a new method to detect nonlinearity in a time series synthesizing surrogate data using a kolmogorov smirnoff tested hidden markov model abstract a way of statistically testing for nonlinearity in a time series is to employ the method of surrogate data this method often makes use of the fourier transform ft in order to generate the surrogate as various authors have shown this can lead to artefacts in the surrogates and spurious detection of nonlinearity can result this paper documents a new method to synthesize surrogate data using a 1st order hidden markov model hmm combined with a kolmogorov smirnoff test ks test to determine the required resolution of the hmm significance test results for a sinewave henon map and gaussian noise time series are presented it is demonstrated that ks tested hmm surrogates can be successfully used to distinguish between a deterministic and stochastic time series then by applying a simple test for linearity using linear and nonlinear predictors it is possible to determine the nature of the deterministic class and hence conclude whether the system is linear deterministic or nonlinear deterministic furthermore it is demonstrated that the method works for periodic functions too where ft surrogates break down

bertrand numeration systems and recognizability abstract there exist various well known characterizations of sets of numbers recognizable by a finite automaton when they are represented in some integer base p 2 we show how to modify these characterizations when integer bases p are replaced by linear numeration systems whose characteristic polynomial is the minimal polynomial of a pisot number we also prove some related interesting properties

on number systems with finite degree of ambiguity abstract we show that it is decidable whether or not a given n recognizable set is representable by a number system having finite degree of ambiguity as a corollary we obtain an algorithm for computing the degree of ambiguity of a given set defined by a number system

effect of colored noise on networks of nonlinear oscillators we discuss noise induced pattern formation in different two dimensional networks of nonlinear oscillators namely a sequence of biochemical reactions and the lorenz system the main focus of the work is on the dependence of these patterns on the correlation time i e the color of exponentially correlated gaussian noise it is seen that in the nonchaotic case the homogeneity or average cluster size goes through a minimum with higher correlation time while in its chaotic regime the lorenz system shows a higher degree of synchronization when the correlation time of the noise is increased in order to elucidate the origin of this phenomenon the effect of colored noise on the individual oscillator is investigated it is shown that the specific dependence of the network s homogeneity on the noise correlation time arises from an interplay of the collective behavior and the properties of the single oscillators doi 10 1103 physreve 64 021105

short and long run causality measures theory and inference abstract the concept of causality introduced by wiener wiener n 1956 the theory of prediction in e f beckenback ed the theory of prediction mcgraw hill new york chapter 8 and granger granger c w j 1969 investigating causal relations by econometric models and cross spectral methods econometrica 37 424 459 is defined in terms of predictability one period ahead this concept can be generalized by considering causality at any given horizon h as well as tests for the corresponding non causality dufour j m renault e 1998 short run and long run causality in time series theory econometrica 66 1099 1125 dufour j m pelletier d renault e 2006 short run and long run causality in time series inference journal of econometrics 132 2 337 362 instead of tests for non causality at a given horizon we study the problem of measuring causality between two vector processes existing causality measures have been defined only for the horizon 1 and they fail to capture indirect causality we propose generalizations to any horizon h of the measures introduced by geweke geweke j 1982 measurement of linear dependence and feedback between multiple time series journal of the american statistical association 77 304 313 nonparametric and parametric measures of unidirectional causality and instantaneous effects are considered on noting that the causality measures typically involve complex functions of model parameters in var and varma models we propose a simple simulation based method to evaluate these measures for any varma model we also describe asymptotically valid nonparametric confidence intervals based on a bootstrap technique finally the proposed measures are applied to study causality relations at different horizons between macroeconomic monetary and financial variables in the us

numeration systems linear recurrences and regular sets a numeration system based on a strictly increasing sequence of positive integers u0 1 u1u2 expresses a non negative integer n as a sum n j 0 i ajuj in this case we say the string a i a i 1 a1 a0 is a representation for n

the equivalence problem of multitape finite automata abstract using a result of b h neumann we extend eilenberg s equality theorem to a general result which implies that the multiplicity equivalence problem of two nondeterministic multitape finite automata is decidable as a corollary we solve a long standing open problem in automata theory namely the equivalence problem for multitape deterministic finite automata the main theorem states that there is a finite test set for the multiplicity equivalence of finite automata over conservative monoids embeddable in a fully ordered group

