The Theory of Complex System

This concise primer (based on lectures given at summer schools on complex systems and on a masters degree course in complex systems modeling) will provide graduate students and newcomers to the field with the basic knowledge of the concepts and methods of statistical physics and its potential for application to interdisciplinary topics.

From the 2021 Nobel Prize winner in Physics, an enlightening and personal journey into the practice of groundbreaking science

Genetic Programming Theory and Practice IV was developed from the fourth workshop at the University of Michigan’s Center for the Study of Complex Systems to facilitate the exchange of ideas and information related to the rapidly advancing field of Genetic Programming (GP). Contributions from the foremost international researchers and practitioners in the GP arena examine the similarities and differences between theoretical and empirical results on real-world problems. The text explores the synergy between theory and practice, producing a comprehensive view of the state of the art in GP application.

Half a century ago, S. Chandrasekhar wrote these words in the preface to his 1 celebrated and successful book: In this monograph an attempt has been made to present the theory of stellar dy­ namics as a branch of classical dynamics - a discipline in the same general category as celestial mechanics. [ … ] Indeed, several of the problems of modern stellar dy­ namical theory are so severely classical that it is difficult to believe that they are not already discussed, for example, in Jacobi's Vorlesungen. Since then, stellar dynamics has developed in several directions and at var­ ious levels, basically three viewpoints remaining from which to look at the problems encountered in the interpretation of the phenomenology. Roughly speaking, we can say that a stellar system (cluster, galaxy, etc.) can be con­ sidered from the point of view of celestial mechanics (the N-body problem with N» 1), fluid mechanics (the system is represented by a material con­ tinuum), or statistical mechanics (one defines a distribution function for the positions and the states of motion of the components of the system).

Half a century ago, S. Chandrasekhar wrote these words in the preface to his l celebrated and successful book: In this monograph an attempt has been made to present the theory of stellar dy­ namics as a branch of classical dynamics - a discipline in the same general category as celestial mechanics. [ … J Indeed, several of the problems of modern stellar dy­ namical theory are so severely classical that it is difficult to believe that they are not already discussed, for example, in Jacobi's Vorlesungen. Since then, stellar dynamics has developed in several directions and at var­ ious levels, basically three viewpoints remaining from which to look at the problems encountered in the interpretation of the phenomenology. Roughly speaking, we can say that a stellar system (cluster, galaxy, etc.) can be con­ sidered from the point of view of celestial mechanics (the N-body problem with N » 1), fluid mechanics (the system is represented by a material con­ tinuum), or statistical mechanics (one defines a distribution function for the positions and the states of motion of the components of the system).

The essence of this book can be found in a line written by the ancient Roman Stoic Philosopher Lucius Annaeus Seneca: "Fortune is of sluggish growth, but ruin is rapid". This sentence summarizes the features of the phenomenon that we call "collapse," which is typically sudden and often unexpected, like the proverbial "house of cards."