We examined the learning process with 3 sets of stimuli that have identical symbolic structure but differ in appearance (meaningless letter strings, arrangements of geometric shapes, and sequences of cities). One hypothesis is that the learning process aims to encode symbolic regularity in the same way, largely regardless of appearance. Another is that different types of stimuli bias the learni...

The ability to determine a sequence of actions in order to reach a particular goal is of utmost importance to mobile robots. One major problem with symbolic planning approaches regards assumptions made by the designer while introducing externally specified world models, preconditions and postconditions. To bypass this problem, it would be desirable to develop mechanisms for action planning that...

Mutual information function, which is an alternative to correlation function for symbolic sequences, and a \symbolic spectrum" are calculated for a human DNA sequence containing mostly intron segments, those that do not code for proteins. It is observed that the mutual information function of this sequence decays very slowly, and the correlation length is extremely long (at least 800 bases). Th...

We present a novel compression-based method for measuring similarity between sequences of symbolic, polyphonic music. The method is based on mapping the values of binary chromagrams extracted from MIDI files to tonal centroids, then quantizing the tonal centroid representation values to sequences, and finally measuring the similarity between the quantized sequences using Normalized Compression ...

We extend the sliding block code in symbolic dynamics to transform two sequences of Markov chains with time delay. Under the assumption that chains are irreducible and aperiodic, we prove the central limit theorem (CLT) for the normalized sums of extended sliding block codes from two sequences of Markov chains. We apply the theorem to evaluations of bit error probabilities in asynchronous sprea...

The conversion of symbolic sequences into complex genomic signals allows using signal processing methods for the handling and analysis of nucleotide sequences. This methodology reveals surprizing regularities, both locally and at a global scale, allowing us to predict nucleotides in a sequence, when knowing the preceding ones. Such experiments have a major biologic significance, as they explore...

Transient, macroscopic states of chemical disequilibrium are born out of the microscopic dynamics of molecules. As a reaction mixture evolves, the temporal patterns of chemical species encodes some of this dynamical information, while their statistics are a manifestation of the bulk kinetics. Here, we define a chemically-informed symbolic dynamics as a coarse-grained representation of classical...

This survey article is concerned with the study of bifurcations of piecewise-smooth maps. We review the literature in circle maps and quasicontractions and provide paths through this literature to prove sufficient conditions for the occurrence of two types of bifurcation scenarios involving rich dynamics. The first scenario consists of the appearance of periodic orbits whose symbolic sequences ...

Graphs can be represented symbolically by the Ordered Binary Decision Diagram (OBDD) of their characteristic function. To solve problems in such implicitly given graphs, specialized symbolic algorithms are needed which are restricted to the use of functional operations offered by the OBDD data structure. In this paper, a symbolic algorithm for the all-pairs shortest-paths (APSP) problem in loop...

While associations between number and space, in the form of a spatially oriented numerical representation, have been extensively reported in human adults, the origins of this phenomenon are still poorly understood. The commonly accepted view is that this number-space association is a product of human invention, with accounts proposing that culture, symbolic knowledge, and mathematics education ...