Feeling the pulse on the wrist is the regular diagnostic method in traditional Chinese medicine. However it is natural to ask whether there is any difference between feeling the pulse on the wrist or at any other part of the body: such as the fingertips at which it is easily measured by electronic devices. We employ a series of neural networks to model blood pressure propagation from the wrist to the fingertip. In order to avoid the problem of over-fitting we apply information theoretic criterion to determine the optimal model in these networks and then apply surrogate data method to the residuals in this model. We demonstrate the application of this method to recordings of human pulse in six subjects. Our result indicates that there is no significant difference between pulse waveform measure on the lateral arterial artery (wrist) and at the fingertip.

behavioral models of digital integrated circuit input and output ports for EMC and signal integrity simulations. A practical modeling process is proposed and applied to some example devices. The modeling process is simple and efficient, and it yields models performing at a very high accuracy level.

Nonlinear modeling routines are often applied in an effort to extract underlying determinism from time series data. The best of these methods perform well for short noisy time series when there is determinism in the underlying system. We show that nonlinear modeling does not distinguish between a static nonlinear transformation of linearly filtered noise and dynamic nonlinearity. To relieve this problem we recommend that surrogate data methods should be applied prior to nonlinear modeling, and the results of that analysis used to guide model selection. 1.

Abstract. We consider the problem of inferring kinetic mechanisms for biochemical reactions from time series data. Using a priori knowledge about the structure of chemical reaction kinetics we develop global nonlinear models which use elementary reactions as a basis set, and discuss model construction using top-down and bottom-up approaches. 1

Using optimal control techniques we derive and demonstrate the use of an exact single step control method for directing a nonlinear system to a target orbit and keeping it there. We require that values of the control parameters remain near the uncontrolled settings. The full nonlinearity of the problem in state space variables is retained. The `one step' of the control is typically a composition of known or learned maps over (a) the time required to learn the state, (b) the time to compute the control, and (c) the time to apply the control. No special targeting is required, yet the time to control is quite rapid. Working with the dynamics of a well studied nonlinear electrical circuit, we show how this method works efficiently and accurately in two situations: when the known circuit equations are used, and when control is performed only on a Poincar'e section of the reconstructed phase space. In each case, because the control rule is known analytically, the control strategy is computat...

The technique of surrogate data provides has been used to test for membership of particular classes of linear systems. Existing algorithms provide non-parametric methods to generate surrogates similar to the data and consistent with a given hypothesis. These non-parametric methods allow a wide range of test statistics to be utilized. We suggest an obvious extension of this to classes of nonlinear parametric models. To do so it is necessary to restrict the statistics employed to a relatively broad class. We demonstrate that correlation dimension provides a suitable statistic and apply these methods, together with existing surrogate tests to respiratory data from sleeping infants. Although our data are clearly distinct from the different classes of linear systems we are unable to distinguish between our data and surrogates generated by nonlinear models. Hence we conclude that our data cannot be explained by linearly filtered noise but is consistent with the noisy periodic orbit of a nonl...

Spatio-temporal analysis of nucleate pool boiling: identi®cation of nucleation sites using non-orthogonal

. We present three distinct concepts of what constitutes a scienti. ..c understanding of a dynamical system . The development of each of these paradigms has resulted in a signi...cant expansion in the kind of system that can be investigated. In particular, the recently-developed "algorithm ic modelling paradigm" has allowed us to enlarge the domain of discourse to include complex real-world processes that cannot be necessarily be described by conventional dierential equations. 1. Introduction What do we mean when we say that we understand a dynamical system? In this essay, we identify three distinct paradigms for scienti...c understanding of dynamical systems. These paradigms are the models of knowing of the title. The introduction of new models of knowing has resulted in a signi...cant expansion in the kinds of systems that can be investigated scienti...cally. The ...rst paradigm, which we shall refer to as the Newtonian 1 , was established in the seventeenth century. Accor...

We investigate two techniques for filtering signals from noisy nonlinear systems. Both the dynamics and the observed signals may be subject to noise. The first technique is a modified Kalman filter which accounts for the noise-amplification properties of chaotic systems and has less tendency to diverge than the usual Kalman filter. The second is the noise-reduction algorithm of Hammel, based on the concept of shadowing from dynamical systems theory. 1 Introduction In the work that has been done on filtering of possibly chaotic signals from deterministic nonlinear systems, and in reconstructing the dynamics of such systems from output data, the issue of dynamic noise has not been dealt with fully. In this paper we examine two noise reduction techniques and apply them to nonlinear dynamical systems operating in the chaotic regime. The performance of both algorithms is discussed for data corrupted by observational noise, dynamical noise, or both. The first method, widely used by contro...

The technique of surrogate data analysis may be employed to test the hypothesis that an observed data set was generated by one of several specific classes of dynamical system. Current algorithms for surrogate data analysis enable one, in a generic way, to test for membership of the following three classes of dynamical system: (0) independent and identically distributed noise, (1) linearly filtered noise, and (2) a monotonic nonlinear transformation of linearly filtered noise. We show that one may apply statistics from nonlinear dynamical systems theory, in particular those derived from the correlation integral, as test statistics for the hypothesis that an observed time series is consistent with each of these three linear classes of dynamical system. Using statistics based on the correlation integral we show that it is also possible to test much broader (and not necessarily linear) hypotheses. We illustrate these methods with radial basis models and an algorithm to estimate t...