a coalgebraic perspective on linear weighted automata weighted automata are a generalisation of non deterministic automata where each transition in addition to an input letter has also a quantity expressing the weight e g cost or probability of its execution as for non deterministic automata their behaviours can be expressed in terms of either weighted bisimilarity or weighted language equivalence coalgebras provide a categorical framework for the uniform study of state based systems and their behaviours in this work we show that coalgebras can suitably model weighted automata in two different ways coalgebras on set the category of sets and functions characterise weighted bisimilarity while coalgebras on vect the category of vector spaces and linear maps characterise weighted language equivalence relying on the second characterisation we show three different procedures for computing weighted language equivalence the first one consists in a generalisation of the usual partition refinement algorithm for ordinary automata the second one is the backward version of the first one the third procedure relies on a syntactic representation of rational weighted languages

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

border collision period doubling scenario using a one dimensional dynamical system representing a poincare return map for dynamical systems ofthe lorenz type we investigate the border collision period doubling bifurcation scenario in contrast to theclassical period doubling scenario this scenario is formed by a sequence of pairs of bifurcations whereby eachpair consists of a border collision bifurcation and a pitchfork bifurcation the characteristic properties of thisscenario like symmetry breaking and symmetry recovering as well as emergence of coexisting attractors andnoninvariant attractive sets are investigated doi 10 1103 physreve 70 026222 pacs number s 05 45 ac 82 40 bj 95 10 fhi introduction

determinization of weighted finite automata over strong bimonoids we consider weighted finite automata over strong bimonoids where these weight structures can be considered as semirings which might lack distributivity then in general the well known run semantics initial algebra semantics and transition semantics of an automaton are different we prove an algebraic characterization for the initial algebra semantics in terms of stable finitely generated submonoids moreover for a given weighted finite automaton we construct the nerode automaton and myhill automaton both being crisp deterministic which are equivalent to the original automaton with respect to the initial algebra semantics respectively the transition semantics we prove necessary and sufficient conditions under which the nerode automaton and the myhill automaton are finite and we provide efficient algorithms for their construction also for a given weighted finite automaton we show sufficient conditions under which a given weighted finite automaton can be determinized preserving its run semantics

discontinuity induced bifurcation cascades in flows and maps with application to models of the yeast cell cycle abstract this paper applies methods of numerical continuation analysis to document characteristic bifurcation cascades of limit cycles in piecewise smooth hybrid dynamical system models of the eukaryotic cell cycle and associated period adding cascades in piecewise defined maps with gaps a general theory is formulated for the occurrence of such cascades for example given the existence of a period two orbit with one point on the system discontinuity and with appropriate constraints on the forward trajectory for nearby initial conditions in this case it is found that the bifurcation cascade for nearby parameter values exhibits a scaling relationship governed by the largest in magnitude floquet multiplier here required to be positive and real in complete agreement with the characteristic scaling observed in the numerical study a similar cascade is predicted and observed in the case of a saddle node bifurcation of a period two orbit away from the discontinuity provided that the associated center manifold is found to intersect the discontinuity transversally

crises sudden changes in chaotic attractors and transient chaos abstract the occurrence of sudden qualitative changes of chaotic dynamics as a parameter is varied is discussed and illustrated it is shown that such changes may result from the collision of an unstable periodic orbit and a coexisting chaotic attractor we call such collisions crises phenomena associated with crises include sudden changes in the size of chaotic attractors sudden appearances of chaotic attractors a possible route to chaos and sudden destructions of chaotic attractors and their basins this paper presents examples illustrating that crisis events are prevalent in many circumstances and systems and that just past a crisis certain characteristic statistical behavior whose type depends on the type of crisis occurs in particular the phenomenon of chaotic transients is investigated the examples discussed illustrate crises in progressively higher dimension and include the one dimensional quadratic map the two dimensional henon map systems of ordinary differential equations in three dimensions and a three dimensional map in the case of our study of the three dimensional map a new route to chaos is proposed which is possible only in invertible maps or flows of dimension at least three or four respectively based on the examples presented the following conjecture is proposed almost all sudden changes in the size of chaotic attractors and almost all sudden destruction or creations of chaotic attractors and their basins are due to crises

