Before we apply nonlinear techniques, for example those inspired by chaos theory, to dynamical phenomena occurring in nature, it is necessary to first ask if the use of such advanced techniques is justified by the data. While many processes in nature seem very unlikely a priori to be linear, the possible nonlinear nature might not be evident in specific aspects of their dynamics. The method of surrogate data has become a very popular tool to address such a question. However, while it was meant to provide a statistically rigorous, foolproof framework, some limitations and caveats have shown up in its practical use. In this paper, recent efforts to understand the caveats, avoid the pitfalls, and to overcome some of the limitations, are reviewed and augmented by new material. In particular, we will discuss specific as well as more general approaches to constrained randomisation, providing a full range of examples. New algorithms will be introduced for unevenly sampled and multivariate da...

A novel `Delay Vector Variance' (DVV) method for detecting the presence of determinism and nonlinearity in a time series is introduced. The method is based upon the examination of local predictability of a signal. Additionally, it spans the complete range of local linear models due to the standardisation to the distribution of pairwise distances between delay vectors. This provides consistent and easy-tointerpret diagrams, which convey information about the nature of a time series. In Preprint submitted to Elsevier Science 3 April 2002 order to gain further insight into the technique, a DVV scatter diagram is introduced, which plots the DVV curve against that for a globally linear model (surrogate data). This way, the deviation from the bisector line represents a qualitative measure of nonlinearity, which can be used additionally for constructing a quantitative measure for statistical testing. The proposed method is compared to existing methods on synthetic, as well as standard real-world signals, and is shown to provide more consistent results overall, compared to other, established nonlinearity analysis methods.

Recently, we introduced a new test for distinguishing regular from chaotic dynamics in deterministic dynamical systems and argued that the test had certain advantages over the traditional test for chaos using the maximal Lyapunov exponent. In this paper, we investigate the capability of the test to cope with moderate amounts of noisy data. Comparisons are made between an improved version of our test and both the “tangent space ” and “direct method ” for computing the maximal Lyapunov exponent. The evidence of numerical experiments, ranging from the logistic map to an eight-dimensional Lorenz system of differential equations (the Lorenz 96 system), suggests that our method is superior to tangent space methods and that it compares very favourably with direct methods.

A method for extracting information (or knowledge) about the nature of a signal is presented, this is achieved by tracking the dynamics of the mixing parameter within a hybrid filter rather than the actual filter performance. Implementations of the hybrid filter for tracking the nonlinearity and the sparsity of a signal are illustrated and simulations on benchmark synthetic data in a prediction configuration support the analysis. It is then shown that by combining the information obtained from both hybrid filters it is possible to use this method to gain a more complete understanding of the nature of signals and changes in signal modality. Index Terms — adaptive filters, collaborative signal processing, distributed signal processing, signal modality characterisation 1.

In this article, we introduce a methodology for comparing the nonlinearities present in sets of time series using four different nonlinearity measures, one of which, the `Delay Vector Variance' method, is a novel approach to the characterisation of a time series. It is then applied to examine the difference in nonlinearity between fMRI signals that have been recorded using different contrast agents. Recently, an exogenous contrast agent (MION) has been introduced for fMRI, which has been shown to increase the functional sensitivity compared to the traditional BOLD technique.

We present a method for extracting information (or knowledge) about the nature of a signal, this is achieved by employing recent developments in signal characterisation for online analysis of the changes in signal modality. We show that it is possible to use the fusion of the outputs of adaptive filters to produce a single collaborative hybrid filter and that by tracking the dynamics of the mixing parameter of this filter rather than the actual filter performance, a clear indication as to the nature of the signal is given. Implementations of the proposed hybrid filter in both the real R and complex C domains are analysed and the potential of such a scheme for tracking signal nonlinearity in both domains is highlighted. Simulations on linear and nonlinear signals in a prediction configuration support the analysis; real world applications of the approach have been illustrated on electroencephalogram (EEG), radar and wind data. 1.1

Abstract. The problem of investigation of temporal and/or spatial behavior of highly nonlinear or complex natural systems has long been of fundamental scientific interest. At the same time it is presently well understood that identification of dynamics of processes in complex natural systems, through their qualitative description and quantitative evaluation, is far from a purely academic question and has an essential practical importance. This is quite understandable as systems with complex dynamics abound in nature and examples can be found in very different areas such as medicine and biology (rhythms, physiological cycles, epidemics), atmosphere (climate and weather change), geophysics (tides, earthquakes, volcanoes, magnetic field variations), economy (financial markets behavior, exchange rates), engineering (friction, fracturing), communication (electronic networks, internet packet dynamics) etc. The past two decades of research on qualitative and especially quantitative investigations of dynamics of real processes of different origin brought significant progress in the understanding of behavior of natural processes. At the same time serious drawbacks have also been revealed. This is why exhaustive investigation of

Abstract. We consider convolving a Gaussian of a varying scale ɛ against a Borel measure μ on Euclidean δ-dimensional space. The L q norm of the result is differentiable in ɛ. We calculate this derivative and show how the upper order of its growth relates to the lower Rényi dimension of μ. We assume q is strictly between 1 and ∞ and that μ is finite with compact support. Consider choosing a sequence ɛn of scales for the Gaussians gɛ(x) =ɛ −δ e −(|x|/ɛ)2 Let �f�q denote the L q norm for Lebesgue measure. The differences ˛ ‚ gɛn+1 ∗ μ ‚ ˛ −�gɛn ∗ μ� q q˛ between the norms at adjacent scales ɛn and ɛn−1 canbemadetogrow more slowly than any positive power of n by setting the ɛn by a power rule. The correct exponent in the power rule is determined by the lower Rényi dimension. We calculate and find bounds on the derivative of the Gaussian kernel versions of the correlation integral. We show that a Gaussian kernel version of the Rényi entropy sum is continuous.

The unpredictability of the occurrence of epileptic seizures contributes to the burden of the disease to a major degree. Thus, various methods have been proposed to predict the onset of seizures based on EEG recordings. A nonlinear feature motivated by the correlation dimension is a seemingly promising approach. In a previous study this method was reported to identify `preictal dimension drops' up to 19 min before seizure onset, exceeding the variability of interictal data sets of 30±50 min duration. Here we have investigated the sensitivity and speci®city of this method based on invasive longterm recordings from 21 patients with medically intractable partial epilepsies, who underwent invasive

Abstract — In this paper a new RF (Radio Frequency) detection system has been descried. The proposed intrusion detection system uses one or more RF transmitters that emit RF into the space along with a well planed network of RF receivers for detection, the use of Degree of Angle (DOA) has been considered to locate intrusion. The captured RF signals are processed using developed digital space algorithms. Though in many aspects, the system works similar to that of ultrasound detector but, in this paper the immediate advantages of proposed RF Intrusion Detection System (RFIDS) with better clarity, higher frequency and higher speed of processing are highlighted. This system exhibits consistent reliable pattern of detection clearly distinguishable before and after intrusion. In such cases, even if the direct path is not obstructed, the reflected paths are definitely affected and hence the captured signals differ and can be analysed. In the proposed technique unlike the other sensory detection systems, there is no blind spot, which gives a truly contravene-less indoor intrusion detection system.