nonlinear dynamics in coupled fuzzy control systems i coherence and chaos frustration in triangle configuration abstract nonlinear dynamics and chaos are studied in a system for which a complete set of equations of motion such as equations of newton navier stokes and van der pol is not available as a very general system as such we consider coupled classical spins pendulums each of which is under control by a fuzzy system that is designed to align the spin to an unstable fixed point the fuzzy system provides a deterministic procedure to control an object without use of a differential equation the positions and velocities of the spins are monitored periodically and each fuzzy control gives a momentum to its associated spin in the reverse directions if the monitoring is made with an interval short enough the spin spin interactions are overwhelmed by the fuzzy control and the system converges to a state as designed however a long interval monitoring induces dynamics of too late response and thereby results in chaos a great variety of dynamics are generated under very delicate balance between the fuzzy control and the spin spin interaction in which two independent mechanisms of creating negative and positive liapunov exponents interact with each other

locally nilpotent derivations over a ufd and an application to rank two locally nilpotent derivations ofk x1 xn abstract given a ufd r containing the rational numbers we study locally nilpotent r derivations of the polynomial ring r x y in particular we give a generalization of rentschler s theorem and a criterion for the existence of a slice these results are then applied to describe rank two locally nilpotent derivations of k x 1 x n where k is a field of characteristic zero we also give an example of a nontriangulable locally nilpotent derivation of k x y z whose set of fixed points is a line

simple examples of affine manifolds with infinitely many exotic models we give a simple general method of constructing affine varieties with infinitely many exotic models in particular we show that for every d 1 there exists a stein manifold of dimension d which has uncountably many different structures of affine variety

coexistence of exponentially many chaotic spin glass attractors a chaotic network of size n with delayed interactions which resembles a pseudoinverse associative memory neural network is investigated for a load p n 1 where p stands for the number of stored patterns the chaotic network functions as an associative memory of 2p attractors with macroscopic basin of attractions which decrease with at finite a chaotic spin glass phase exists where the number of distinct chaotic attractors scales exponentially with n each attractor is characterized by a coexistence of chaotic behavior and freezing of each one of the n chaotic units or freezing with respect to the p patterns results are supported by large scale simulations of networks composed of bernoulli map units and mackey glass time delay differential equations

cluster splitting bifurcation in a system of coupled maps abstract we consider cluster splitting bifurcations in a system of globally coupled maps as coupling parameter decreases at these transitions the number of clusters i e groups of elements with identical dynamics increases we demonstrate that different cascades of cluster splitting can occur depending on statistics of redistribution of the oscillators between new born clusters

spatio temporal intermittency in coupled map lattices abstract the transition to turbulence in a one dimensional array of maps coupled by diffusion is shown to display critical properties resembling those of directed percolation the analogy is supported by the reconstruction of a probabilistic cellular automation with closely similar statistical properties numerical results suggest however that spatio temporal intermittency does not belong to the same universality class as directed percolation

random coupling of chaotic maps leads to spatiotemporal synchronization we investigate the spatiotemporal dynamics of a network of coupled chaotic maps with varying degrees of randomness in coupling connections while strictly nearest neighbor coupling never allows spatiotemporal synchronization in our system randomly rewiring some of those connections stabilizes entire networks at x where x is the strongly unstable fixed point solution of the local chaotic map in fact the smallest degree of randomness in spatial connections opens up a window of stability for the synchronized fixed point in coupling parameter space further the coupling b i f r at which the onset of spatiotemporal synchronization occurs scales with the fraction of rewired sites p as a power law for 0 1 p 1 is we also show that the regularizing effect of random connections can be understood from stability analysis of the probabilistic evolution equation for the system and approximate analytical expressions for the range and b i f r are obtained

the equitable dispersion problem most optimization problems focus on efficiency based objectives given the increasing awareness of system inequity resulting from solely pursuing efficiency we conceptualize a number of new element based equity oriented measures in the dispersion context we propose the equitable dispersion problem that maximizes the equity among elements based on the introduced measures in a system defined by inter element distances given the proposed optimization framework we develop corresponding mathematical programming formulations as well as their mixed integer linear reformulations we also discuss computational complexity issues related graph theoretic interpretations and provide some preliminary computational results