dynamics and bifurcations of nonsmooth systems a survey abstract in this survey we discuss current directions of research in the dynamics of nonsmooth systems with emphasis on bifurcation theory an introduction to the state of the art also for non specialists is complemented by a presentation of the main open problems we illustrate the theory by means of elementary examples the main focus is on piecewise smooth systems which have recently attracted a lot of attention but we also briefly discuss other important classes of nonsmooth systems such as nowhere differentiable ones and differential variational inequalities this extended framework allows us to put the diverse range of papers and surveys in this special issue in a common context a dedicated section is devoted to concrete applications that stimulate the development of the field this survey is concluded by an extensive bibliography

the bandcount increment scenario iii deformed structures bifurcation structures in two dimensional parameter spaces formed by chaotic attractors alone are still a long way from being understood completely in a series of three papers we investigated the chaotic domain without periodic inclusions for a map which is considered by many authors as some kind of one dimensional canonical form for discontinuous maps in part i the basic structures in the chaotic region are explained by the bandcount increment scenario in part ii fine self similar substructures nested into the bandcount increment scenario are explained by the bandcount adding and doubling scenarios nested into each other ad infinitum hereby we fixed in both previous parts one of the parameters to a non generic value and studied the remaining two dimensional parameter subspace in this part iii finally we investigated the structures under variation of this third parameter remarkably this step is the most important with respect to practical applications since it cannot be expected that these operate exactly at the previously investigated specific value

a comparison of generalized cross validation and modified maximum likelihood for estimating the parameters of a stochastic process wahba compared the performance of generalized cross validation gcv and modified maximum likelihood mml procedures for choosing the smoothing parameter of a smoothing spline this work makes a more careful study of the two procedures when the stochastic model motivating the modified maximum likelihood estimate is correct it is shown that in the case of the linear smoothing spline with equally spaced observations both estimates are asymptotically normal with the gcv estimate having twice the asymptotic variance of the mml estimate the impact of using these estimates on the subsequent predictions is also calculated

estimating properties of autoregressive forecasts abstract forecasting requires estimates of the error of prediction however such estimates for autoregressive forecasts depend nonlinearly on unknown parameters and distributions substitution estimators of mean squared error mse possess bias that varies with the underlying model and gaussian based prediction intervals fail if the data are not normally distributed this article proposes methods that avoid these problems a second order taylor expansion produces an estimator of mse that is unbiased and leads to accurate prediction intervals for gaussian data bootstrapping also suggests an estimator of mse but it is approximately the problematic substitution estimator bootstrapping also yields prediction intervals however whose coverages are invariant of the sampling distribution and asymptotically approach the nominal content parameter estimation increases the error in autoregressive forecasts this additional error inflates one step prediction mean squared error pmse by a factor of 1 p t wh

properties of predictors for autoregressive time series abstract the prediction of the n s th observation of the pth order autoregressive process is investigated the mean square of the predictor error through terms of order n 1 conditional on yn y n 1 y n p 1 is obtained for the stationary normal process the mean squared error expression is similar to the usual regression formula for the variance of the predictor error the usual regression formula for the estimated variance of a predictor error and its generalization to s period prediction is shown to provide a consistent estimator of the mean squared error of the least squares predictor for both stationary and non stationary processes

prediction tests for structural stability abstract three groups of test statistics for testing structural stability are compared the statistics are based on predictions from univariate time series models the first group ignores the specification and estimation variability the second group ignores only the specification uncertainty while the statistics in the third group take into account both specification and estimation variability although corresponding statistics in the three groups have identical asymptotic distributions their small sample distributions differ markedly it is suggested to use the statistics in the third group in practice

minimization algorithms for sequential transducers abstract we present general algorithms for minimizing sequential finite state transducers that output strings or numbers the algorithms are shown to be efficient since in the case of acyclic transducers and for output strings they operate in o s e v e v f p max 1 steps where s is the sum of the lengths of all output labels of the resulting transducer e the set of transitions of the given transducer v the set of its states f the set of final states and p max one of the longest of the longest common prefixes of the output paths leaving each state of the transducer the algorithms apply to a larger class of transducers which includes subsequential transducers

the bandcount increment scenario ii interior structures bifurcation structures in the two dimensional parameter spaces formed by chaotic attractors alone are still far away from being understood completely in a series of three papers we investigate th