on dol power series abstract we study d0l power series we show how elementary morphisms introduced by ehrenfeucht and rozenberg can be used in connection with power series characterize the sequences of rational numbers and integers which can appear as coefficients in d0l power series and establish various decidability results

linear numeration systems of order two abstract a numeration system is a sequence of integers such that any integer can be represented by means of the sequence using integers of bounded size we study numeration systems defined by linear recurrences of order two we give a necessary and sufficient condition on the system such that every integer has a canonical representation we show that this canonical representation can be computed from any representation by a rational function this rational function is the composition of two subsequential functions that are simply obtained from the system the addition of two integers represented in the system can be performed by a subsequential machine

generalization of automatic sequences for numeration systems on a regular language let l be an infinite regular language on a totally ordered alphabet feeding a finite deterministic automaton with output with the words of l enumerated lexicographically with respect to leads to an infinite sequence over the output alphabet of the automaton this process generalizes the concept of k automatic sequence for abstract numeration systems on a regular language instead of systems in base k here we study the first properties of these sequences and their relations with numeration systems

simplified conditions for noncausality between vectors in multivariate arma models this article derives necessary and sufficient conditions for noncausality between two vectors of variables in stationary invertible arma processes earlier conditions proposed by boudjellaba dufour and roy 1992a are shown to hold under weaker regularity assumptions and then generalized to cover the important case where the two vectors do not necessarily embody all the variables considered in the analysis the conditions so obtained can be considerably simpler and easier to implement than earlier ones testing of the conditions derived is also discussed and the results are applied to a model of canadian money income and interest rates

bounded delay l codes abstract three natural notions of bounded delay for l codes are investigated all interrelations many of them rather surprising between ordinary codes of bounded delay and l codes of bounded delay of various types are established

a periodically forced piecewise linear oscillator a single degree of freedom non linear oscillator is considered the non linearity is in the restoring force and is piecewise linear with a single change in slope such oscillators provide models for mechanical systems in which components make intermittent contact a limiting case in which one slope approaches infinity an impact oscillator is also considered harmonic subharmonic and chaotic motions are found to exist and the bifurcations leading to them are analyzed

modeling multiple time series with applications abstract an approach to the modeling and analysis of multiple time series is proposed properties of a class of vector autoregressive moving average models are discussed modeling procedures consisting of tentative specification estimation and diagnostic checking are outlined and illustrated by three real examples

granger causality in multiple time series abstract the concept of granger causality is formulated for a finite dimensional multiple time series special attention is given to causality patterns in autoregressive series and it is shown how these patterns can be tested under quite general assumptions using a 2 statistic the power of the test is discussed and it is shown that the 2 statistic results from a lagrange multiplier test in the gaussian case the causality test is tried both on artificial data and some economic time series finally we consider the problem of constrained estimation in models with a known causality structure

on lengths of words in context free languages we consider slender languages that is languages for which the number of words of the same length is bounded from above by a constant we prove that the slenderness problem is decidable for context free languages and that the maximal number of words of the same length in a given context free language is computable some effective representations of slender context free languages as well as other related decidability problems are investigated

bases and ambiguity of number systems abstract the degree of ambiguity of a given number system can be effectively computed we show also that all degrees of ambiguity do exist both as regards number systems and the sets represented by them in contrast to language theory there are inherently unambiguous sets the paper contains also results concerning the possibility of changing the base of a number system

nonlinear hypotheses inequality restrictions and non nested hypotheses exact simultaneous tests in linear regressions in the context of the classical linear model the problem of comparing two arbitrary hypotheses on the regression coefficients is considered problems involving nonlinear hypotheses inequality restrictions or non nested hypotheses are included as special cases exact bounds on the null distribution of likelihood ratio statistics are derived the bounds are based on the central fisher distribution and are very easy to use in an important special case a bounds test similar to the durbin watson test is proposed multiple testing problems are also studied the bounds obtained for a single pair of hypotheses are shown to enjoy a simultaneity property that allows one to combine any number of tests this result extends to nonlinear hypotheses a well known result given by scheffe for linear hypotheses a method of building bounds induced tests is also suggested

