the pim simplex method an extension of the pim triple method to saddles with an arbitrary number of expanding directions abstract the growing interest in non attracting chaotic sets of high dimensional dynamical systems requires the development of numerical techniques for their study the pim triple method h e nusse j a yorke physica d 36 1989 137 is a very good method to obtain trajectories on saddles with one positive lyapunov exponent in this paper we combine the same ideas with an algorithm for finding local extrema of multi variable functions to develop an extension of the method the pim simplex method that is suitable for the study of sets with an arbitrary number of expanding directions

nonregular languages in the kicked rotor a symbolic dynamics of the markov chain model for trajectories of the kicked rotor standard map in sticky regions near resonant orbits is developed two sets of trajectories are shown to correspond to a context free and a context sensitive language respectively

graphical representations for ising systems in external fields a graphical representation based on duplication is developed that is suitable for the study of ising systems in external fields two independent replicas of the ising system in the same field are treated as a single four state ashkin teller model bonds in the graphical representation connect the ashkin teller spins for ferromagnetic systems it is proved that ordering is characterized by percolation in this representation the representation leads immediately to cluster algorithms some applications along these lines are discussed

exact significance test for markov order abstract we describe an exact significance test of the null hypothesis that a markov chain is n th order the procedure utilizes surrogate data to yield an exact test statistic distribution valid for any sample size surrogate data are generated using a novel algorithm that guarantees per shot a uniform sampling from the set of sequences that exactly match the n th order properties of the observed data using the test the markov order of tel aviv rainfall data is examined

hamiltonian structure and integrability of the stationary kuramoto sivashinsky equation in this article the stationary kuramoto sivashinsky ks equation is studied it is shown first that this equation can be transformed into a one dimensional hamiltonian system describing the motion of a particle in a time dependent potential second working with this formalism and coming back then to the initial ks equation a subset of initial conditions is derived for which the corresponding solutions u x will behave like the dominant pole 120 x x0 3 deduced from the painleve analysis and will explode in a finite time finally special attention is given to the well known kuramoto tsuzuki solution and it is shown that provided the independent variable x is initialized in a specified domain this solution explodes also like 120 x x0 3

coherent states measurement entropy coherent states cs quantum entropy can be split into two components the dynamical entropy is linked with the dynamical properties of a quantum system the measurement entropy which tends to zero in the semiclassical limit describes the unpredictability induced by the process of a quantum approximate measurement we study the cs measurement entropy for spin coherent states defined on the sphere discussing different methods dealing with the limit time tends to infinity in particular we propose an effective technique of computing the entropy by iterated function systems the dependence of cs measurement entropy on the character of the partition of the phase space is analysed

the topology of nested homoclinic and heteroclinic tangles abstract homoclinic and heteroclinic tangles are fundamental phase space structures that help in organizing the transport defined by a chaotic map on a two dimensional phase space previous work introduced the technique of homotopic lobe dynamics to study the topology of a homoclinic tangle the present work generalizes homotopic lobe dynamics to describe the topology of a network of nested homoclinic and or heteroclinic tangles using this theory we demonstrate that the topological analysis of a network of nested tangles can lead to an efficient symbolic description of a chaotic phase space even in the vicinity of islands of stability by increasing the amount of topological information used e g by introducing additional tangles at finer scales this technique suggests an efficient route for defining accurate symbolic dynamics for phase spaces that exhibit a mixture of chaos and regularity

a new measurement of financial time irreversibility based on information measures method abstract in this paper we propose a new measurement of time irreversibility based on information measures method to analyze the financial stock markets in order to examine the effectiveness of this method we employ it into arfima models applying the new method to quantifying time irreversibility of 33 financial indices evolving over the period 2002 2016 we conclude that the stock daily prices of the companies are indeed time irreversible and the degree of irreversibility varies with time for each company according to the values of irreversibility we could rank the companies also we obtain that the values of annualized irreversibility may have little effect on the coefficient of variation moreover in order to find patterns arising among different periods we use the principal component analysis pca and hierarchical clustering the results obtained by these two standard techniques in data mining are in agreement

dual monte carlo and cluster algorithms we discuss the development of cluster algorithms from the viewpoint of probability theory and not from the usual viewpoint of a particular model from the viewpoint of probability theory we detail the nature of a cluster algorithm make explicit the assumptions embodied in all clusters of which we are aware and define the construction of free cluster algorithms we also illustrate these procedures by rederiving the swendsen wang algorithm presenting the details of the loop algorithm for a worldline simulation of a quantum ital s 1 2 model and proposing a free cluster version of the swendsen wang replica method for the random ising model how the principle of maximum entropy might be used to aid the construction of cluster algorithms is also discussed