an improved algorithm for determinization of weighted and fuzzy automata for a given weighted finite automaton over a strong bimonoid we construct its reduced nerode automaton which is crisp deterministic and equivalent to the original weighted automaton with respect to the initial algebra semantics we show that the reduced nerode automaton is even smaller than the nerode automaton which was previously used in determinization related to this semantics we determine necessary and sufficient conditions under which the reduced nerode automaton is finite and provide an efficient algorithm which computes the reduced nerode automaton whenever it is finite in determinization of weighted finite automata over semirings and fuzzy finite automata over lattice ordered monoids this algorithm gives smaller crisp deterministic automata than any other known determinization algorithm

uniform moment bounds of fisher s information with applications to time series in this paper a uniform over some parameter space moment bound for the inverse of fisher s information matrix is established this result is then applied to develop moment bounds for the normalized least squares estimate in nonlinear stochastic regression models the usefulness of these results is illustrated using time series models in particular an asymptotic expression for the mean squared prediction error of the least squares predictor in autoregressive moving average models is obtained this asymptotic expression provides a solid theoretical foundation for some model selection criteria

the bifurcation to homoclinic tori in the quasiperiodically forced duffing oscillator abstract using recently developed techniques of wiggins 1988 we study the bifurcation to homoclinic tori in the quasiperiodically forced duffing oscillator we show how homoclinic tori give rise to chaotic dynamics for single degree of freedom quasiperiodically forced oscillators in much the same way as smale horseshoes in the periodically forced case we give a complete description of the bifurcation set in the five dimensional parameter space for the two frequency forced duffing oscillator and then show how the two frequency results can be used to understand the effects of an arbitrary but finite number of frequencies

bias in dynamic panel models under time series misspecification abstract we consider within group estimation of higher order autoregressive panel models with exogenous regressors and fixed effects where the lag order is possibly misspecified even when disregarding the misspecification bias the fixed effect bias formula is quite different from the correctly specified case though its asymptotic order remains the same under the stationarity we suggest bias reduction methods under the possible time series misspecification

double crises in two parameter dynamical systems a crisis is a sudden discontinuous change in a chaotic attractor as a system parameter is varied we investigate phenomena observed when two parameters of a dissipative system are varied simultaneously following a crisis along a curve in the parameter plane two such curves intersect at a point we call a double crisis vertex the phenomena we study include the double crisis vertex at which an interior and a boundary crisis coincide and related forms of double crisis we show how an experimenter can infer a crisis from observations of other related crises at a vertex

nondeterministic moore automata and brzozowski s minimization algorithm moore automata represent a model that has many applications in this paper we define a notion of coherent nondeterministic moore automaton nma and show that such a model has the same computational power of the classical deterministic moore automaton we consider also the problem of constructing the minimal deterministic moore automaton equivalent to a given nma we propose an algorithm that is a variant of brzozowski s minimization algorithm in the sense that it is essentially structured as reverse operation and subset construction performed twice moreover we explore more general classes of nma and analyze the applicability of the algorithm for some of such classes the algorithm does not return the minimal equivalent deterministic automaton

effects of not knowing the order of an autoregressive process on the mean squared error of prediction i abstract given a realization of t consecutive observations of an autoregressive process x of unknown order m a process of an arbitrary order p is assumed to be fitted for predicting the future values of another process xtilde t where xtilde t is independent of xt but otherwise has identical probabilistic structure the mean squared error of prediction when the autoregressive coefficients are estimated by least squares is obtained to terms of order t 1 the bias in estimating the autoregressive coefficients is examined the results are illustrated for three processes with m 2 by considering fitting of a process with p 1

on detection of multi band chaotic attractors in this work we present two numerical methods for the detection of the number of bands of a multi band chaotic attractor the first method is more efficient but can be applied only for dynamical systems with a continuous system function whereas the second one is applicable for dynamical systems with a discontinuous system function as well using the developed methods we investigate a one dimensional piecewise linear map and report for both cases of a continuous and a discontinuous system functions some new bifurcation scenarios involving multi band chaotic attractors

determinization of transducers over finite and infinite words we study the determinization of transducers over finite and infinite words the first part of the paper is devoted to finite words we recall the characterization of subsequential functions due to choffrut we describe here a known algorithm to determinize a transducer in the case of infinite words we consider transducers with all their states final we give an effective characterization of sequential functions over infinite words we describe an algorithm to determinize transducers over infinite words this part contains the main novel results of the paper