influence of strong noise on the decline and propagation of population in the delayed malthus verhulst model abstract the effects of strong noise on the decline and propagation processes of a population in the malthus verhulst model with time delay are investigated by a stochastic simulation time delays in two different processes are concurrent in ecosystems the simulation results indicate that the stability of the population is enhanced by the decreasing multiplicative noise intensity and the increasing delay time the replacement of old individuals with young ones is accelerated by an increasing multiplicative noise intensity an increasing additive noise intensity and a decreasing delay time an increasing multiplicative noise intensity will drive the population of species to fluctuate more largely

externally controlled attractor selection in a high dimensional system a high dimensional dynamical system with global couplings that can serve as a prototype for systems with very large numbers of attractors like memory is investigated and shown to be controllable by external inputs by changing the duration that noise is added final attractors are selected as the number of degrees of freedom of the nonsynchronized elements decreases one by one over time furthermore it is found that this selection of attractors is also possible by controlling the sweeping speed of a parameter the mechanism for this controlled selection is explained and shown to be rather general applications to attractor switching are given

a general variable neighborhood search for solving the uncapacitated single allocation p hub median problem we present a new general variable neighborhood search approach for the uncapacitated single allocation p hub median problem in networks this np hard problem is concerned with locating hub facilities in order to minimize the traffic between all origin destination pairs we use three neighborhoods and efficiently update data structures for calculating new total flow in the network in addition to the usual sequential strategy a new nested strategy is proposed in designing a deterministic variable neighborhood descent local search our experimentation shows that general variable neighborhood search based heuristics outperform the best known heuristics in terms of solution quality and computational effort moreover we improve the best known objective values for some large australia post and planetlab instances results with the new nested variable neighborhood descent show the best performance in solving very large test instances

less is more solving the max mean diversity problem with variable neighborhood search abstract within the broad class of diversity dispersion problems we find an important variant known as the max mean diversity problem which requires finding a subset of a given set of elements in order to maximize the quotient of the sum of all edges belonging to that subset and the cardinality of the subset in this paper we develop a new application of general variable neighborhood search for solving this problem extensive computational results show that our new heuristic significantly outperforms the current state of the art heuristic moreover the best known solutions have been improved on 58 out of 60 large test instances from the literature in other words despite the simplicity of our method which is a desirable property for any heuristic we achieve significantly better results than a more complex heuristic that represents the state of the art thus simplicity can lead to more efficient and effective methods when heuristics are used less can be more

order matters a variable neighborhood search for the swap body vehicle routing problem abstract this article presents investigations on the performance of standard and problem specific neighborhood operators for the swap body vehicle routing problem more specifically our work analyzes the contribution of each operator to the solution quality in addition an experimental setting is defined that can be utilized to identify promising sequences in a variable neighborhood search the experiments verify that the sequence matters since two best known solutions can be equaled and 16 out of 18 solutions can be improved with a maximal improvement of 2 25 and an average improvement of 0 70

ultradiffusion the relaxation of hierarchical systems the authors show that the dynamics of relaxation in hierarchical structures leads to an anomalous decay process which they term ultradiffusion using renormalisation group techniques they explicitly calculate the behaviour of the autocorrelation function in a one dimensional hierarchical system and show its universal power law decay as a function of temperature the authors also demonstrate analytically the emergence of a hierarchy of time scales this phenomenon is relevant to systems ranging from macromolecules to computing structures

solving the maximum min sum dispersion by alternating formulations of two different problems abstract the maximum min sum dispersion problem aims to maximize the minimum accumulative dispersion among the chosen elements it is known to be strongly np hard problem in this paper we present heuristic where the objective functions of two different problems are shifted within variable neighborhood search framework though this heuristic can be seen as an extended variant of variable formulation search approach that takes into account alternative formulations of one problem the important difference is that it allows using alternative formulations of more than one optimization problem here we use one alternative formulation that is of max sum type of the originally max min type maximum diversity problem computational experiments on the benchmark instances used in the literature show that the suggested approach improves the best known results for most instances in a shorter computing time

