Earlier comprehensive mathematical methods were developed for the study of periodicity of continuous and discrete numerical sequences, using Fourier transformation and allowing the definition of the spectral density of a numerical sequence. However, such an application of a Fourier transform demands presentation of a symbolic sequence as a numerical sequence in which the properties of any symbo...

Beta-splines are a class of splines with applications in the construction of curves and surfaces for computer-aided geometric design. One of the salient features of the Beta-spline is that the curves and surfaces thus constructed are geometrically continuous, a more general notion of continuity than the one used in ordinary B-splines. The basic building block for Beta-splines of order k is a se...

In recent years, there has been a number of papers about the combinatorial notion of symbolic complexity: this is the function counting the number of factors of length n for a sequence. The complexity is an indication of the degree of randomness of the sequence: a periodic sequence has a bounded complexity, the expansion of a normal number has an exponential complexity. For a given sequence, th...

In this paper, motivated by the interest and relevance of the study of tumor growth models, a central point of our investigation is the study of the chaotic dynamics and the bifurcation structure of Weibull-Gompertz-Fréchet’s functions: a class of continuousdefined one-dimensional maps. Using symbolic dynamics techniques and iteration theory, we established that depending on the properties of t...

This paper addresses the issue of discovering key sequences from time series data for pattern classification. The aim is to find from a symbolic database all sequences that are both indicative and non-redundant. A sequence as such is called a key sequence in the paper. In order to solve this problem we first we establish criteria to evaluate sequences in terms of the measures of evaluation base...

Abstract Logic-based machine learning aims to learn general, interpretable knowledge in a data-efficient manner. However, labelled data must be specified structured logical form. To address this limitation, we propose neural-symbolic framework, called Feed-Forward Neural-Symbolic Learner (FFNSL) , that integrates logic-based system capable of from noisy examples, with neural networks, order uns...

We begin a systematic study of Euclidean Piecewise Isometric Dynamical Systems (p.i.d.s.) with a particular focus on the interplay between geometry, and symbolic dynamics , and the group of isometries associated with p.i.d.s. We investigate various aspects of the dynamical information contained in the coding: symbolic growth and the periodic behavior of codings and cells. This theoretical inves...

A method based on mapping a symbolic sequence into a set of patterns (strings resulting from the sequence parsing) is proposed as a tool for the reconstruction of ancestral sequences. The set union of patterns comprises all the patterns present in the family of related proteins sequences of an extant species. The set of most frequent patterns among protein sequences is selected and concatenated...