on generalized dtol systems and their fixed points abstract we study a generalization of dt0l systems obtained by considering noncommutative polynomials together with mappings attaching a morphism to each variable we call the least fixed points of such pairs generalized dt0l languages and study their basic properties

detecting unstable periodic orbits in chaotic continuous time dynamical systems we extend the recently developed method for detecting unstable periodic points of chaotic time discrete dynamical systems to find unstable periodic orbits in time continuous systems given by a set of ordinary differential equations this is achieved by the reduction of the continuous flow to a poincar e map which is then searched for periodic points the algorithm has global convergence properties and needs no a priori knowledge of the system it works well for both dissipative and hamiltonian dynamical systems which is demonstrated by exploring the lorenz system and the hydrogen atom in a strong magnetic field the advantages and general features of the approach are discussed in detail

the use and usefulness of numeration systems the proper choice of a counting system may solve mathematical problems or lead to improved algorithms this is illustrated by a problem in combinatorial group theory compression of sparse binary strings encoding of contiguous binary strings of unknown lengths ranking of permutations and combinations strategies of games and other examples two abstract counting systems are given from which the concrete ones used for the applications can be derived

l codes and number systems abstract the notion of an l code is introduced as a generalization of the customary notion of a code attention is focused on unary l codes where the target alphabet consists of one letter only unary l codes can be identified with such number systems where the representation is unique surprisingly many unary morphisms are l codes furthermore even for non l codes there is only one exceptional length we also give a complete classification for the binary case

birth and death of the double scroll abstract the double scroll is a chaotic attractor observed from an extremely simple electronic circuit made of 4 linear circuit elements 2 capacitors 1 inductor and 1 resistor and a 2 terminal nonlinear resistor characterized by a 3 segment piecewise linear v i characteristic this nonlinear resistor can be built in the laboratory using 2 transistors and diodes the qualitative behavior of the double scroll attractor has been described elsewhere where each cross section of the double scroll attractor is shown to consist of 2 tightly wound spirals our objective in this paper is to present a bifurcation analysis of this circuit in terms of 2 basic parameters various bifurcation phenomena such as hopf bifurcation period doubling cascades rossler s spiral and screw type attractors periodic windows shilnikov phenomenon double scroll and boundary crisis are described in particular special emphasis is given to the mechanisms leading to the birth and the death of the double scroll attractor all bifurcation phenomena described in this paper are observed not only experimentally but also confirmed by digital computer simulations moreover an analytical foundation of the double scroll family of equations has been developed and used to explain in a rigorous way all observed bifurcation phenomena in addition rossler s spiral type and screw type attractors have been observed from the same circuit where the nonlinear resistor has only one break point i e it is described by a 2 segment piecewise linear v i characteristic this means that extremely complicated non periodic chaotic waveforms can arise in the simplest third order uncoupled electrical circuit in which all elements except one a resistor are linear and passive and in which the constitutive relation of the nonlinear resistor is made of the simplest conceivable nonlinearity namely 2 straight line segments

on the sequentiality of the successor function abstract letube a strictly increasing sequence of integers by a greedy algorithm every nonnegative integer has a greedyu representation the successor function maps the greedyu representation ofnonto the greedyu representation ofn 1 we characterize the sequencesusuch that the successor function associated withuis a left resp a right sequential function we also show that the odometer associated touis continuous if and only if the successor function is right sequential

measurement of linear dependence and feedback between multiple time series abstract measures of linear dependence and feedback for multiple time series are defined the measure of linear dependence is the sum of the measure of linear feedback from the first series to the second linear feedback from the second to the first and instantaneous linear feedback the measures are nonnegative and zero only when feedback causality of the relevant type is absent the measures of linear feedback from one series to another can be additively decomposed by frequency a readily usable theory of inference for all of these measures and their decompositions is described the computations involved are modest