entropy and bifurcations in a chaotic laser we compute bounds on the topological entropy associated with a chaotic attractor of a semiconductor laser with optical injection we consider the poincare return map to a fixed plane and are able to compute the stable and unstable manifolds of periodic points globally even though it is impossible to find a plane on which the poincare map is globally smoothly defined in this way we obtain the information that forms the input of the entropy calculations and characterize the boundary crisis in which the chaotic attractor is destroyed this boundary crisis involves a periodic point with negative eigenvalues and the entropy associated with the chaotic attractor persists in a chaotic saddle after the bifurcation

variance reduced estimator of the connected two point function in the presence of a broken z 2 symmetry the exchange or geometric cluster algorithm allows us to define a variance reduced estimator of the connected two point function in the presence of a broken z 2 symmetry we present numerical tests for the improved blume capel model on the simple cubic lattice we perform simulations for the critical isotherm the low temperature phase at vanishing external field and for comparison also the high temperature phase for the connected two point function a substantial reduction of the variance can be obtained allowing us to compute the correlation length with high precision based on these results estimates for various universal amplitude ratios that characterize the universality class of the three dimensional ising model are computed

discontinuity of the magnetization in one dimensional 1 x y 2 ising and potts models results from percolation theory are used to study phase transitions in one dimensional ising and q state potts models with couplings of the asymptotic form j sub x y approx const absolute value x y sup 2 for translation invariant systems with well defined lim sub x infinity x sup 2 j sub x j sup possibly o or infinity we establish 1 there is no long range order at inverse temperatures beta with beta j sup less than or equal to1 2 if beta j sup q then by sufficiently increasing j sub 1 the spontaneous magnetization m is made positive 3 in models with 0 j sup infinity the magnetization is discontinuous at the transition point as originally predicted by thouless and obeys m beta sub c less than or equal to 1 beta sub c j sup sup 1 2 4 for ising q 2 models with j sup infinity it is noted that the correlation function decays as beta approx c beta absolute value x y sup 2 whenever beta beta sub c points 1 3 are deduced from previous percolation results by utilizing the fortuin kasteleyn representation which also yields other results of independent interest relating potts models with different values of q

on some criteria for estimating the order of a markov chain tong 1975 has proposed a procedure for estimating the order of a markov chain based on akaike s information criterion aic in this paper the asymptotic distribution of the aic estimator is derived and it is shown that the estimator is inconsistent as an alternative to the aic procedure the bayesian information criterion bic proposed by schwarz 1978 is shown to be consistent these two procedures yield different estimated orders when applied to specific samples of meteorological observations for parameters based on these meteorological examples the aic and bic procedures are compared by means of simulation for finite samples the results obtained have practical implications concerning whether in the routine fitting of precipitation data it is necessary to consider higher than first order markov chains

on kinetic ising models in one dimension it is shown that glauber dynamics in 1d ising spin systems is not universal this is illustrated on a periodic model with a basic unit cell j1 jn containing an arbitrary set of n ferromagnetic coupling constants the dynamic critical exponent z is calculated exactly as z 1 max ji min ji the known value z 2 is recovered only for n 1 the extension of this result to other types of dynamics is briefly discussed

testing the order of discrete markov chains using surrogate data tests of the null hypothesis that a symbolic sequence is of nth markov order are described these tests are based on resampling methods similar to the method of surrogate data used to test continuous time series for nonlinear structure the size and power of these symbolic surrogate tests are estimated using binary and heptary test sequences of known order conditioning on a sufficient statistic under the null hypothesis yields an estimated true size which closely approximates the nominal size and increases the power of the test with respect to the unconditional test we apply one method to a symbolic sequence derived from the rossler system and to a binary and heptary representation of an interspike interval sequence of an electroreceptor of the weakly electric eel apteronotus leptorhynchus

monte carlo study of the random field ising model using a cluster flipping monte carlo algorithm combined with a generalization of the histogram reweighting scheme of ferrenberg and swendsen we have studied the equilibrium properties of the thermal random field ising model on a cubic lattice in three dimensions we have equilibrated systems of l x l x l spins with values of l up to 32 and for these systems the cluster flipping method appears to a large extent to overcome the slow equilibration seen in single spin flip methods from the results of our simulations we have extracted values for the critical exponents and the critical temperature and randomness of the model by finite size scaling for the exponents we find v 1 02 0 06 b 0 06 0 07 y 1 9 0 2 and mean y 2 9 0 2

