measuring the strangeness of strange attractors we study the correlation exponent v introduced recently as a characteristic measure of strange attractors which allows one to distinguish between deterministic chaos and random noise the exponent v is closely related to the fractal dimension and the information dimension but its computation is considerably easier its usefulness in characterizing experimental data which stem from very high dimensional systems is stressed algorithms for extracting v from the time series of a single variable are proposed the relations between the various measures of strange attractors and between them and the lyapunov exponents are discussed it is shown that the conjecture of kaplan and yorke for the dimension gives an upper bound for v various examples of finite and infinite dimensional systems are treated both numerically and analytically

quantifying the closeness of fractal measures numerically fractal measures are represented by finite sets of discrete points e g those generated by trajectories we introduce a cross correlation integral to evaluate the distinctness and overlap of two such sets and present a criterion to determine up to what precision the two sets are realizations of the same measure

recurrence plots revisited abstract we show that recurrence plots rps give detailed characterizations of time series generated by dynamical systems driven by slowly varying external forces for deterministic systems we show that rps of the time series can be used to reconstruct the rp of the driving force if it varies sufficiently slowly if the driving force is one dimensional its functional form can then be inferred up to an invertible coordinate transformation the same results hold for stochastic systems if the rp of the time series is suitably averaged and transformed these results are used to investigate the nonlinear prediction of time series generated by dynamical systems driven by slowly varying external forces we also consider the problem of detecting a small change in the driving force and propose a surrogate data technique for assessing statistical significance numerically simulated time series and a time series of respiration rates recorded from a subject with sleep apnea are used as illustrative examples

gauss map of minimal surfaces with ramification we prove that for any complete minimal surface m immersed in r n if in cp n 1 there are q n n 1 2 hyperplanes h j in general position such that the gauss map of m is ramified over h j with multiplicity at least e j for each j and formule then m must be flat

time series and dependent variables we present a new method for analyzing time series which is designed to extract inherent deterministic dependencies in the series the method is particularly suited to series with broad band spectra such as chaotic series with or without noise we derive quantities j e based on conditional probabilities whose magnitude roughly speaking is an indicator of the extent to which the kth element in the series is a deterministic function of the k j th element to within a measurement uncertainty e we apply our method to a number of deterministic time series generated by chaotic processes such as the tent logistic and h non maps as well as to sequences of quasi random numbers in all cases the 6j correctly indicate the expected dependencies we also show that the j are robust to the addition of substantial noise in a deterministic process in addition we derive a predictability index which is a measure of the extent to which a time series is predictable given some tolerance e finally we discuss the behavior of the 6i as e approaches zero

uncovering dynamic behaviors underlying experimental oil water two phase flow based on dynamic segmentation algorithm abstract characterizing complex dynamic behaviors arising from various inclined oil water two phase flow patterns is a challenging problem in the fields of nonlinear dynamics and fluid mechanics we systematically carried out inclined oil water two phase flow experiments for measuring the time series conductance fluctuating signals of different flow patterns we using the dynamic segmentation algorithm incorporating with phase space reconstruction analyze the measured experimental signals to uncover the dynamic behaviors underlying different flow patterns specifically given a time series from a two phase flow we move a sliding pointer over the time series and for each position of the pointer we calculate the dynamic difference measure of the phase space orbits generated from the segment to the left and to the right of the pointer a number of experimental signals under different flow conditions are investigated in order to reveal the dynamical characteristics of inclined oil water flows the results indicate that the heterogeneity of dynamic difference measure series is sensitive to the transition among different flow patterns and the standard deviation of dynamic difference measure series can yield quantitative insights into the nonlinear dynamics of the two phase flow these properties render the dynamic segmentation algorithm based approach particularly useful for uncovering the dynamic behaviors of inclined oil water two phase flows