estimation of large scale dimension densities we propose a technique to calculate large scale dimension densities in both higher dimensional spatio temporal systems and low dimensional systems from only a few data points where known methods usually have an unsatisfactory scaling behavior this is mainly due to boundary and finite size effects with our rather simple method we normalize boundary effects and get a significant correction of the dimension estimate this straightforward approach is based on rather general assumptions so even weak coherent structures obtained from small spatial couplings can be detected with this method which is impossible by using the lyapunov dimension density we demonstrate the efficiency of our technique for coupled logistic maps coupled tent maps the lorenz attractor and the roessler attractor

on lindenmayerian algebraic sequences abstract we define and study lindenmayerian algebraic sequences these sequences are a generalization of algebraic sequences k regular sequences and automatic sequences

a linear theory for noncausality abstract different definitions of noncausality according to granger sims haugh and pierce are analyzed in terms of orthogonality in the hilbert space of square integrable variables conditions when necessary are given for their respective equivalence some problems of testability are mentioned finally noncausality is also analyzed in terms of rational expectations extending previous results of sims author

the ring of k regular sequences ii in this paper we continue our study of k regular sequences begun in 1992 we prove some new results give many new examples from the literature and state some open problems

real numbers having ultimately periodic representations in abstract numeration systems using a genealogically ordered infinite regular language we know how to represent an interval of r numbers having an ultimately periodic representation play a special role in classical numeration systems the aim of this paper is to characterize the numbers having an ultimately periodic representation in generalized systems built on a regular language the syntactical properties of these words are also investigated finally we show the equivalence of the classical expansions with our generalized representations in some special case related to a pisot number

ambiguity and decision problems concerning number systems the representation of integers in arbitrary number systems is considered the main emphasis is on problems concerning ambiguity completeness and equivalence a rather general automata theoretic method for solving such in essence purely number theoretic problems is developed the method seems to be applicable in a variety of different situations

parameter adaptive identical synchronization disclosing lorenz chaotic masking a parameter adaptive rule that globally synchronizes oscillatory lorenz chaotic systems with initially different parameter values is reported in principle the adaptive rule requires access to the three state variables of the drive system but it has been readapted to work with the exclusive knowledge of only one variable a potential message carrier the rule is very robust and can be used to trace parameter modulation conveying hidden messages the driven system is defined according to a drive driven type of coupling that guarantees synchronization if parameters are identical from any arbitrary initial state the parameters of the driven system are dynamically adapted to reach convergence to the drive parameter values at this point synchronization mismatch or parameter tracing is used to unmask any potential hidden message

chaos in a three dimensional single loop feedback system with a piecewice linear feedbackk function abstract this paper describes chaotic behaviour in a single loop feedback system of low order the system is particularly simple and because it is piecewise linear and hence can be undersdtood globally a description of the flow much more complete than usual can be given an orbit structure is suggested for the system after a minor approximation is considered the approximation gives two equivalent discrete one dimensional maps of the interval to itself and these maps are discussed in the light of recent work the validity of the approximation is confirmed by computer simulation

a generalization of automatic sequences abstract we generalize the uniform tag sequences of cobham which arise as images of fixed points of k uniform homomorphisms to the case where the homomorphism is not necessarily uniform but rather satisfies the analogue of an algebraic equation we show that these sequences coincide with 1 a the class of sequences accepted by a finite automaton with generalized digits as input and 2 b generalizations of the locally catenative formula of rozenberg and lindenmayer examples include the infinite fibonacci word which is generated as the fixed point of the homomorphism a ab b a and sequences of rauzy and de bruijn

detecting nonstationarity and state transitions in a time series one cause of complexity in a time series may be due to nonstationarity and transience in this paper we analyze the nonstationarity and transience in a number of dynamical systems we find that the nonstationarity in the metastable chaotic lorenz system is due to nonrecurrence the latter determines a lack of fractal structure in the signal in 1 f alpha noise we find that the associated correlation dimension are local graph dimensions calculated from sojourn points we also design a transient lorenz system with a slowly oscillating controlling parameter and a transient rossler system with a slowly linearly increasing parameter with parameter ranges covering a sequence of chaotic dynamics with increased phase incoherence state transitions from periodic to chaotic and vice versa are identified together with different facets of nonstationarity in each phase

