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...

With the recent development of deep learning, research in AI has gained new vigor and prominence. While machine learning has succeeded in revitalizing many research fields, such as computer vision, speech recognition, and medical diagnosis, we are yet to witness impressive progress in natural language understanding. One of the reasons behind this unmatched expectation is that, while a bottom-up...

INTRODUCTION 425 DEFINING PLAY 426 THEORIES OF PLAY 428 Piaget 428 Vygotsky 429 VARIETIES OF PLAY AND THEIR DEVELOPMENTAL COURSE 430 Sensorimotor and Object Play 430 Physical or Locomotor Play 430 Rough-and-Tumble Play 431 Exploratory Play 431 Construction Play 432 Symbolic Play 432 Summary 433 CONTEMPORARY ISSUES IN PLAY RESEARCH 433 Pretend Play and Theory of Mind 433 Symbolic Understanding 4...

Concurrently, a symbolic approach for analog system-level fault diagnosis and a systematic approach to maximize the fault location capability are proposed. This unified approach is realized as a result of combining the simulation before test (SBT) fault dictionary diagnosis method with a symbolic approach. The traditional SBT fault dictionary method is often costly and inefficient because of a ...

We consider the problem of determining multiple steady states for positive real values in models of biological networks. Investigating the potential for these in models of the mitogen-activated protein kinases (MAPK) network has consumed considerable effort using special insights into the structure of corresponding models. Here we apply combinations of symbolic computation methods for mixed equ...

Existing symbolic music comparison systems generally consider monophonic music or monophonic reduction of polyphonic music. Adaptation of alignment algorithms to music leads to accurate systems, but their extensions to polyphonic music raise new problems. Indeed, a chord may match several consecutive notes, or the difference between two similar motifs may be a few swapped notes. Moreover, the s...

D Conventional logic-programming languages rely fundamentally on symbolic computation with quantifier-free terms. Much theoretical logic uses the richer vocabulary of quantified terms, however. In this paper we sketch some first steps in a program of research for developing data structures and algorithms to support efficient computation directly on quantified terms. We describe a simple concept...

Existing symbolic music comparison systems generally consider monophonic music or monophonic reduction of polyphonic music. Adaptation of alignment algorithms to the music leads to accurate systems, but extensions to polyphonic music arise new problems. Indeed, a chord may match several notes, or the difference between two similar motifs may be a few swapped notes. Moreover, it is difficult to ...

In this paper we outline a connection between substitution dynamical systems and systems of partial isometries of IR. Let τ be a primitive substitution and (X,T ) the associated minimal subshift. Associated to each real geometric realization G of τ is a system of partial isometries IG . The subshift (X,T ) generated by τ provides a symbolic coding of the dynamics of IG . This allows us to deduc...

In this paper we outline a connection between substitution dynamical systems and systems of partial isometries of R. Let τ be a primitive substitution and (X, T ) the associated minimal subshift. Associated to each real geometric realization G of τ is a system of partial isometries IG . The subshift (X, T ) generated by τ provides a symbolic coding of the dynamics of IG . This allows us to dedu...