an ising model of transcription polarity in bacterial chromosomes abstract bacterial genes form clusters of the same transcription polarity and typically exhibit a preference to be coded on the leading strand of replication an ising model is proposed to quantify these two phenomena by analogy to the behavior of magnetic dipoles spins in a one dimensional lattice corresponding to magnetic forces that co orient adjacent spins and align them with an externally applied field we imagine pseudo forces that influence transcription polarity bonds of uniform strength 1 2 j between adjacent sites will model the adhesive or repulsive interactions while a polarity entraining force of strength h has the direction of replication ten bacterial chromosomes are reduced to spin configurations from which the model parameters are estimated by the method of maximum likelihood under the assumption of thermal equilibrium following the application of established methods to locate replication origins and termini 2 tests show that the model fits the data well in about half the cases but cluster size exhibits excess variance in general these findings lead to a speculative interpretation of the pseudo forces as the net effects of numerous insertions and deletions that succeed or fail according to their impact on the motions of enzymatic complexes involved in replication and transcription

traveling wave oscillatory patterns in a signed kuramoto sivashinsky equation with absorption abstract in this paper a proof of a part of a conjecture raised in galaktionov and svirshchevskii 2007 concerning existence and global uniqueness of an asymptotically stable periodic orbit in a fourth order piecewise linear ordinary differential equation is presented the fourth order equation comes from the study of traveling wave patterns in a signed kuramoto sivashinsky equation with absorption the proof is twofold first the problem of solving for the periodic orbit is transformed into a zero finding problem on r 4 which is solved with a computer assisted proof based on newton s method and the contraction mapping theorem second the rigorous bounds about the periodic orbit in phase space are combined with the theory of discontinuous dynamical systems to prove that the orbit is asymptotically stable

cluster monte carlo algorithms for random ising models abstract variations of the swendsen wang and wolff cluster flip algorithms are proposed to perform monte carlo simulations of ising models with random bonds and random fields including systems with frustration the new methods are tested by applying them to small lattices and comparing the results with exact data

equivalent n person games and the null space of the shapley value two n person games may be said to be equivalent if they have the same shapley value in this paper we attempt to simplify the determination of the equivalence of two games we do this by recognizing that a pair of games are equivalent if and only if their difference lies in the null space of the shapley value using the representation theory of the symmetric groups we construct a direct sum decomposition of this null space into invariant subspaces we then use this same theory to derive a characterization of a very general type of value of which the shapley value is one particular example

entropy and local uncertainty of data from sensory neurons we present an empirical comparison between neural interspike interval sequences obtained from two different kinds of sensory receptors both differ in their internal structure as well as in the strength of correlations and the degree of predictability found in the respective spike trains as a further tool in this context we suggest the local uncertainty assigning a well defined predictability to individual spikes the local uncertainty is demonstrated to reveal significant patterns within the interspike interval sequences even when its overall structure is almost random our approach is based on the concept of symbolic dynamics and information theory

comparison of several generating partitions of the henon map the existence and uniqueness of generating partitions in non hyperbolic dynamical systems is usually studied in a simple exemplary system namely the henon map at standard parameter values a 1 4 and b 0 3 we compare its standard partition with three other binary partitions which are quite different from the standard partition but also appear to be generating one of these partitions passes twice through the same orbit of homoclinic tangencies providing a counterexample to a recent conjecture by jaeger and kantz j phys a math gen 30 l567 introducing some simple rules to manipulate symbolic sequences we show how to translate symbolic sequences produced by one partition into sequences produced by the other partitions this proves that all these partitions are as good approximations to generating partitions as the standard partition we also construct an infinite number of binary partitions which are all quite similar to the standard partition derive their translation rules and prove the same equivalence it is not known for sure whether any of these partitions is indeed generating but if one of them is generating then they all are

the steady states of the kuramoto sivashinsky equation abstract the kuramoto sivashinsky equation is one of the simple nonlinear partial differential equations it represents a system in which the transport of energy through nonlinear mode coupling produces a balance between long wavelength instability and short wavelength dissipation the steady states and their stabilities give a foundation for understanding the dynamics of the system they are distinguished according to their energy levels and fall into different branches that are identified by their harmonic content various types of solution include laminar states n cell states long wave distorbed n cell states the giant states and steady traveling solutions the linear stability around the steady states gives a guide to the origin of additional steady states through bifurcation and to the identification of each steady state the index rule is also useful conjectured form the numerical observation the parameter dependence of the steady traveling waves is estimated in the limit of large values of the parameter in addition a singular perturbation calculation of traveling waves near bifurcation is carried out the dynamics of a system can be guided by the systematic study of the bifurcation and stability for example if all the stationary and periodic solutions are unstable for some parameter range chaotic behavior of the system is expected since any orbit governed by the equation has to wander around forever in the phase space the orbits will then lie on strange attractors

