This chapter presents an improved method called the “Adaptive Interbeat Interval Analysis (AIIA) method”. The AIIA method uses the Simple K-Means algorithm for symbolization, which offers a new way to represent subtle variations between two interbeat intervals without human intervention. After symbolization, it uses the n-gram algorithm to generate different kinds of symbolic sequences. Each sy...

The mutual relationship among Markov partitions is investigated for one-dimensional piecewise monotonic map. It is shown that if a Markov partition is regarded as a map-refinement of the other Markov partition, that is, a concept we newly introduce in this article, one can uniquely translate a set of symbolic sequences by one Markov partition to those by the other or vice versa. However, the se...

This paper introduces a new similarity measure, the covering similarity, that we formally define for evaluating the similarity between a symbolic sequence and a set of symbolic sequences. A pair-wise similarity can also be directly derived from the covering similarity to compare two symbolic sequences. An efficient implementation to compute the covering similarity is proposed that uses a suffix...

Object-oriented unit tests consist of sequences of method invocations. Behavior of an invocation depends on the method’s arguments and the state of the receiver at the beginning of the invocation. Correspondingly, generating unit tests involves two tasks: generating method sequences that build relevant receiverobject states and generating relevant method arguments. This paper proposes Symstra, ...

Integrate-and-Fire Mode (IFM) is a quite simple neuron model, however, it is possible to simulate circle map. With the aid of IFM, the circle map iteration of phase can be implemented, meanwhile the symbolic sequences are acquired conveniently from Integrate-and-Fire process. In this paper, the study of phase circle map model and its symbolic dynamics is made. Firstly, the partition of symbols ...

Morphisms are homomorphisms under the concatenation operation of the set of words over a finite set. Changing the elements of the finite set does not essentially change the morphism. We propose a way to select a unique representing member out of all these morphisms. This has applications to the classification of the shift dynamical systems generated by morphisms. In a similar way, we propose th...

The concept of symbolic sequences play important role in study of complex systems. In the work we are interested in ultrametric structure of the set of cyclic sequences naturally arising in theory of dynamical systems. Aimed at construction of analytic and numerical methods for investigation of clusters we introduce operator language on the space of symbolic sequences and propose an approach ba...