tabu search and grasp for the maximum diversity problem in this paper we develop new heuristic procedures for the maximum diversity problem mdp this np hard problem has a significant number of practical applications such as environmental balance telecommunication services or genetic engineering the proposed algorithm is based on the tabu search methodology and incorporates memory structures for both construction and improvement although proposed in seminal tabu search papers memory based constructions have often been implemented in naive ways that disregard important elements of the fundamental tabu search proposals we will compare our tabu search construction with a memory less design and with previous algorithms recently developed for this problem the constructive method can be coupled with a local search procedure or a short term tabu search for improved outcomes extensive computational experiments with medium and large instances show that the proposed procedure outperforms the best heuristics reported in the literature within short computational times

legendrian fronts for affine varieties in this article we study weinstein structures endowed with a lefschetz fibration in terms of the legendrian front projection first we provide a systematic recipe for translating from a weinstein lefschetz bifibration to a legendrian handlebody then we present several new applications of this technique to symplectic topology this includes the detection of flexibility and rigidity for several families of weinstein manifolds and the existence of closed exact lagrangian submanifolds in particular we prove that the koras russell cubic is stein deformation equivalent to c3 and we verify the affine parts of the algebraic mirrors of two weinstein 4 folds

pattern dynamics in spatiotemporal chaos pattern selection diffusion of defect and pattern competition intermettency abstract a class of coupled map lattices is investigated as a model for the spatiotemporal chaos as the parameters are changed phase transitions among the patterns are observed pattern selection through the chaotic motion of domain is observed chaos is suppressed by the selection selection of the zigzag pattern is studied where localized defects which separate the two anti phase domains are found they change chaotically in time and move randomly in space the diffusion of defect is related with its chaotic motion collapse of zigzag pattern and the defect turbulence are studied in connection with the crisis in high dimensional dynamical systems pattern selection with longer wavelengths is found in the stronger coupling regime transition from pattern selection phase to fully developed turbulence occurs via the intermittency selective flicker like noise and the pareto distribution of lifetime of pattern are observed at the intermittency regime for the quantitative characterization of each phase pattern distributions pattern transition matrix static and dynamical entropies lifetime distribution of pattern spatiotemporal power spectra and lyapunov spectra are calculated phase transition from the pattern selection to fully developed turbulence is investigated with the use of these quantifiers where some order parameters and critical indeces are introduced

solving the maximally diverse grouping problem by skewed general variable neighborhood search the maximally diverse grouping problem requires finding a partition of a given set of elements into a fixed number of mutually disjoint subsets or groups in order to maximize the overall diversity between elements of the same group in this paper we develop a new variant of variable neighborhood search for solving the problem the extensive computational results show that our new heuristic significantly outperforms the current state of the art moreover the best known solutions have been improved on 531 out of 540 test instances from the literature

partition complexity in a network of chaotic elements a network of chaotic elements is investigated with the use of globally coupled maps elements can split into clusters with synchronized oscillation in a partially ordered phase the clustering has an inhomogeneous tree structure like replica symmetry breaking in spin glass the clustering has large variety by attractors and strongly depends on initial conditions the variety of clusterings is characterized by the distribution of partitions originated in spin glass theory the qualitative similarity and quantitative disagreement of the given attractors with a spin glass are clarified

embeddings of hypersurfaces in affine spaces abstract in this paper we address the following two general problems given two algebraic varieties in cn find out whether or not they are 1 isomorphic and 2 equivalent under an automorphism of cn although a complete solution of either of those problems is out of the question at this time we give here some handy and useful invariants of isomorphic as well as of equivalent varieties furthermore and more importantly we give a universal procedure for obtaining all possible algebraic varieties isomorphic to a given one and use it to construct numerous examples of isomorphic but inequivalent algebraic varieties in cn among other things we establish the following interesting fact for isomorphic hypersurfaces p x1 xn 0 and q x1 xn 0 the number of zeros of grad p might be different from that of grad q this implies in particular that although the fibers p 0 and q 0 are isomorphic there are some other fibers p c and q c which are not we construct examples like this for any n 2