constrained realization monte carlo method for hypothesis testing abstract we compare two theoretically distinct approaches to generate artificial or surrogate data for testing hypotheses about a given data set the first and more straightforward approach is to fit a single best model to the original data and then to generate surrogate data sets that are typical realizations of that model the second approach concentrates not on the model but directly on the original data it attempts to constrain the surrogate data sets so that they exactly agree with the original data for a specified set of sample statistics examples of these two approaches are provided for two simple cases a test for deviations from a gaussian distribution and a test for serial dependence in a time series additionally we consider test for nonlinearity in time series based on a fourier transform ft method and on more conventional autoregressive moving average arma fits to the data the comparative performance of hypothesis testing schemes based on these two approaches is found to depend on whether or not the discriminating statistic is pivotal a statistic is pivotal if its distribution is the same for all processes consistent with the null hypothesis the typical realization method requires that the discriminating statistic satisfy this property the constrained realization approach on the other hand does not share this requirement and can provide an accurate and powerful test without having to sacrifice flexibility in the choice of discriminating statistic

measuring correlations in symbol sequences abstract the paper is devoted to relations between correlation functions and mutual information it is shown that in sequences over an alphabet of symbols statistical dependences are measured by 1 2 independent parameters however not all of them can be determined by autocorrelation functions appropriate sets of correlation functions including crosscorrelations are introduced which allow the detection of all dependences the results are exemplified for binary ternary and quaternary symbol sequences as an application it is discussed that a nonuniform codon usage in protein coding dna sequences introduces periodic correlations even at distances in the order of 1000 base pairs

back in the saddle again a computer assisted study of the kuramoto sivashinsky equation a numerical and analytical study of the kuramoto sivashinsky partial differential equation pde in one spatial dimension with periodic boundary conditions is presented the structure stability and bifurcation characteristics of steady state and time dependent solutions of the pde for values of the parameter alpha less than 40 are examined the numerically observed primary and secondary bifurcations of steady states as well as bifurcations to constant speed traveling waves limit cycles are analytically verified persistent homoclinic and heteroclinic saddle connections are observed and explained via the system symmetries and fixed point subspaces of appropriate isotropy subgroups of o 2 their effect on the system dynamics is discussed and several tertiary bifurcations observed numerically are presented

structure of generating partitions for two dimensional maps we discuss the non uniqueness of the generating partitions of two dimensional maps and we give new explanations for ambiguities that are to be expected in the construction of generating partitions if a parameter is varied both points are discussed with the help of the connecting lines of homoclinic tangencies in the entire phase space i e also outside the attractor that can be calculated very easily with a new algorithm introduced recently

kuramoto sivashinsky dynamics on the center unstable manifold this paper studies the dynamical behavior of solutions of the kuramoto sivashinsky partial differential equation with periodic boundary conditions on a spatial interval 0 h the length h is the bifurcation parameter and reduction is made to a two complex dimensional system on a local center unstable manifold near the second bifurcation point h 2 from the trivial solution the resulting o 2 equivariant system displays all the behavior found in high precision simulations of the partial differential equation near this bifurcation point in particular bifurcation sequences to stable traveling waves unstable modulated traveling waves and attracting heteroclinic cycles are reproduced qualitatively and quantitatively within 1 in the parameter range h 2 pm 20 a clear understanding of the global dynamical behavior in this region is thus obtained

graphical representations and cluster algorithms for critical points with fields a two replica graphical representation and associated cluster algorithm is described that is applicable to ferromagnetic ising systems with arbitrary fields critical points are associated with the percolation threshold of the graphical representation results from numerical simulations of the ising model in a staggered field are presented the dynamic exponent for the algorithm is measured to be less than 0 5

the orthogonal decomposition of games and an averaging formula for the shapley value in this paper we attempt to decompose a game v into two different components one lying in the null space of the shapley value and the other in its orthogonal complement we observe that the shapley value of the former must be 0 so that the shapley value of the latter coincides with the value of the original game in this way we arrive at a new explicit formula for the shapley value which unlike the typical one involves averages of player worths across coalition sizes central to our ideas is the game theoretic contrast between the spaces in which each component lies

a procedure for finding numerical trajectories on chaotic saddles abstract examples are common in dynamical systems in which there are regions containing chaotic sets that are not attractors if almost every trajectory eventually leaves some region but the region contains a chaotic set then typical trajectories will behave chaotically for a while and then will leave the region and so we will observe chaotic transients the main objective that will be addressed is the dynamic restraint problem given a region that contains a chaotic set but does not contain an attractor find a chaotic trajectory numerically that remains in the regionfor an arbituarily long period of time systems with horseshoes have such regions as do systems with fractal basin boundaries as does the henon map for suitably chosen parameters we present a numerical technique for finding trajectories which will stay in such chaotic sets for arbitrarily long periods of time and it leads to a saddle straddle trajectory the method is called the pim triple procedure since it is based on so called pim triples a pim proper interior maximum triple is three points a c b in a straight line segment such that the interior point c i e c is between a and b has the maximum escape time that is its escape time from the region is greater than the escape time of both a and b proper means the segment from a to b is smaller than a previously obtained segment we show rigorously that the pim triple procedure works in ideal situations we find it works well even in less than ideal cases this procedure can also be used for the computation of lyapunov exponents furthermore the accessible pim triple procedure a refined pim triple procedure for finding accessible trajectories on the chaotic saddle will also be discussed

