Complexes

A month late, but I share a draft where we propose a simple measure of antifragility and apply it to random and biological Boolean networks. Spoiler: biological networks are antifragile. Abstract: Antifragility is a property that enhances the capability of a system in response to external perturbations. Although the concept has been applied in many areas, a practical measure of antifragility has not been developed yet. Here we propose a simply calculable measure of antifragility, based on the change of "satisfaction" before and after adding perturbations, and apply it to random Boolean networks (RBNs). Using the measure, we found that ordered RBNs are the most antifragile. Also, we demonstrate that seven biological systems are antifragile. Our measure and results can be used in various applications of Boolean networks (BNs) including creating antifragile engineering systems, identifying the genetic mechanism of antifragile biological systems, and developing new treatment st...

In this chapter review measures of emergence, self-organization, complexity, homeostasis, and autopoiesis based on information theory. These measures are derived from proposed axioms and tested in two case studies: random Boolean networks and an Arctic lake ecosystem. Emergence is defined as the information produced by a system or process. Self-organization is defined as the opposite of emergence, while complexity is defined as the balance between emergence and self-organization. Homeostasis reflects the stability of a system. Autopoiesis is defined as the ratio between the complexity of a system and the complexity of its environment. The proposed measures can be applied at multiple scales, which can be studied with multi-scale profiles. Information Measures of Complexity, Emergence, Self-organization, Homeostasis, and Autopoiesis Nelson Fernandez, Carlos Maldonado, Carlos Gershenson http://arxiv.org/abs/1304.1842

Complexity and Information: Measuring Emergence, Self-organization, Homeostasis, and Autopoiesis at Multiple Scales Keynote talk at the 5th International Workshop on Guided Self-Organization . University of Sydney, Australia, September 26th, 2012. youtu.be/Ba0zSNYkWtw?a   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. We use information theory to provide abstract and concise measures of complexity, emergence, self-organization, homeostasis, and autopoiesis. 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. Autopoiesis can be measured as the ratio between the ...

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 (focussing on the information produced by a system), emergence becomes the opposite of self-organization, while complexity represents their balance. We use computational experiments on random Boolean networks and elementary cellular automata to illustrate our measures at multiple scales. Gershenson, C. & N. Fernández (2012). Complexity and Information: Measuring Emergence, Self-organization, and Homeostasis at Multiple Scales. C3 Report 2012.03.  http://arxiv.org/abs/1205.2026