border collision bifurcations including period two to period three for piecewise smooth systems abstract we examine bifurcation phenomena for maps that are piecewise smooth and depend continuously on a parameter in the simplest case there is a surface in phase space along which the map has no derivative or has two one sided derivatives is the border of two regions in which the map is smooth as the parameter is varied a fixed point e may collide with the border and we may assume that this collision occurs at 0 a variety of bifurcations occur frequently in such situations but never or almost never occur in smooth systems in particular e may cross the border and so will exist for 0 but it may be a saddle in one case say 0 for 0 there may be a stable period 3 orbit which similarly shrinks to e0 as 0 hence one observes the following stable periodic orbits a stable period 2 orbit collapses to a point and is reborn as a stable period 3 orbit we also see analogously stable period 2 to stable period p orbit bifurcations with p 5 11 52 or period 2 to quasi periodic or even to a chaotic attractor we believe this phenomenon will be seen in many applications

unfolding a chaotic bifurcation the differential equation of the sinusoidally forced pendulum is studied by digital simulation in a regime where two simple symmetrically related chaotic attractors grow and merge continuously as the forcing amplitude is increased by introducing a small constant bias in the forcing to break the symmetry two discontinuous bifurcations unfold from the single merging event considering both forcing amplitude and bias together as controls a codimension two bifurcation of chaotic attractors is defined whose geometric structure in control phase space is closely related to the elementary cusp catastrophe the chaotic bifurcations are explained in terms of homoclinic structures smale cycles in the poincare map

properties of predictors in misspecified autoregressive time series models abstract this article investigates major effects of misspecification in stationary linear time series models when we fit a pth order autoregressive model the true model can be an autoregressive moving average model we derive the formulas of bias and mean squared error mse of the least squares estimator and the hth period ahead prediction mse in the time domain contrary to previous studies the process in estimation is not necessarily independent of the process in prediction and the distribution of process is not necessarily gaussian we examine the effects of this dependence and nonnormality on prediction in misspecified models

subsampling and model selection in time series analysis in this paper the subsampling method of carlstein 1986 is used to estimate the risk of prediction for time series data we extend carlstein s result by proving strong consistency of the subsampling estimator and we propose a procedure for selecting a time series model empirically from a set of possibly nonnested and misspecified models by using estimated risk of prediction as a selection criterion when this procedure is applied to the selection of the order of an autoregressive model it is shown to be a consistent order selector if an appropriate subsample size is chosen we propose a practical model selection procedure with a common subsample size chosen by hall jing s 1996 procedure

the bandcount increment scenario i basic structures bifurcation structures in two dimensional parameter spaces formed only by chaotic attractors are still far away from being understood completely in a series of three papers we investigate the chaotic domain without periodic inclusions for a map which is considered by many authors as some kind of one dimensional canonical form for discontinuous maps in the first part we report a novel bifurcation scenario formed by crises bifurcations which includes multi band chaotic attractors with arbitrary high bandcounts and determines the basic structure of the chaotic domain

fibonacci heaps and their uses in improved network optimization algorithms in this paper we develop a new data structure for implementing heaps priority queues our structure fibonacci heaps abbreviated f heaps extends the binomial queues proposed by vuillemin and studied further by brown f heaps support arbitrary deletion from an n item heap in o log n amortized time and all other standard heap operations in o 1 amortized time using f heaps we are able to obtain improved running times for several network optimization algorithms in particular we obtain the following worst case bounds where n is the number of vertices and m the number of edges in the problem graph o n log n m for the single source shortest path problem with nonnegative edge lengths improved from o m log m n 2 n o n 2 log n nm for the all pairs shortest path problem improved from o nm log m n 2 n o n 2 log n nm for the assignment problem weighted bipartite matching improved from o nm log m n 2 n o m m n for the minimum spanning tree problem improved from o m log log m n 2 n where m n min i u log i n m n note that m n log n if m n of these results the improved bound for minimum spanning trees is the most striking although all the results give asymptotic improvements for graphs of appropriate densities

conditions for the existence of maximal factorizations abstract extending classical algorithms for ordinary weighted or string to string automata to automata with underlying more general algebraic structures is of significant practical and theoretical interest however the generalization of classical algorithms sets certain assumptions on the underlying structure in this respect the maximal factorization turns out to be a sufficient condition for many practical problems e g minimization and canonization recently an axiomatic approach on monoid structures suggested that monoids with most general equalizer mge monoids provide an alternative framework to achieve similar results in this paper we study the fundamental relation between monoids admitting a maximal factorization and mge monoids we describe necessary conditions for the existence of a maximal factorization and provide sufficient conditions for an mge monoid to admit a maximal factorization