queues stacks and transcendentality at the transition to chaos abstract we examine the one humped map at the period doubling transition to chaos and ask whether its long term memory is stack like last in first out or queue like first in first out we show that it can be recognized by a real time automaton with one queue or two stacks and give several new grammatical characterizations of it we argue that its memory has a queue like character since a single stack does not suffice we also show that its dynamical zeta function generating function and growth function are transcendental the same results hold for any period multiplying cascade we suggest that transcendentality might be a sign of dynamical phase transitions in other systems as well

cluster algorithm for hard spheres and related systems in this paper we present a cluster algorithm for the simulation of hard spheres and related systems in this algorithm a copy of the configuration is rotated with respect to a randomly chosen pivot point the two systems are then superposed and clusters of overlapping spheres in the joint system are isolated each of these clusters can be flipped independently a process which generates non local moves in the original configuration a generalization of this algorithm which works perfectly well at small density can be made to work successfully at densities around the solid liquid transition point in the two dimensional hard sphere system

symbol statistics and spatio temporal systems abstract we consider the problem of estimating parameters from time series observations of spatio temporal systems two types of models are considered a a one dimensional coupled map lattice with nearest neighbor diffusive coupling and b the complex ginzburg landau equation in one and two spatial dimensions model parameters are to be estimated using time series observations from only a few sites a symbolic partition of the time series is introduced and the probabilities of observing various symbol sequences in the data are measured the parameter fitting is accomplished by adjusting parameters of the model until it produces time series whose symbol sequences have the same probabilities as the data we show that it is possible to reliably estimate the parameters from a single time series when the spatio temporal dynamics is turbulent i e it displays a wide range of space and time scales with no discernible patterns

chaotic dynamics markovian coarse graining and information abstract the conditions for mapping chaotic dynamics into a markov chain through finite coarse graining are derived a chapman kolmmogorov equation giving rise to an h theorem is deduced in which the transition probability matrix is expressed entirely in terms of the properties of the underlying deterministic dynamics and of the phase space partition the validity of the conditions ensuring the mapping is verified on simple models of dissipative as well as conservative dynamical systems the implications of the results in the problem of irreversibility and the relation between deterministic chaos information and complexity are discussed

cluster monte carlo algorithms abstract the swendsen wang and wolff monte carlo algorithms are described in some detail using the potts model as an example various generalizations are then reviewed and some applications are discussed two complete fortran programs for the algorithms are provided

value theory without efficiency a semivalue is a symmetric positive linear operator on a space of games which leaves the additive games fixed such an operator satisfies all of the axioms defining the shapley value with the possible exception of the efficiency axiom the class of semivalues is completely characterized for the space of finite player games and for the space pna of nonatomic games

complexity and fisher information the connection between an observer based theory of measurement and a hierarchical classification of complex systems in terms of topological exponents is discussed this leads to generalized definitions of complexity that capture different aspects of the structure of the trajectory space of complex systems

variational method for finding periodic orbits in a general flow a variational principle is proposed and implemented for determining unstable periodic orbits of flows as well as unstable spatiotemporally periodic solutions of extended systems an initial loop approximating a periodic solution is evolved in the space of loops toward a true periodic solution by a minimization of local errors along the loop the newton descent partial differential equation that governs this evolution is an infinitesimal step version of the damped newton raphson iteration the feasibility of the method is demonstrated by its application to the henon heiles system the circular restricted three body problem and the kuramoto sivashinsky system in a weakly turbulent regime

test to determine the markov order of a time series the markov order of a time series is an important measure of the memory of a process and its knowledge is fundamental for the correct simulation of the characteristics of the process for this reason several techniques have been proposed in the past for its estimation however most of this methods are rather complex and often can be applied only in the case of markov chains here we propose a simple and robust test to evaluate the markov order of a time series only the first order moment of the conditional probability density function characterizing the process is used to evaluate the memory of the process itself this measure is called the expected value markov evm order we show that there is good agreement between the evm order and the known markov order of some synthetic time series