detecting switch dynamics in chaotic time waveform using a parametrized family of nonlinear predictors abstract an algorithm is presented for detecting switch dynamics in chaotic time waveform by the switch dynamics we mean that the chaotic time waveform is measured from a dynamical system whose bifurcation parameters are occasionally switched among a set of slightly different parameter values first the switched chaotic time waveform is divided into windows of short term time waveforms from the set of windowed time waveforms qualitatively similar parametrized family of nonlinear predictors is constructed qualitatively similar parametrized family means that the family of nonlinear predictors exhibits qualitatively similar bifurcation phenomena as the original by characterizing the windows of short term chaotic time waveforms in terms of the qualitative parameters of nonlinear predictors switch dynamics of their associated bifurcation parameters are detected for the lorenz equations the rossler equations and the mackey glass equations efficiency of the algorithm is demonstrated in the experiment chaotic time waveforms contaminated with observational noise is considered

algebroid functions wirsing s theorem and their relations in this paper we first point out a relationship between the second main theorem for algebriod functions in nevanlinna theory and wirsing s theorem in diophantine approximation this motivates a unified proof for both theorems the second part of this paper deals with moving targets problem for holomorphic maps to riemann surfaces its counterpart in diophantine approximation follows from a recent work of thomas j tucker in this paper we point out tucker s result in the special case of the approximation by rational points could be obtained by doing a translation and applying the corresponding result with fixed target however we could not completely recover tucker s result concerning the approximation by algebraic points in the last part of this paper cases in higher dimensions are studied some partial results in higher dimensions are obtained and some conjectures are raised

seizure warning algorithm based on optimization and nonlinear dynamics there is growing evidence that temporal lobe seizures are preceded by a preictal transition characterized by a gradual dynamical change from asymptomatic interictal state to seizure we herein report the first prospective analysis of the online automated algorithm for detecting the preictal transition in ongoing eeg signals such the algorithm constitutes a seizure warning system the algorithm estimates stlmax a measure of the order or disorder of the signal of eeg signals recorded from individual electrode sites the optimization techniques were employed to select critical brain electrode sites that exhibit the preictal transition for the warning of epileptic seizures specifically a quadratically constrained quadratic 0 1 programming problem is formulated to identify critical electrode sites the automated seizure warning algorithm was tested in continuous long term eeg recordings obtained from 5 patients with temporal lobe epilepsy for individual patient we use the first half of seizures to train the parameter settings which is evaluated by roc receiver operating characteristic curve analysis with the best parameter setting the algorithm applied to all cases predicted an average of 91 7 of seizures with an average false prediction rate of 0 196 per hour these results indicate that it may be possible to develop automated seizure warning devices for diagnostic and therapeutic purposes

schmidt s subspace theorem with moving targets in recent years due to work of vojta lang osgood etc people have started to realize that there is a close relationship between nevanlinna theory and diophantine approximation p vojta has compiled a dictionary see vojta v1 providing correspondences for the concepts fundamental to the two theories the second main theorem for meromorphic functions is the most important result in nevanlinna theory and its counterpart in number theory via vojta s dictionary is roth s theorem in 1929 r nevanlinna conjectured that the second main theorem remains correct if distinct points in p1 c are replaced by distinct holomorphic maps ai c p1 c with tai r o tf r where tf r is the nevanlinna characteristic function of the holomorphic map f c p1 c see rs 1 for the definition after many attempts by various people osgood proved the conjecture in 1985 which is now known as the second main theorem with moving targets in 1986 steinmetz gave another simple and elegant proof recently vojta v 2 and v 3 formulated and proved its counterpart in number theory theorem a roth s theorem with moving targets let k be a number field and let s be a finite set of places of k let q z 0 and let 0 then there does not exist an infinite sequence of distinct tuples

stationarity and nonstationarity in time series analysis abstract in this paper we introduce a new class of methods to test model and describe nonstationary processes to frame these methods we generalize the dynamical description of autonomous systems to the case of nonautonomous systems of particular interest are systems for which the driving force is recurrent for these systems we describe a method to find recurrences and to improve the statistics in reconstructing the tine series and consequently to improve the predictability another objective is a proper description of the nonstationarity all these methods are applied to four examples

holomorphic curves and integral points off divisors we deal with the distributions of holomorphic curves and integral points off divisors we will simultaneously prove an optimal dimension estimate from above of a subvariety w off a divisor d which contains a zariski dense entire holomorphic curve or a zariski dense d integral point set provided that in the latter case everything is defined over a number field then if the number of components of d is large the estimate leads to the constancy of such a holomorphic curve or the finiteness of such an integral point set at the beginning we extend logarithmic bloch ochiai s theorem to the kahler case

