On a Method for the Hierarchical Modeling of Complex Hamiltonian Systems

Abstract The intransparency of complex systems is a long-standing challenge in the quest for methods to model and understand them. One attempt to structure such models is to identify hierarchies. Despite the intuitive nature of hierarchies, formalizing the latter is a surprisingly intricate task in general.

One such method for Hamiltonian systems is the Mori-Zwanzig formalism. The core idea is the separation of timescales, where one has slow timescales separated from fast timescales, where the latter appear as "noise" on the slow timescale. In other words, the fast timescales are treated as effectively uncorrelated with respect to the slow one, reminiscent to Haken's formulation of synergetics.

Choosing a suitable inner product, the ensuing decomposition results a natural cascade of hierarchies. We show that these hierarchies can be used to described intricate systems such as the spectra of orientation glasses. We will then give an outlook on how this method might be generalized to other types of hierarchical decompositions.

This talk covers, amongst other, joint work with Rudolf Feile and Paul Leiderer.

Biography Professor of Artificial Intelligence at the Department of Computer Science, Director of the Centre for Artificial Intelligence and Robotics Research (CAIRR) and Head of the Adaptive Systems Research Group at the University of Hertfordshire. His research interests concentrate on the understanding and modeling of collective complex systems and intelligent decision-making, especially in the context of cognition in artificial and biological agents. His research ranges from fundamental questions, such as the role of embodiment, intrinsic motivations, taskless utilities, self-organization and Artificial Life, to questions from cognitive science, psychology, social science, and biology.