sensitivity of long periodic orbits of chaotic systems the properties of long numerically determined periodic orbits of two low dimensional chaotic systems the lorenz equations and the kuramoto sivashinsky system in a minimal domain configuration are examined the primary question is to establish whether the sensitivity of period averaged quantities with respect to parameter perturbations computed over long orbits can be used as a sufficiently good proxy for the response of the chaotic state to finite amplitude parameter perturbations to address this question an inventory of thousands of orbits at least two orders of magnitude longer than the shortest admissible cycles is constructed the expectation of period averages floquet exponents and sensitivities over such set is then obtained it is shown that all these quantities converge to a limiting value as the orbit period is increased however while period averages and floquet exponents appear to converge to analogous quantities computed from chaotic trajectories the limiting value of the sensitivity is not necessarily consistent with the response of the chaotic state similar to observations made with other shadowing algorithms

continuous symmetry reduction and return maps for high dimensional flows we present two continuous symmetry reduction methods for reducing highdimensional dissipative flows to local return maps in the hilbert polynomial basis approach the equivariant dynamics is rewritten in terms of invariant coordinates in the method of moving frames or method of slices the state space is sliced locally in such a way that each group orbit of symmetry equivalent points is represented by a single point in either approach numerical computations can be performed in the original state space representation and the solutions are then projected onto the symmetry reduced state space the two methods are illustrated by reduction of the complex lorenz system a 5 dimensional dissipative flow with rotational symmetry while the hilbert polynomial basis approach appears unfeasible for high dimensional flows symmetry reduction by the method of moving frames offers hope

the kuramoto sivashinsky equation a bridge between pde s and dynamical systems abstract through extensive numerical simulation we have characterized the transition to chaos of the solutions to the kuramoto sivashinsky equation the attracting solution manifolds undergo a complex bifurcation sequence including multimodal fixed points invariant tori traveling wave trains and homoclinic orbits we relate this behavior to earlier work where the kuramoto sivashinsky equation was shown to behave as a finite dimensional dynamical system of ordinary differential equations

partitioning the phase space in a natural way for scattering systems in this paper we demonstrate a recent procedure for the construction of a symbolic dynamics for open systems by applying it to a model potential the driven inverted gaussian which has proven very useful in describing laser atom interaction the symbolic dynamics and the corresponding partition of the poincare map are natural from the point of view of an asymptotic observer since the resulting branching tree coincides with the one extracted from the scattering functions in general the whole procedure is approximate because it only describes the globally unstable part of the chaotic invariant set that is the part that can be seen by an asymptotic observer in scattering data it ignores kolmogorov arnold moser islands and their fractal surroundings

microextensive chaos of a spatially extended system by analyzing chaotic states of the one dimensional kuramoto sivashinsky equation for system sizes l in the range 79l ll 93 we show that the lyapunov fractal dimension d scales microextensively increasing linearly with l even for increments ensuremath delta l that are small compared to the average cell size of 9 and to various correlation lengths this suggests that a spatially homogeneous chaotic system does not have to increase its size by some characteristic amount to increase its dynamical complexity

exploring the intrinsic information loss in single humped maps by refining multi symbol partitions abstract we study the intrinsic information flow for a class of chaotic maps by applying the concept of conditional entropy for an infinite alphabet our procedure consists in refining partitions and thereby revealing the information flow step by step we prove that in the case of an infinite number of symbols the information about the initial conditions is lost linearly in time

replica exchange algorithm and results for the three dimensional random field ising model the random field ising model with gaussian disorder is studied using a different monte carlo algorithm the algorithm combines the advantages of the replica exchange method and the two replica cluster method and is much more efficient than the metropolis algorithm for some disorder realizations three dimensional systems of size 24 3 are studied each realization of disorder is simulated at a value of temperature and uniform field that is adjusted to the phase transition region for that disorder realization energy and magnetization distributions show large variations from one realization of disorder to another for some realizations of disorder there are three well separated peaks in the magnetization distribution and two well separated peaks in the energy distribution suggesting a first order transition

testing nonlinear markovian hypotheses in dynamical systems abstract we present a statistical approach for detecting the markovian character of dynamical systems by analyzing their flow of information especially in the presence of noise which is mostly the case for real world time series the calculation of the information flow of the underlying system via the concept of symbolic dynamics is rather problematic since one has to use infinitesimal partitions we circumvent this difficulty by measuring the information flow indirectly more precisely we calculate a measure based on higher order cumulants which quantifies the statistical dependencies between the past values of the time series and the point r steps ahead as an extension of theiler s method of surrogate data theiler et al 1992 this cumulant based information flow a function of the look ahead r is used as the discriminating statistic in testing the observed dynamics against a hierarchy of null hypotheses corresponding to nonlinear markov processes of increasing order this procedure is iterative in the sense that whenever a null hypothesis is rejected new data sets can be generated corresponding to better approximations of the original process in terms of information flow since we use higher order cumulants for calculating the discriminating statistic our method is also applicable to small data sets numerical results on artificial and real world examples including non chaotic nonlinear processes autoregressive models and noisy chaos show the effectiveness of our approach

