This paper presents a new algorithm that combines perturbation theory and genetic programming for modeling and forecasting real-world chaotic time series. Both perturbation theory and time series modeling have to build symbolic models for very complex system dynamics. Perturbation theory does not work without well-defined system equation. Difficulties in modeling time series lie in the fact tha...

This paper is to complete and improve the work reported in 1, 2], using the Lanczos-method (in Coleman's version) to approximate the Bessel functions Y 0 (z) and Y 1 (z). We introduce symbolic representations of the scaled Faber polynomials on any fan-shaped section of the complex plane. These Faber polynomials are used as the perturbation terms in the-method. Numerical comparison among the pow...

This paper deals with the summation problem of power series of the form Sb a(f ;x) = ∑ a≤k≤b f(k)x k, where 0 ≤ a < b ≤ ∞, and {f(k)} is a given sequence of numbers with k ∈ [a, b) or f(t) is a differentiable function defined on [a, b). We present a symbolic summation operator with its various expansions, and construct several summation formulas with estimable remainders for Sb a(f ;x), by the ...

The performance of (bio-)signal classification strongly depends on the choice of suitable features (also called parameters or biomarkers). In this article we evaluate the discriminative power of ordinal pattern statistics and symbolic dynamics in comparison with established heart rate variability parameters applied to beat-to-beat intervals. As an illustrative example we distinguish patients su...

Let $K$ be a field of characteristic$p>0$, $K[[x]]$, the ring of formal power series over $ K$,$K((x))$, the quotient field of $ K[[x]]$, and $ K(x)$ the fieldof rational functions over $K$. We shall give somecharacterizations of an algebraic function $fin K((x))$ over $K$.Let $L$ be a field of characteristic zero. The power series $finL[[x]]$ is called differentially algebraic, if it satisfies...