## Computing anticipatory systems: CASYS'05, seventh international conference, Liège, Belgium, 8-13 August 2005All papers were peer-reviewed. These proceedings include the invited papers as well as those papers that received a best paper award. This conference was enhanced by the presence of Brian D. Josephson, Nobel Prize in Physics, who presented an invited lecture on "General Principles for Brain Design," included in these proceedings. The content of these proceedings deals with the most recent research and development in the area of theoretical developments and applications in the modeling and computing of anticipatory systems in any fields of natural and artificial systems. A computing anticipatory system is a system that computes its current states in taking into account its past and present states but also its potential future states. Strong anticipation refers to an anticipation of events built by or embedded in a system. Weak anticipation refers to an anticipation of events predicted or forecasted from a model of a system. Specific topics include: physics, quantum mechanics, relativity; anticipatory systems, incursion, hyperincursion; logical and dynamical systems; computing systems; soft computing; cognitive systems; neuroscience, biosystems; risk management, economy; as well as engineering systems. |

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### Contents

General Principles for Brain Design | 3 |

The Dual Incursive System of the Discrete Harmonic Oscillator | 11 |

The Superposed Hyperincursive System of the Discrete Harmonic Oscillator | 65 |

Copyright | |

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### Common terms and phrases

2006 American Institute algorithm anticipation application atomic sentences attachment space behavior boson causal cellular automata closure cognitive complete lattice complex components Computing Anticipatory Systems concept corresponding D. M. Dubois dark energy defined dimension dynamics edited by D. M. element energy environment example external fermion FIGURE fMRI formal function fuzzy given global gravitational gustatory harmonic oscillator hyperincursive incursive algorithms initial conditions input Institute of Physics interaction Intranet linear logic loop magnetic mathematical means measurements neural nilpotent object observed operator organization paper parameters particle phase space plasma Plasmodium possible predictions present problem quantum mechanics recursive relation represent representation self-organization Seventh International Conference Simula simulation solution space-time spatial spinbacks stability structure superposed oscillator symmetry temporal tensor theorem theory Titius-Bode law trajectory transformation vacuum vacuum energy Value Potentials variables vector Viable System Model