on the geometric structure of non hyperbolic attractors the authors discuss the f alpha spectrum of non hyperbolic attractors of the henon type they elucidate the origin of the phase transition found in a previous paper and give a lower bound to the spectrum in the non hyperbolic phase where kaplan yorke type formulae no longer hold their results disagree with other recent attempts numerical simulations for the henon map agree with analytical estimates

high dimensional lattice gases we investigate the critical behaviour of hard core lattice gases in four five and six dimensions by means of monte carlo simulations in order to suppress critical slowing down we use a geometrical cluster monte carlo algorithm in particular nearest neighbour exclusion lattice gases on simple hypercubic lattices are investigated these models undergo ising like ordering transitions where the majority of the lattice gas particles settle on one of two sublattices a finite size scaling analysis of the simulation data confirms that these lattice gases display classical critical behaviour the results agree with the renormalization predictions at and above the upper critical dimensionality in particular the predicted value of the binder cumulant is confirmed

the simple cubic lattice gas with nearest neighbour exclusion ising universality abstract the lattice gas with nearest neighbour exclusion on the simple cubic lattice is studied by means of statistically accurate monte carlo simulations with an efficient cluster algorithm our results for critical exponents are y h 2 47 1 and y t 1 60 2 these results agree well with the three dimensional ising universality class we explain the discrepancy with an earlier study the critical activity is z c 1 0559 1 the size distribution of the clusters indicates that the percolation threshold of the cluster formation process of the monte carlo algorithm coincides with the critical point

long range correlations between letters and sentences in texts abstract we mapped three long texts to random walks and calculated several correlation measures as holder exponents higher order cumulants and power spectra by means of computer experiments we have found that shuffling on or below the sentence level generates strings showing no anomalous diffusion no higher order cumulants and no power spectra with 1 f shape in this way we have shown that the long correlations reflected in these measures are not based on correlations inside sentences but reflect the large scale structure beyond the sentence level

steady solutions of the kuramoto sivashinsky equation abstract steady solutions of the kuramoto sivashinsky equation are studied these solutions are defined on the whole x line and propagate with a constant speed c 2 in time for large c 2 it is shown that the solution is unique and has a conical form for small c 2 there is a periodic solution and an infinite set of quasi periodic solutions as asserted by moser s twist map theorem numerical computations for intermediate values of c 2 suggest that below c 1 6 of every speed there is a continuum of odd quasi periodic solutions or a cantor set of chaotic solutions wrapped by infinite sequences of conic solutions

generalized markov coarse graining and spectral decompositions of chaotic piecewise linear maps spectral decompositions of the evolution operator for probability densities are obtained for the most general one dimensional piecewise linear markov maps and a large class of repellers the eigenvalues obtained with respect to the space of functions piecewise analytic over the minimal markov partition equal the reciprocals of the zeros of the ruelle zeta functions the logarithms of the zeros correspond to the decay rates of time correlation functions of analytic observables when the system is mixing the space can also be extended to include piecewise analytic observables permitted to have discontinuities at the elements of any given periodic orbit s so that local behavior of observables can be considered the new spectra associated with the extension are surprisingly simple and are related to the relative stability factors of the given orbit s finally arbitrarily slowly decaying periodic and aperiodic nonanalytic eigenmodes are constructed

testing for nonlinearity in time series the method of surrogate data we describe a statistical approach for identifying nonlinearity in time series the method first specifies some linear process as a null hypothesis then generates surrogate data sets which are consistent with this null hypothesis and finally computes a discriminating statistic for the original and for each of the surrogate data sets if the value computed for the original data is significantly different than the ensemble of values computed for the surrogate data then the null hypothesis is rejected and nonlinearity is detected we discuss various null hypotheses and discriminating statistics the method is demonstrated for numerical data generated by known chaotic systems and applied to a number of experimental time series which arise in the measurement of superfluids brain waves and sunspots we evaluate the statistical significance of the evidence for nonlinear structure in each case and illustrate aspects of the data which this approach identifies

associated consistency characterization of two linear values for tu games by matrix approach hamiache assigns to every tu game a so called associated game and then shows that the shapley value is characterized as the unique solution for tu games satisfying the inessential game property continuity and associated consistency the latter notion means that for every game the shapley value of the associated game is equal to the shapley value of the game itself in this paper we show that also the eans value as well as the cis value is characterized by these three properties for appropriately modified notions of the associated game this shows that these three values only differ with respect to the associated game the characterization is obtained by applying the matrix approach as the pivotal technique for characterizing linear values of tu games in terms of associated consistency

