Complexity and Information: Measuring Emergence, Self-organization, and Homeostasis at Multiple Scales

Concepts used in the scientific study of complex systems have become so widespread that their use and abuse has led to ambiguity and confusion in their meaning. In this paper we use information theory to provide abstract and concise measures of complexity, emergence, self-organization, and homeostasis. The purpose is to clarify the meaning of these concepts with the aid of the proposed formal measures. In a simplified version of the measures (focusing on the information produced by a system), emergence becomes the opposite of self-organization, while complexity represents their balance. Homeostasis can be seen as a measure of the stability of the system. We use computational experiments on random Boolean networks and elementary cellular automata to illustrate our measures at multiple scales.Comment: 42 pages, 11 figures, 2 table

From Simple to Complex and Ultra-complex Systems:\ud A Paradigm Shift Towards Non-Abelian Systems Dynamics

Atoms, molecules, organisms distinguish layers of reality because of the causal links that govern their behavior, both horizontally (atom-atom, molecule-molecule, organism-organism) and vertically (atom-molecule-organism). This is the first intuition of the theory of levels. Even if the further development of the theory will require imposing a number of qualifications to this initial intuition, the idea of a series of entities organized on different levels of complexity will prove correct. Living systems as well as social systems and the human mind present features remarkably different from those characterizing non-living, simple physical and chemical systems. We propose that super-complexity requires at least four different categorical frameworks, provided by the theories of levels of reality, chronotopoids, (generalized) interactions, and anticipation

From Giant H II regions and H II galaxies to globular clusters and compact dwarf ellipticals

Massive starforming regions like Giant HII Regions (GHIIR) and HII Galaxies (HIIG) are emission line systems ionized by compact young massive star clusters (YMC) with masses ranging from $10^4$M$_\odot$ to $10^8$M$_\odot$. We model the photometric and dynamical evolution over a Hubble time of the massive gravitationally bound systems that populate the tight relation between absolute blue magnitude and velocity dispersion ($M_{B}-\sigma$) of GHIIR and HIIG and compare the resulting relation with that one of old stellar systems: globular clusters, elliptical galaxies, bulges of spirals. After 12~Gyr of evolution their position on the $\sigma$ vs. M$_B$ plane coincides -- depending on the initial mass -- either with the globular clusters for systems with initial mass $M < 10^6$M$_\odot$ or with a continuation of the ellipticals, bulges of spirals and ultracompact dwarfs for YMC with $M >10^6$M$_\odot$. The slope change in the $M_{B}-\sigma$ and $M_B$-size relations at cluster masses around $10^6$M$_\odot$ is due to the larger impact of the dynamical evolution on the lower mass clusters. We interpret our result as an indication that the YMC that ionize GHIIR and HIIG can evolve to form globular clusters and ultra compact dwarf ellipticals in about 12 Gyr so that present day globular clusters and ultra compact dwarf ellipticals may have formed in conditions similar to those observed in today GHIIR and HIIG.Comment: 11 pages, 6 figures, accepted for publication in MNRA