greedy randomized adaptive search procedure with exterior path relinking for differential dispersion minimization we propose several new hybrid heuristics for the differential dispersion problem the best of which consists of a grasp with sampled greedy construction with variable neighborhood search for local improvement the heuristic maintains an elite set of high quality solutions throughout the search after a fixed number of grasp iterations exterior path relinking is applied between all pairs of elite set solutions and the best solution found is returned exterior path relinking or path separation a variant of the more common interior path relinking is first applied in this paper in interior path relinking paths in the neighborhood solution space connecting good solutions are explored between these solutions in the search for improvements exterior path relinking as opposed to exploring paths between pairs of solutions explores paths beyond those solutions this is accomplished by considering an initiating solution and a guiding solution and introducing in the initiating solution attributes not present in the guiding solution to complete the process the roles of initiating and guiding solutions are exchanged extensive computational experiments on 190 instances from the literature demonstrate the competitiveness of this algorithm

effective metaheuristic algorithms for the minimum differential dispersion problem abstract this paper presents tabu search and memetic search algorithms for solving the minimum differential dispersion problem the tabu search algorithm employs a neighborhood decomposition candidate list strategy and a rarely used solution based tabu memory unlike the typical attribute based tabu list the solution based tabu strategy leads to a more highly focused intensification process and avoids tuning the tabu tenure while employing coordinated hash functions that accelerate the determination of tabu status the memetic search algorithm incorporates the tabu search procedure within it and makes use of a crossover operator that generates solution assignments by an evaluation mechanism that includes both quality and distance criteria experimental results on a benchmark testbed of 250 problems reveal that our tabu search algorithm is capable of discovering better solutions for 179 71 6 of the problem instances while our memetic search algorithm finds better solutions for 157 62 8 of the instances collectively yielding better solutions for 181 72 4 of the test problems than recently reported state of the art algorithms

on a class of danielewski surfaces in affine 3 space abstract in l makar limanov on groups of automorphisms of a class of surfaces israel j math 69 1990 250 256 and l makar limanov on the group of automorphisms of a surface x n y p z israel j math 121 2001 113 123 l makar limanov computed the automorphism groups of surfaces in c 3 defined by the equations x n z p y 0 where n 1 and p y is a nonzero polynomial similar results have been obtained by a crachiola a crachiola on automorphisms of danielewski surfaces j algebraic geom 15 2006 111 132 for surfaces with equations x n z y 2 x y 0 where n 2 and 0 0 defined over arbitrary base fields here we consider more general surfaces defined by equations x n z q x y 0 where n 2 and q x y is a polynomial with coefficients in an arbitrary base field k we characterize among them the ones which are danielewski surfaces in the sense of a dubouloz danielewski fieseler surfaces transformation groups 10 2 2005 139 162 and we compute their automorphism groups we study closed embeddings of these surfaces in affine 3 space we show that in general their automorphisms do not extend to automorphisms of the ambient space finally we give explicit examples of c actions on a surface in a c 3 which can be extended holomorphically but not algebraically to c actions on a c 3

holomorphic families of nonequivalent embeddings and of holomorphic group actions on affine space we construct holomorphic families of proper holomorphic embeddings of mathbb c k into mathbb c n 0 textless k textless n 1 so that for any two different parameters in the family no holomorphic automorphism of mathbb c n can map the image of the corresponding two embeddings onto each other as an application to the study of the group of holomorphic automorphisms of mathbb c n we derive the existence of families of holomorphic mathbb c actions on mathbb c n n ge5 so that different actions in the family are not conjugate this result is surprising in view of the long standing holomorphic linearization problem which in particular asked whether there would be more than one conjugacy class of mathbb c actions on mathbb c n with prescribed linear part at a fixed point