graphical representations and cluster algorithms ii we continue the study initiated in part i of graphical representations and cluster algorithms for various models in or related to statistical mechanics for certain models e g the blume emery griffths model and various generalizations we develop fortuin kasteleyn type representations which lead immediately to swendsen wang type algorithms for other models e g the random cluster model that are defined by a graphical representation we develop cluster algorithms without reference to an underlying spin system in all cases phase transitions are related to percolation or incipient percolation in the graphical representation which via the ic algorithm allows for the rapid simulation of these systems at the transition point pertinent examples include the continuum widom rowlinson model the restricted 1 step solid on solid model and the xy model

order and complexity in the kuramoto sivashinsky model of weakly turbulent interfaces abstract we present a large number of new geometric ergodic and statistical properties of the kuramoto sivashinsky equation modeling interfacial turbulence in various physical contexts in addition this equation has the remarkable property of inertial manifolds where some finite dimensional dynamical system is rigorously equivalent to this infinite dimensional partial differential equation in moderate size domains up to ten periods in length a low dimensional vector field skeleton underpins even strongly chaotic regimes and controls the bifurcations of the inertial manifold the extreme numerical sensitivity of chaos in this dissipative pde requires very high precision methods despite the geometrical complexities of the bifurcation structure some statistical properties remain remarkably simple there is overwhelming evidence that for some parameter values a permanent unsteady state exists an unexpectedly simple diffusive relaxation of the large scale fluctuations is extracted from extensive numerical simulations in these calculations we observe long time tails for the correlation functions of relevant quantities we propose an explanation in terms of an effective viscosity and compare the transport in the weakly turbulent interface with related theories for random interfaces and developed turbulence

partitioning two dimensional mixed phase spaces abstract hamiltonian systems typically exhibit a mixture of chaos and regularity complicating any scheme to partition phase space and extract a symbolic description of the dynamics in particular the dynamics in the vicinity of stable islands can exhibit complicated topology that is qualitatively distinct from that away from the islands we develop an approach to partition the chaotic phase space of a general dynamical system represented by a two dimensional map homeomorphism this approach can accommodate mixed phase space structure with an arbitrarily high degree of accuracy the partitioning scheme is built around networks of nested heteroclinic tangles fundamental geometric objects that organize phase space transport these tangles can be used to progressively approximate the dynamics in the vicinity of stable island chains the net result is a symbolic approximation to the dynamics in the chaotic sea and an associated phase space partition which includes the influence of stable islands and which is approximately markov

flows and decompositions of games harmonic and potential games in this paper we introduce a novel flow representation for finite games in strategic form this representation allows us to develop a canonical direct sum decomposition of an arbitrary game into three components which we refer to as the potential harmonic and nonstrategic components we analyze natural classes of games that are induced by this decomposition and in particular focus on games with no harmonic component and games with no potential component we show that the first class corresponds to the well known potential games we refer to the second class of games as harmonic games and demonstrate that this new class has interesting properties which contrast with properties of potential games exploiting the decomposition framework we obtain explicit expressions for the projections of games onto the subspaces of potential and harmonic games this enables an extension of the equilibrium properties of potential and harmonic games to nearby games

generating partition for the standard map a procedure to obtain the symbolic dynamics for conservative dynamical systems is introduced with reference to the standard map in a strongly chaotic regime the method extends an approach previously developed for highly dissipative systems it is based on the construction of a generating partition from homoclinic tangencies and fibers of invariant manifolds it is found that some arbitrariness in the construction of the partition is unavoidable

numerical simulation of asymptotic states of the damped kuramoto sivashinsky equation the damped kuramoto sivashinsky equation has emerged as a fundamental tool for the understanding of the onset and evolution of secondary instabilities in a wide range of physical phenomena most existing studies about this equation deal with its asymptotic states on one dimensional settings or on periodic square domains we utilize a large scale numerical simulation to investigate the asymptotic states of the damped kuramoto sivashinsky equation on annular two dimensional geometries and three dimensional domains to this end we propose an accurate efficient and robust algorithm based on a recently introduced numerical methodology namely isogeometric analysis we compared our two dimensional results with several experiments of directed percolation on square and annular geometries and found qualitative agreement

unstable recurrent patterns in kuramoto sivashinsky dynamics we undertake an exploration of recurrent patterns in the antisymmetric subspace of the one dimensional kuramoto sivashinsky system for a small but already rather turbulent system the long time dynamics takes place on a low dimensional invariant manifold a set of equilibria offers a coarse geometrical partition of this manifold the newton descent method enables us to determine numerically a large number of unstable spatiotemporally periodic solutions the attracting set appears surprisingly thin its backbone consists of several smale horseshoe repellers well approximated by intrinsic local one dimensional return maps each with an approximate symbolic dynamics the dynamics appears decomposable into chaotic dynamics within such local repellers interspersed by rapid jumps between them