The yuan-dollar returns prior to the 2005 revaluation show a Sierpinski triangle in an iterated function system clumpiness test. Yet the fractal vanishes after the revaluation. The Sierpinski commonly emerges in the chaos game, where randomness coexists with deterministic rules (M.F. Barnsley,...

This work presents a novel method of reconstructing some relevant characteristics of exchange rate time series by the superposition of two components: a mostly deterministic one, the chaos game as expressed by the Yuan/USD exchange rate and a purely stochastic one, Gaussian white noise. We...

Abstract Linear fractional Galton–Watson branching processes in i.i.d. random environment are, on the quenched level, intimately connected to random difference equations by the evolution of the random parameters of their linear fractional marginals. On the other hand, any random difference...

In this paper biological sequences are modelled by stationary ergodic sequences. A new family of statistical tests to characterize the randomness of the inputs is proposed and analyzed. Tests for independence and for the determination of the appropriate order of a Markov chain are constructed...

Iterated function system (IFS) models have been explored to represent discrete sequences where the attractor of an IFS is self-affine either in R2 or R3 (R is the set of real numbers). In this paper, the self-affine IFS model is extended from R3 to Rn (n is an integer and greater than 3), which...

Global transposable characteristics in the complete DNA sequence of the Saccharomyces cevevisiae yeast is determined by using the metric representation and recurrence plot methods. On the basis of the correlation distance of nucleotide strings, 16 chromosome sequences of the yeast, which are...

We use the wavelet transform to explore the complexity of DNA sequences. Long-range correlations are clearly identified and shown to be related to the sequence GC content. The significance of this observation to gene evolution is discussed.

The aim of this paper is to show, using some of Barnsley's ideas, how it is possible to generalize a fractal interpolation problem to certain post critically finite (PCF) compact sets in ℝn. We use harmonic functions to solve this fractal interpolation problem.

A two-dimensional modified Lévy-walk model for the DNA sequences with only three parameters is proposed. This model is applied to simulate real DNA sequence data of the Saccharomyces cerevisiae genome. DNA sequences are converted into one- and two-dimensional random walk mappings for...

Genome signatures are statistical properties of DNA sequences that provide information on the underlying species. It is not understood, how such species-discriminating statistical properties arise from processes of genome evolution and from functional properties of the DNA. Investigating the...