numeration systems on a regular language arithmetic operations recognizability and formal power series abstract generalizations of numeration systems in which n is recognizable by a finite automaton are obtained by describing a lexicographically ordered infinite regular language l for these systems we obtain a characterization of recognizable sets of integers in terms of n rational formal series after a study of the polynomial regular languages we show that if the complexity of l is n l resp if l is the complement of a polynomial language then multiplication by n preserves recognizability only if l 1 resp if for some n finally we obtain sufficient conditions for the notions of recognizability for abstract systems and some positional number systems to be equivalent

testing causality using efficiently parametrized vector arma models we outline a practical methodology for fitting to data vector autoregressive moving average models and employ these models to test for granger causality the procedures are applied to data on employment and hourly wages in manufacturing in the united states

lattice bhatnagar gross krook model for the lorenz attractor abstract in this paper we propose a new lattice bhatnagar gross krook model for simulation of the lorenz attractor the new model is based on a nonlinear diffusion reaction system we formulate a lattice bhatnagar gross krook model for the nonlinear diffusion reaction system by using a method of higher moments of the lattice boltzmann equation as a special case where the diffusion effect disappears we get the lorenz equation in the model we obtain a series of lattice boltzmann equations at different time scales and the conservation law at time scale t0 the equilibrium distribution functions are simpler than those for the standard lattice boltzmann model the numerical examples show that the method can be used to simulate the lorenz equation

on lindenmayerian algebraic power series abstract we define lindenmayerian algebraic power series and study their properties these series generalize both algebraic series and etol languages

testing causality between two vectors in multivariate autoregressive moving average models abstract in the analysis of economic time series a question often raised is whether a vector of variables causes another one in the sense of granger most of the literature on this topic is concerned with bivariate relationships or uses finite order autoregressive specifications the purpose of this article is to develop a causality analysis in the sense of granger for general vector autoregressive moving average arma models we give a definition of granger noncausality between vectors which is a natural and simple extension of the notion of granger noncausality between two variables in our context this definition is shown to be equivalent to a more complex definition proposed by tjostheim for the class of linear invertible processes we derive a necessary and sufficient condition for noncausality between two vectors of variables when the latter do not necessarily include all the variables considered in the analysis this result is then specialized to the class of stationary invertible arma process

automata and languages generalized to ω continuous semirings abstract we generalize the following two language and automata theoretic results to continuous semirings i the family of languages accepted by finite automata is the smallest class containing all finite languages and closed under union product and star kleene s theorem ii the family of languages accepted by pushdown automata is the family ofcontext free languages

decimations of languages and state complexity let the words of a language l be arranged in increasing radix order l w 0 w 1 w 2 we consider transformations that extract terms from l in an arithmetic progression for example two such transformations are even l w 0 w 2 w 4 and odd l w 1 w 3 w 5 lecomte and rigo observed that if l is regular then so are even l odd l and analogous transformations of l we find good upper and lower bounds on the state complexity of this transformation we also give an example of a context free language l such that even l is not context free

on d0l systems with immigration abstract we study dol systems with immigration we show that sequence and growth equivalence are decidable we establish regularity and decidability results concerning degrees of ambiguity as a consequence of results about subword complexity we show that regularity and regularity are decidable for languages generated by growing systems

lorenz like systems and classical dynamical equations with memory forcing an alternate point of view for singling out the origin of chaos an alternate view for the emergence of chaos in lorenz like systems is presented in this paper for such purpose the lorenz problem is reformulated in a classical mechanical form and it turns out to be equivalent to the problem of a damped and forced one dimensional motion of a particle in a two well potential with a forcing term depending on the memory of the particle past motion the dynamics of the original lorenz system in the proposed particle phase space can then be rewritten in terms of a one dimensional first exit time problem the emergence of chaos turns out to be due to the discontinuous solutions of the transcendental equation ruling the time for the particle to cross the intermediate potential wall the whole problem is tackled analytically deriving a piecewise linearized lorenz like system that preserves all the essential properties of the original model