Additive one-dimensional cellular automata are chaotic according to Devaney's definition of chaos

AbstractWe study the chaotic behavior of a particular class of dynamical systems: cellular automata. We specialize the definition of chaos given by Devaney for general dynamical systems to the case of cellular automata. A dynamical system (X,F) is chaotic according to Devaney's definition of chaos if its transition map F is sensitive to the initial conditions, topologically transitive, and has dense periodic orbits on X. Our main result is the proof that all the additive one-dimensional cellular automata defined on a finite alphabet of prime cardinality are chaotic in the sense of Devaney

Mind out of matter: topics in the physical foundations of consciousness and cognition

This dissertation begins with an exploration of a brand of dual aspect monism and some problems deriving from the distinction between a first person and third person point of view. I continue with an outline of one way in which the conscious experience of the subject might arise from organisational properties of a material substrate. With this picture to hand, I first examine theoretical features at the level of brain organisation which may be required to support conscious experience and then discuss what bearing some actual attributes of biological brains might have on such experience. I conclude the first half of the dissertation with comments on information processing and with artificial neural networks meant to display simple varieties of the organisational features initially described abstractly.While the first half begins with a view of conscious experience and infers downwards in the organisational hierarchy to explore neural features suggested by the view, attention in the second half shifts towards analysing low level dynamical features of material substrates and inferring upwards to possible effects on experience. There is particular emphasis on clarifying the role of chaotic dynamics, and I discuss relationships between levels of description of a cognitive system and comment on issues of complexity, computability, and predictability before returning to the topic of representation which earlier played a central part in isolating features of brain organisation which may underlie conscious experience.Some themes run throughout the dissertation, including an emphasis on understanding experience from both the first person and the third person points of view and on analysing the latter at different levels of description. Other themes include a sustained effort to integrate the picture offered here with existing empirical data and to situate current problems in the philosophy of mind within the new framework, as well as an appeal to tools from mathematics, computer science, and cognitive science to complement the more standard philosophical repertoire

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal