and hybrid systems in this paper we present various algorithms both for stability and performance analysis of discrete time piece wise affine pwa systems for stability different classes of lyapunov functions are considered and it is shown how to compute them through linear matrix inequalities that take into account the switching structure of the systems we also show that the continuity of the lyapunov function is not required in discrete time moreover the tradeoff between the degree of conservativeness and computational requirements is discussed finally by using arguments from the dissipativity theory for nonlinear systems we generalize our approach to analyze the l 2 gain of pwa systems

nonlinear adaptive control using networks of piecewise linear approximators presents a stable nonparametric adaptive control approach using a piecewise local linear approximator the continuous piecewise linear approximator is developed and its universal approximation capability is proved the controller architecture is based on adaptive feedback linearization plus sliding mode control a time varying activation region is introduced for efficient self organization of the approximator during operation we modify the adaptive control approach for piecewise linear approximation and self organizing structures in addition we provide analyses of asymptotic stability of the tracking error and parameter convergence for the proposed adaptive control scheme with the online self organizing structure the method with a deadzone is also discussed to prevent a high frequency input which might excite the unmodeled dynamics in practical applications the application of the piecewise linear adaptive control method is demonstrated by a computational simulation