"A generic scheme for choosing models and characterizations of complex systems"
What is the relationship between a model of a complex system and the system itself? Are some models better then others? What is an "approximation" for a complex system. What does it mean for a property to be "characteristic" for a structure? The talk introduces a generic, systematic approach to these questions. It is based on the observation, that useful computational methods have both low computational and low algorithmic complexity. A mathematical formalism is developed that integrates these ideas with a realistic model of a computer controlled experiment. As a demonstration, the formalism, is applied to the problem of modeling and characterizing the spatio-temporally chaotic solutions of the Kuramoto-Sivashinsky equation. Compared to earlier work that applies concepts of computer science to structure in complex systems (often under the keyword of "emergence"), the approach used here considers both problems that of modeling and that of characterizing, and their relationship. As a result, approximate descriptions of complex systems can be obtained without having to reduce the information about the system state "manually" as the first step in the analysis. By taking the tradeoff in the cost of program length and execution time explicitly into account, the large variety of description that exists for typical complex systems is reproduced. By the inclusion of statistical tests and models into the formalism, the conceptual framework is expanded, so that many practical problems that naturally occur in the study of complex systems, are better modeled.