This chapter reviews 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 different scales, which can be studied with multi-scale profiles.

1 aFernández, Nelson1 aMaldonado, Carlos1 aGershenson, Carlos1 aProkopenko, Mikhail uhttp://arxiv.org/abs/1304.184201436nas a2200205 4500008004100000245006300041210006200104300001600166490000700182520082000189100002201009700001801031700002601049700002301075700002301098700001901121700002701140700002301167856004001190 2014 eng d00aMeasuring the Complexity of Self-organizing Traffic Lights0 aMeasuring the Complexity of Selforganizing Traffic Lights a2384–24070 v163 aWe apply measures of complexity, emergence, and self-organization to an urban traffic model for comparing a traditional traffic-light coordination method with a self-organizing method in two scenarios: cyclic boundaries and non-orientable boundaries. We show that the measures are useful to identify and characterize different dynamical phases. It becomes clear that different operation regimes are required for different traffic demands. Thus, not only is traffic a non-stationary problem, requiring controllers to adapt constantly; controllers must also change drastically the complexity of their behavior depending on the demand. Based on our measures and extending Ashby's law of requisite variety, we can say that the self-organizing method achieves an adaptability level comparable to that of a living system.1 aZubillaga, Darío1 aCruz, Geovany1 aAguilar, Luis, Daniel1 aZapotécatl, Jorge1 aFernández, Nelson1 aAguilar, José1 aRosenblueth, David, A.1 aGershenson, Carlos uhttp://dx.doi.org/10.3390/e1605238401262nas a2200133 4500008004100000245010700041210006900148300001000217490000700227520080700234100002301041700002301064856004101087 2012 eng d00aComplexity and Information: Measuring Emergence, Self-organization, and Homeostasis at Multiple Scales0 aComplexity and Information Measuring Emergence Selforganization a29-440 v183 aConcepts 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.1 aGershenson, Carlos1 aFernández, Nelson uhttp://dx.doi.org/10.1002/cplx.2142400527nas a2200133 4500008004100000245011300041210007000154260003700224100002300261700001900284700002300303700002000326856004700346 2012 eng d00aSistemas Dinámicos como Redes Computacionales de Agentes para la evaluación de sus Propiedades Emergentes.0 aSistemas Dinámicos como Redes Computacionales de Agentes para la aUniversidad Central de Venezuela1 aFernández, Nelson1 aAguilar, José1 aGershenson, Carlos1 aTerán, Oswaldo uhttp://turing.iimas.unam.mx/sos/?q=node/15