robust space time intermittency and 1 f noise abstract we investigate a type of intermittency that occurs in space as well as time studying a one dimensional lattice of coupled quadratic maps this system naturally forms spatial domains motion of the domain walls causes spatially localized changes from chaotic to almost periodic behavior the almost periodic phases have eigenvalues quite close to one resulting in long lived laminar bursts with a 1 f low frequency spectrum this behavior has aspects of both crutchfield and pomeau manneville intermittency unlike pomeau manneville however the behavior that we observe here is quite robust under changes of parameters

large deviations from the thermodynamic limit in globally coupled maps abstract systems of a large number n of globally coupled maps have become popular as a relatively simple prototype of high dimensional dynamics showing many interesting and typical phenomena like synchronisation cluster formation and multistability and having potential applications in systems like josephson junction arrays or in biophysical models while much progress has been made in the explanation of the macroscopic behaviour of such systems in the limit n there is still need for a sound theory about the asymptotic behaviour of finite n systems as n approaches infinity this article introduces a method by which it is possible to obtain asymptotic estimates for finite size effects that show up as long term deviations from the thermodynamic limit behaviour this method works for systems of globally coupled noisy maps and is based upon the concept of quasipotentials originally developed by freidlin wentzell and others for describing the influence of small random perturbations on the long term behaviour of dynamical systems the problems of explicitly computing quasipotentials in the present context and potential approximation schemes are discussed all the concepts described in this article are illustrated with a simple example

synchronized clusters in coupled map networks i numerical studies we study the synchronization of coupled maps on a variety of networks including regular one and two dimensional networks scale free networks small world networks tree networks and random networks for small coupling strengths nodes show turbulent behavior but form phase synchronized clusters as coupling increases when nodes show synchronized behavior we observe two interesting phenomena first there are some nodes of the floating type that show intermittent behavior between getting attached to some clusters and evolving independently second we identify two different ways of cluster formation namely self organized clusters which have mostly intracluster couplings and driven clusters which have mostly intercluster couplings the synchronized clusters may be of dominant self organized type dominant driven type or mixed type depending on the type of network and the parameters of the dynamics we define different states of the coupled dynamics by considering the number and type of synchronized clusters for the local dynamics governed by the logistic map we study the phase diagram in the plane of the coupling constant and the logistic map parameter ensuremath mu for large coupling strengths and nonlinear coupling we find that the scale free networks and the caley tree networks lead to better cluster formation than the other types of networks with the same average connectivity for most of our study we use the number of connections of the order of the number of nodes as the number of connections increases the number of nodes forming clusters and the size of the clusters in general increase

how fast elements can affect slow dynamics a chain of coupled chaotic elements with different time scales is studied in contrast with the adiabatic approximation we find that correlations between elements are transferred from faster to slower elements when the differences in the time scales of the elements lie within a certain range for such correlations to occur three features are essential strong correlations among the elements a bifurcation in the dynamics of the fastest element by changing its control parameter and cascade propagation of the bifurcation by studying coupled rossler equations we demonstrate that fast elements can affect the dynamics of slow elements when these conditions are satisfied the relevance of our results to biological memory is briefly discussed

macroscopic chaos in globally coupled maps abstract we study the coherent dynamics of globally coupled maps showing macroscopic chaos with this term we indicate the hydrodynamical like irregular behavior of some global observables with typical times much longer than the times related to the evolution of the single or microscopic elements of the system the usual lyapunov exponent is not able to capture the essential features of this macroscopic phenomenon using the recently introduced notion of finite size lyapunov exponent we characterize in a consistent way these macroscopic behaviors basically at small values of the perturbation we recover the usual microscopic lyapunov exponent while at larger values a sort of macroscopic lyapunov exponent emerges which can be much smaller than the former a quantitative characterization of the chaotic motion at hydrodynamical level is then possible even in the absence of the explicit equations for the time evolution of the macroscopic observables

