342 research outputs found
Quantum Algorithmic Integrability: The Metaphor of Polygonal Billiards
An elementary application of Algorithmic Complexity Theory to the polygonal
approximations of curved billiards-integrable and chaotic-unveils the
equivalence of this problem to the procedure of quantization of classical
systems: the scaling relations for the average complexity of symbolic
trajectories are formally the same as those governing the semi-classical limit
of quantum systems. Two cases-the circle, and the stadium-are examined in
detail, and are presented as paradigms.Comment: 11 pages, 5 figure
Unreduced Dynamic Complexity: Towards the Unified Science of Intelligent Communication Networks and Software
Operation of autonomic communication networks with complicated user-oriented functions should be described as unreduced many-body interaction process. The latter gives rise to complex-dynamic behaviour including fractally structured hierarchy of chaotically changing realisations. We recall the main results of the universal science of complexity (http://cogprints.org/4471/) based on the unreduced interaction problem solution and its application to various real systems, from nanobiosystems (http://cogprints.org/4527/) and quantum devices to intelligent networks (http://cogprints.org/4114/) and emerging consciousness (http://cogprints.org/3857/). We concentrate then on applications to autonomic communication leading to fundamentally substantiated, exact science of intelligent communication and software. It aims at unification of the whole diversity of complex information system behaviour, similar to the conventional, "Newtonian" science order for sequential, regular models of system dynamics. Basic principles and first applications of the unified science of complex-dynamic communication networks and software are outlined to demonstrate its advantages and emerging practical perspectives
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