We overview and discuss several methods for the Fourier analysis of symbolic data, such as DNA sequences, emphasizing their mutual connections. We consider the indicator sequence approach, the vector and the symbolic autocorrelation methods, and methods such as the spectral envelope, that for each frequency optimize the symbolic-no-numeric mapping to emphasize any periodic data features. We dis...

Jeerey 10] proposed a graphic representation of DNA sequences using Barns-ley's iterative function systems. In spite of further developments in this direction 19, 25, 13], the proposed graphic representation of DNA sequences has been lacking a rigorous connection between its spatial scaling characteristics and the statistical characteristics of the DNA sequences themselves. We 1) generalize Jee...

Based on the numerical representations by T basic vectors of a symbolic sequence consisting of T symbols, first, we prove mathematical that the total Fourier spectrum of the sequence is the square of the length of the sequence. In the meantime, we define the indicator sequences vector. Using the orthogonal or row orthogonal transformations of the indicator sequences vector, we construct some sp...

We investigate the complexity of short symbolic sequences of chaotic dynamical systems by using lossless compression algorithms. In particular, we study Non-Sequential Recursive Pair Substitution (NSRPS), a lossless compression algorithm first proposed by W. Ebeling et al. [Math. Biosc. 52, 1980] and Jiménez-Montaño et al. [arXiv:cond-mat/0204134, 2002]) which was subsequently shown to be optim...

Symbolic codes for rotational orbits and “islands-around-islands” are constructed for the quadratic, area-preserving Hénon map. The codes are based upon continuation from an anti-integrable limit or, alternatively, from the horseshoe. Given any sequence of rotation numbers we obtain symbolic sequences for the corresponding elliptic and hyperbolic rotational orbits. These are shown to be consist...

The aim of this study is to evaluate how far the nonlinear symbolic dynamics approach helps to characterize the nonlinear properties of speech and thereby discriminate between voiced and unvoiced speech segments. The symbolic dynamics calculations were performed on voiced speech, unvoiced speech and silence data. Differences were found in histogram properties and complexity measures of symbol s...

The characteristics of long-term, symbolic learning were investigated using Soar and ACT-R models of a task to rearrange blocks into specific configurations. Long sequences of problems were run collecting data to answer fundamental questions about long-term, symbolic learning. The questions were whether symbolic learning continues indefinitely, how learned knowledge is used, and whether perform...

We construct a well ordered symbolic dynamics plane for the stadium billiard. In this symbolic plane the forbidden and the allowed orbits are separated by a monotone pruning front, and allowed orbits can be systematically generated by sequences of approximate finite grammars. 1 ‡ Permanent address: Phys Dep., University of Oslo, Box 1048, Blindern, N-0316 Oslo

We have found that there are more than a dozen classical generating functions that could be suitably symbolized to yield various symbolic sum formulas by employing Mullin-Rota’s theory of binomial enumeration. Various special formulas and identities involving well-known number sequences or polynomial sequences are presented as illustrative examples. The convergence of the symbolic summations is...

BACKGROUND Biological signals may carry specific characteristics that reflect basic dynamics of the body. In particular, heart beat signals carry specific signatures that are related to human physiologic mechanisms. In recent years, many researchers have shown that representations which used non-linear symbolic sequences can often reveal much hidden dynamic information. This kind of symbolizati...