affine varieties with equivalent cylinders abstract a well known cancellation problem asks when for two algebraic varieties v 1 v 2 c n the isomorphism of the cylinders v 1 c and v 2 c implies the isomorphism of v 1 and v 2 in this paper we address a related problem when the equivalence under an automorphism of c n 1 of two cylinders v 1 c and v 2 c implies the equivalence of their bases v 1 and v 2 under an automorphism of c n we concentrate here on hypersurfaces and show that this problem establishes a strong connection between the cancellation conjecture of zariski and the embedding conjecture of abhyankar and sathaye we settle the problem in the affirmative for a large class of polynomials on the other hand we give examples of equivalent cylinders with inequivalent bases those cylinders however are not hypersurfaces another result of interest is that for an arbitrary field k the equivalence of two polynomials in m variables under an automorphism of k x 1 x n n m implies their equivalence under a tame automorphism of k x 1 x 2 n

the discrete p dispersion problem considered is the problem of selecting p out of n given points in some space such that the minimum distance between pairs of selected points is maximized this objective may be appropriate if the selected points correspond to facility sites and the objective is to have as dispersed a set as possible this problem is np complete related graph theoretical problems are discussed integer programming models are proposed and an outline is given on a line search procedure to solve this problem optimally using a branch and bound procedure problems with n 40 and p 16 can be solved on a microcomputer the heuristic developed to get an initial lower bound finds an optimal solution for most of our random test problems also described is an extension to the basic problem that allows for preselected points which may correspond to existing facility locations this more general version can be solved by slight modifications of the algorithms

embeddings of danielewski surfaces a danielewski surface is defined by a polynomial of the form p x nz p y define also the polynomial p x nz r x p y where r x is a non constant polynomial of degree n 1 and r 0 1 we show that when n 2 and deg p y 2 the general fibers of p and p are not isomorphic as algebraic surfaces but that the zero fibers are isomorphic consequently for every non special danielewski surface s there exist non equivalent algebraic embeddings of s in 3 using different methods we also give non equivalent embeddings of the surfaces xz y d n 1 for an infinite sequence of integers d n we then consider a certain algebraic action of the orthogonal group mathcal o 2 on 4 which was first considered by schwarz and then studied by masuda and petrie who proved that this action could not be linearized this was done by comparing the strata of this action to those of the induced tangent space action inequivalent embeddings of a certain singular danielewski surface s in 3 are found we generalize their result and show how this leads to an example of two smooth algebraic hypersurfaces in 3 which are algebraically non isomorphic but holomorphically isomorphic

on the strength of attractors in a high dimensional system milnor attractor network robust global attraction and noise induced selection abstract strength of attractor is studied by the return rate to itself after perturbations for a multi attractor state of a globally coupled map it is found that fragile milnor attractors have a large basin volume at the partially ordered phase such dominance of fragile attractors is understood by robustness of global attraction in the phase space change of the attractor strength and basin volume against the parameter and size are studied in the partially ordered phase the dynamics is often described as milnor attractor network which leads to a new interpretation of chaotic itinerancy noise induced selection of fragile attractors is found that has a sharp dependence on the noise amplitude relevance of the observed results to neural dynamics and cell differentiation is also discussed

spatiotemporal chaos and noise low dimensional chaotic dynamical systems can exhibit many characteristic properties of stochastic systems such as broad fourier spectra they are distinguishable from stochastic processes through finite values for their dimension lyapunov exponents and kolmogorov sinai entropy we discuss how these characteristic observables are modified in spatiotemporal chaotic systems like coupled map lattices we analyze with the help of lyapunov concepts how the stochastic limit is approached and how these properties can be observed directly through local dimension measurements from reconstructed time series finally we discuss the interaction of spatiotemporal attractors with external noise and possible connections to problems of pattern selection and stability

