0. Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Part I. Renewal theorems in symbolic dynamics . . . . . . . . . . . . 1. Background: Shifts, suspension flows, thermodynamic formalism . 2. 3. 4. 5. 6. 7. 1 5 5 Renewal measures and renewal theorems . . . . . . . . . . . . . . 7 A modification for finite sequences . . . . . . . . . . . . . . . . . 10 Equidistribution theo...

We introduce the notion of aperiodicity measure for in nite symbolic sequences. Informally speaking, the aperiodicity measure of a sequence is the maximum number (between 0 and 1) such that this sequence di ers from each of its non-identical shifts in at least fraction of symbols being this number. We give lower and upper bounds on the aperiodicity measure of a sequence over a xed alphabet. We ...

The decimal expansion of real numbers, familiar to us all, has a dramatic generalization to representation of dynamical system orbits by symbolic sequences. The natural way to associate a symbolic sequence with an orbit is to track its history through a partition. But in order to get a useful symbolism, one needs to construct a partition with special properties. In this work we develop a genera...

Inductive learning is the method of learning from observations. Inductive learning has important applications over a wide range of area including pattern recognition, language acquisition, bio-informatics and intelligent agent design. Because of such diverse applicability, inductive learning methods including automata learning, grammar induction, hidden markov model learning and symbolic statis...

A recent theory of pigeons' equivalence-class formation (Urcuioli, 2008) predicts that reflexivity, an untrained ability to match a stimulus to itself, should be observed after training on two "mirror-image" symbolic successive matching tasks plus identity successive matching using some of the symbolic matching stimuli. One group of pigeons was trained in this fashion; a second group was traine...

Recently, we proposed a new measure of complexity for symbolic sequences (Sequence Compositional Complexity, SCC) based on the entropic segmentation of a sequence into compositionally homogeneous domains. Such segmentation is carried out by means of a conceptually simple, computationally efficient heuristic algorithm. SCC is now applied to the sequences generated by several stochastic models wh...

Most of the western tonal music is based on the concept of tonality or key. It is often desirable to know the tonality of a song stored in a symbolic format (digital scores), both for content based management and musicological studies to name just two applications. The majority of the freely available symbolic music is coded in MIDI format. But, unfortunately many MIDI sequences do not contain ...

The decimal expansion real numbers, familiar to us all, has a dramatic generalization to representation of dynamical system orbits by symbolic sequences. The natural way to associate a symbolic sequence with an orbit is to track its history through a partition. But in order to get a useful symbolism, one needs to construct a partition with special properties. In this work we develop a general t...

This paper deals with the connection of symbolic and subsymbolic systems. It focuses on connectionistic systems processing symbolic data. We examine the capability of learning symbolic data with various neural architectures which constitute partially dynamic approaches: discrete time partially recurrent neural networks as a simple and well established model for processing sequences, and advance...

The symbolic-numeric computing described here consists of an extensive symbolic pre-processing of systems of differential-algebraic equations (DAE), followed by the numerical integration of the system obtained. The application area is multibody dynamics. We deal symbolically with a DAE system using differentiation and elimination methods to find all the hidden constraints, and produce a system ...