minimization of rational word functions rational functions from a free monoid into another are characterized by the finiteness of the index of some congruence naturally associated with the function a sequential bimachine is constructed computing the function which is completely canonical and in some sense minimal this generalizes the nerode criterion and the minimal automaton of a rational language and similar results for sequential functions

deterministic synchronization of automations with bounded delay resume nous montrons qu un automate a delai borne sous sequentiel i e deterministe sur les entrees est equivalent a un automate en ligne c est a dire lettre a lettre apres une periode transitoire fixe ou l automate lit le debut de l entree sans rien sortir et sous sequentiel les resultats de synchronisation etablis anterieurement pour les automates a delai borne ne preservaient pas la sous sequentialite

economy of description for single valued transducers abstract in this article questions of economy of description are investigated in connection with single valued finite transducers the following results are shown 1 any single valued real time transducer m with n states can be effectively transformed into an equivalent unambiguous realtime transducer having at most 2n states 2 let m be a single valued real time transducer with n states and output alphabet which is equivalent to some deterministic real time or subsequential transducer m then m can be effectively transformed into such an m having at most 1 2n max 2 2n3i states where i is a local structural parameter of m 3 for any single valued real time transducer m it is decidable in deterministic polynomial time whether or not it is equivalent to some deterministic real time transducer to some subsequential transducer respectively the results 1 3 can be extended to the case where m is not necessarily real time the upper bound in 1 is at most one state off the optimal upper bound any possible improvement of the upper bound in 2 is greater than or equal to 2n 1

the bias of autoregressive coefficient estimators abstract this article presents simple expressions for the bias of estimators of the coefficients of an autoregressive model of arbitrary but known finite order the results include models both with and without a constant term the effects of overspecification of the model order on the bias are described the emphasis is on least squares and yule walker estimators but the methods extend to other estimators of similar design although only the order t 1 component of the bias is captured where t is the series length this asymptotic approximation is shown to be very accurate for least squares estimators through some numerical simulations the simulations examine fourth order autoregressions chosen to resemble some data series from the literature the order t 1 bias approximations for yule walker estimators need not be accurate especially if the zeros of the associated polynomial have moduli near 1 examples are given where the approximation is accurate and where it is useless the bias expressions are

accumulated prediction errors information criteria and optimal forecasting for autoregressive time series the predictive capability of a modification of rissanen s accumulated prediction error ape criterion ape n is investigated in infinite order autoregressive ar oo models instead of accumulating squares of sequential prediction errors from the beginning ape n is obtained by summing these squared errors from stage n n where n is the sample size and 1 n n 1 1 n may depend on n under certain regularity conditions an asymptotic expression is derived for the mean squared prediction error mspe of an ar predictor with order determined by ape n this expression shows that the prediction performance of ape n can vary dramatically depending on the choice of n another interesting finding is that when n approaches 1 at a certain rate ape n can achieve asymptotic efficiency in most practical situations an asymptotic equivalence between ape n and an information criterion with a suitable penalty term is also established from the mspe point of view this offers new perspectives for understanding the information and prediction based model selection criteria finally we provide the first asymptotic efficiency result for the case when the underlying ar oo model is allowed to degenerate to a finite autoregression

order selection for same realization predictions in autoregressive processes assume that observations are generated from an infinite order autoregressive ar process shibata ann statist 8 1980 147 164 considered the problem of choosing a finite order ar model allowing the order to become infinite as the number of observations does in order to obtain a better approximation he showed that for the purpose of predicting the future of an independent replicate akaike s information criterion aic and its variants are asymptotically efficient although shibata s concept of asymptotic efficiency has been widely accepted in the literature it is not a natural property for time series analysis this is because when new observations of a time series become available they are not independent of the previous data to overcome this difficulty in this paper we focus on order selection for forecasting the future of an observed time series referred to as same realization prediction we present the first theoretical verification that aic and its variants are still asymptotically elficient in the sense defined in section 4 for same realization predictions to obtain this result a technical condition easily met in common practice is introduced to simplify the complicated dependent structures among the selected orders estimated parameters and future observations in addition a simulation study is conducted to illustrate the practical implications of aic this study shows that aic also yields a satisfactory saute realization prediction in finite samples on the other hand a limitation of aic in same realization settings is pointed out it is interesting to note that this limitation of aic does not exist for corresponding independent cases