clustering coding switching hierarchical ordering and control in a network of chaotic elements abstract a network of chaotic elements is investigated with the use of globally coupled maps a simple coding of many attractors with clustering is shown through the coding the attractors are organized so that their change exhibits bifurcation like phenomena a precision dependent tree is constructed which leads to the similarity of our attractor with those of spin glasses hierarchical dynamics is constructed on the tree which leads to the dynamical change of trees and the temporal change of effective degrees of freedom by a simple input on a site we can switch among attractors and tune the strength of chaos a threshold on a cluster size is found beyond which a peculiar posi nega switch occurs possible application to biological information processing is discussed with the emphasis on the fuzzy switch chaotic search and hierarchical code categorization

less is more basic variable neighborhood search for minimum differential dispersion problem abstract in this paper we propose a basic variable neighborhood search for solving minimum differential dispersion problem using only the swap neighborhood structure in both descent intensification and shaking diversification steps it has become a trend in the metaheuristic literature to use hybrid metaheuristics i e combination of several metaheuristic paradigms for solving some particular optimization problem we show that our simple method which relies on the basic variable neighborhood search significantly outperforms the hybrid one that combines grasp variable neighborhood search and exterior path relinking metaheuristics thus simplicity is not only the desired user friendly property of a heuristic but can lead to more efficient and effective method than if complex hybrid metaheuristic is used less is more

iterated tabu search for the maximum diversity problem in this paper we deal with the maximum diversity problem mdp which asks to select a specified number of elements from a given set so that the sum of distances between the selected elements is as large as possible we develop an iterated tabu search its algorithm for solving this problem we also present a steepest ascent algorithm which is well suited in application settings where solutions of satisfactory quality are required to be provided very quickly computational results for problem instances involving up to 5000 elements show that the its algorithm is a very attractive alternative to the existing approaches in particular we demonstrate the outstanding performance of its on the mdp instances taken from the literature for 69 such instances new best solutions were found

lyapunov analysis and information flow in coupled map lattices abstract lyapunov analysis for the coupled map lattices is presented the co moving lyapunov exponent is calculated which is related with the propagation of the disturbance in space the propagation speed agrees with the zero crossing point of the co moving lyapunov exponent the co moving mutual information flow is introduced which shows the selective transmission of the information at some speed lyapunov spectra and vectors are calculated spatial structures of the vectors are investigated possible analogy with the anderson localization problem is discussed

theory of reentrant excitation in a ring of cardiac tissue a cardiac pathology reentrant tachycardia is caused by the sustained circulation of activation along a reentrant path in cardiac tissue a new theoretical model for wave propagation in discrete excitable media employing coupled maps with continuous time is used to derive analytical stability criteria for the uni directional circulation of the excitation pulse on the ring of cardiac tissue numerical simulations of the model that incorporate experimentally measurable characteristics of the cardiac tissue reproduce the experimental data quantitatively the complex oscillations in the cycle length of unstable tachycardia observed experimentally are quasiperiodic oscillations that arise via the multiple hopf bifurcation in high dimensional maps

less is more basic variable neighborhood search heuristic for balanced minimum sum of squares clustering abstract clustering addresses the problem of finding homogeneous and well separated subsets called clusters from a set of given data points in addition to the points themselves in many applications there may exist constraints regarding the size of the clusters to be found particularly in balanced clustering these constraints impose that the entities be equally spread among the different clusters in this work we present a basic variable neighborhood search heuristic for balanced minimum sum of squares clustering following the recently proposed less is more approach computational experiments and statistical tests show that the proposed algorithm outperforms the current state of the art algorithm for the problem indicating that non sophisticated and easy to implement metaheuristic methods can be sufficient to produce successful results in practice

broken ergodicity and glassy behavior in a deterministic chaotic map a network of n elements is studied in terms of a deterministic globally coupled map which can be chaotic there exists a range of values for the parameters of the map where the number of different macroscopic configurations is very large and there is violation of selfaveraging the time averages of functions which depend on a single element computed over a time t have probability distributions that do not collapse to a delta function for increasing t and n this happens for both chaotic and regular motion i e positive or negative lyapunov exponent