a fast general purpose algorithm for the computation of auto and cross correlation integrals from single channel data abstract we developed an optimized algorithm that allows computation of auto and cross correlation integrals from single channel time series without restricting the range of hypersphere radii and embedding dimensions optimization was achieved by eliminating any multiple computation of subsets entering the distance function in the time delay reconstruction of the phase space repeatedly for increasing embedding dimensions this is most effective when using the maximum norm compared to more naive implementations an improvement of 2 3 was achieved depending on the type of workstation the operating system and the compiler an additional optimization for 80 86 assembly language allows torun the algorithm on a standard personal computer as fast as on a workstation in contrast to other implementations the execution speed of this algorithm is nearly unaffected by the type of underlying data thus it is optimal for real time analyses

testing stationarity in time series we propose a procedure for testing stationarity of time series by combining a test for time independence of the probability density with one of the spectral density the potentials of this test procedure are demonstrated by its application to various types of numerically simulated time series ranging from simple linear stochastic processes to high dimensional transient chaos problems of practical implementation are discussed in particular the relation between the lengths of the time series and its maximal relevant time scales stationarity is then tested for experimental data from geophysics and physiology exchange rates are found to be stationary on time scales of decades in the sense that their spectral densities do not significantly change

an effective schmidt s subspace theorem over function fields we establish an effective version of the schmidt s subspace theorem for higher dimensional function fields of characteristic zero

color texture segmentation using unsupervised graph cuts this paper proposes a novel approach to color texture segmentation based on graph cut techniques which finds an optimal color texture segmentation of a color textured image by regarding it as a minimum cut problem in a weighted graph a new texture descriptor based on the texton theory is introduced to efficiently represent texture attributes of the given image then the segmentation is formulated in terms of energy minimization with graph cuts where color and texton features are modelled with a multivariate finite mixture model with an unknown number of components contrary to previous supervised graph cut approaches our method finds minimum cuts using split moves in an unsupervised way the segmentation result including the number of segments is determined during the split moves without user interaction thus our method is called unsupervised graph cuts experimental results of color texture segmentation using various images including the mit vistex datasets and the berkeley datasets are presented and analyzed in terms of precision and recall to verify its effectiveness

combined analytical and numerical approaches in dynamic stability analyses of engineering systems abstract dynamic stability is a widely studied area that has attracted many researchers from various disciplines although dynamic stability is usually associated with mechanics theoretical physics or other natural and technical disciplines it is also relevant to social economic and philosophical areas of our lives therefore it is useful to occasionally highlight the general aspects of this amazing area to present some relevant examples and to evaluate its position among the various branches of rational mechanics from this perspective the aim of this study is to present a brief review concerning the dynamic stability problem its basic definitions and principles important phenomena research motivations and applications in engineering the relationships with relevant systems that are prone to stability loss encountered in other areas such as physics other natural sciences and engineering are also noted the theoretical background which is applicable to many disciplines is presented in this paper the most frequently used dynamic stability analysis methods are presented in relation to individual dynamic systems that are widely discussed in various engineering branches in particular the lyapunov function and exponent procedures routh hurwitz lienard and other theorems are outlined together with demonstrations the possibilities for analytical and numerical procedures are mentioned together with possible feedback from experimental research and testing the strengths and shortcomings of these approaches are evaluated together with examples of their effective complementing of each other the systems that are widely encountered in engineering are presented in the form of mathematical models the analyses of their dynamic stability and post critical behaviour are also presented the stability limits bifurcation points quasi periodic response processes and chaotic regimes are discussed the limit cycle existence and stability are examined together with their separating roles as attractors and repulsers two levels of stability loss recovery of the system is possible or final collapse is inevitable as can be observed in softening systems are noted time limited excitation and relevant transition effects e g seismic excitation are also discussed together with the evaluation of possible system reliability improvement the dynamic stability investigation of two degrees of freedom aero elastic systems in a linear formulation using several approaches is briefly highlighted further systems modelling problems that arise in transport engineering are also outlined a few hints for applications are given some open problems and possible future research strategies are outlined