multifold predictive validation in armax time series models this article presents a new procedure for multifold predictive validation in time series the procedure is based on the so called filtered residuals in sample prediction errors evaluated in such a way that they are similar to out of sample ones the filtered residuals are obtained from parameters estimated by eliminating from the estimation process the estimated innovations at the points to be predicted thus instead of using the deletion of observations to validate the predictions as in classical cross validation the procedure is based on deletion of the estimated innovations it is proved that the filtered residuals are uncorrelated up to terms of small order with the in sample innovations a property shared with the out of sample residuals the parameters needed for computing the filtered residuals can be obtained by estimating a model with innovational outliers at the points to be predicted the proposed multifold predictive validation is asymptotically equivalent to an efficient model selecti

asymptotic analysis of the squared estimation error in misspecified factor models abstract in this paper we obtain asymptotic approximations to the squared error of the least squares estimator of the common component in large approximate factor models with possibly misspecified number of factors the approximations are derived under both strong and weak factors asymptotics assuming that the cross sectional and temporal dimensions of the data are comparable we develop consistent estimators of these approximations and propose to use them for model comparison and for selection of the number of factors we show that the estimators of the number of factors that minimize these loss estimators are asymptotically loss efficient in the sense of shibata 1980 li 1987 and shao 1997

codimension two bifurcations of nonlinear systems driven by fuzzy noise abstract by means of a fuzzy generalized cell mapping method a duffing van der pol oscillator in the presence of fuzzy noise is studied in a regime where two symmetrically related fuzzy period one attractors grow and merge as the intensity of the fuzzy noise is increased by introducing a small symmetry breaking parameter to break the symmetry the merging explosion bifurcation unfolds to a pattern of two catastrophic and explosive bifurcations considering both the intensity of the fuzzy noise and the symmetry breaking parameter together as controls a codimension two bifurcation of fuzzy attractors is defined and examples of additive and multiplicative fuzzy noise are given such a codimension two bifurcation is fuzzy noise induced effects which cannot be seen in the deterministic systems

amplitude modulated and chaotic dynamics in resonant motion of strings abstract the weakly non linear resonant motions of a stretched string to a harmonic planar excitation are investigated one mode truncation of the in plane and out of plane equation results in a two degree to freedom system which is examined by using the method of averaging and the method of integral manifolds it is shown that the averaged equations for small enough damping possess non planar constant solutions which become unstable by a hopf bifurcation the resulting limit cycle solutions correspond to amplitude modulated whirling or ballooning motions of the string there are two limit cycle branches for the averaged equations one arising due to the hopf bifurcation and the other due to a global saddle node bifurcation the two branches merge as the damping is further reduced also with variation in detuning the isolated branch exhibits period doubling bifurcations chaotic attractors and merging of attractors giving rise to rossler as well as lorentz type solutions the truncated string equations are also directly integrated it is shown that there are non planar periodic responses that bifurcate into amplitude modulated motions on a 2 torus changes in detuning result in torus doubling merging of tori and then destruction of the torus leading to chaotic amplitude modulations the results of asymptotic analysis via the method of averaging are found to be in qualitative agreement with the actual response

when is adaptive better than optimal given a stationary process let us predict it using a first order predictor whose single coefficient is adapted to the current observations using a constant gain identification algorithm we investigate the prediction error variance as a function of the adaptation gain i e the length of the memory the number of observations of the identification scheme an infinite memory corresponds to the asymptotically constant optimal predictor and a finite memory to a locally adaptive time varying predictor we show that in some specified situations the prediction error variance associated with the finite memory adaptation scheme is smaller that the optimal variance this can only occur if the model is misspecified i e the structure of the optimal predictor is too simple

predictions of multivariate autoregressive moving average models summary a simple formula for multiperiod predictions of multivariate autoregressive moving average models is derived the formula is explicitly given as a function of suitably defined parameter matrices and an observation vector and includes simpler models as its special cases the asymptotic prediction mean squared error is also derived for predictions with estimated parameters

boundary crisis in quasiperiodically forced systems abstract we study boundary crisis in quasiperiodically forced dissipative systems using the henon map as a characteristic example the crisis is due to a homoclinic tangency of the stable and unstable manifolds of an accessible invariant circle of saddle type on the basin boundary of the attractor numerical evidence shows that the type of boundary crisis can change as the saddle circle loses its accessibility due to the quasiperiodic forcing this implies the existence of codimension two double crisis vertices where a curve of boundary crisis and a curve of interior crisis meet we argue that bifurcation points of higher codimension must exist in the full parameter space

approximating stable and unstable manifolds in experiments we introduce a procedure to reveal invariant stable and unstable manifolds given only experimental data we assume a model is not available and show how coordinate delay embedding coupled with invariant phase space regions can be used to construct stable and unstable manifolds of an embedded saddle we show that the method is able to capture the fine structure of the manifold is independent of dimension and is efficient relative to previous techniques

weighted finite automata over strong bimonoids we investigate weighted finite automata over strings and strong bimonoids such algebraic structures satisfy the same laws as semirings except that no distributivity laws need to hold we define two different behaviors and prove precise characterizations for them if the underlying strong bimonoid satisfies local finiteness conditions moreover we show that in this case the given weighted automata can be determinized

dynamics of a piecewise linear map with a gap in this paper we consider periodic solutions of discontinuous non smooth maps we show how the fixed points of a general piecewise linear map with a discontinuity a map with a gap behave under parameter variation we show in detail all the possible behaviours of period 1 and period 2 solutions for positive gaps we find that period 2 solutions can exist independently of period 1 solutions conversely for negative gaps period 1 and period 2 solutions can coexist higher periodic orbits can also exist and be stable and we give several examples of how these solutions behave under parameter variation finally we compare our results with those of jain banerjee jain banerjee 2003 int j bifurcat chaos 13 3341 3351 and banerjee et al banerjee et al 2004 ieee trans circ syst ii 51 649 654 and explain their numerical simulations

codimension three bifurcations explanation of the complex one two and three dimensional bifurcation structures in nonsmooth maps many physical and engineering systems exhibit cascades of periodic attractors arranged in period increment and period adding sequences as a parameter is varied such systems have been found to yield piecewise smooth maps and in some cases the obtained map is discontinuous by investigating the normal form of such maps we have detected a type of codimension three bifurcation which serves as the organizing center of periodic and aperiodic dynamics in the parameter space the results will help in understanding the occurrence and structure of such cascades observed in many nonsmooth systems in science and engineering

a proof of choffrut s theorem on subsequential functions we prove an extension of the ginsburg rose theorem and as a corollary choffrut s topological characterization of subsequential functions

the sampling distributions of the predictor for an autoregressive model under misspecifications abstract approximations to the sampling distributions of the predictor are given misspecifying the autoregressive moving average model as an autoregressive model we deal with both conditional and unconditional distributions for the dependent and independent cases according to whether the sample data used in estimation and in prediction are dependent or not the bias and mean squared error are easily obtained from these approximations

complex balancing motions of an inverted pendulum subject to delayed feedback control we show that an inverted pendulum that is balanced on a cart by linear delayed feedback control may exhibit small chaotic motion about the upside down position in periodic windows associated with this chaotic regime we find periodic orbits of arbitrarily high period that correspond to complex balancing motion of the pendulum with bounded velocity of the cart this result shows that complex balancing is possible in a controlled mechanical system with a geometric nonlinearity even when the control law is only linear this is in contrast to other proposed models that require a nonlinearity of the controller such as round off due to digitization we find the complex motion by studying homoclinic bifurcations of a reduced three dimensional vector field near a triple zero eigenvalue singularity more generally the dynamics we describe must be expected in any system with a triple zero singularity and reflection symmetry

using out of sample mean squared prediction errors to test the martingale difference hypothesis abstract we consider using out of sample mean squared prediction errors mspes to evaluate the null that a given series follows a zero mean martingale difference against the alternative that it is linearly predictable under the null of no predictability the population mspe of the null no change model equals that of the linear alternative we show analytically and via simulations that despite this equality the alternative model s sample mspe is expected to be greater than the null s for rolling regression estimators of the alternative model s parameters we propose and evaluate an asymptotically normal test that properly accounts for the upward shift of the sample mspe of the alternative model our simulations indicate that our proposed procedure works well