Complexes

We present a set of Matlab/Octave functions to compute measures of emergence, self-organization, and complexity applied to discrete and continuous data. These measures are based on Shannon’s information and differential entropy. Examples from different datasets and probability distributions are provided to show how to use our proposed code. Santamaría-Bonfil, G., Gershenson, C. & Fernández, N. (2017). A package for measuring emergence, self-organization, and complexity based on Shannon entropy. Frontiers in Robotics and AI , 4 :10. http://journal.frontiersin.org/article/10.3389/frobt.2017.00010/full

Highlights • The useful of quantitative indicators of ecological complexity is evaluated. • Chaos should not be confused with complexity. • Light and temperature cause different ranges of complexity in the gradient. • Homoeostasis variation is related to the seasonal changes and transitions. • Autopoiesis reveals groups with higher and lower degree of autonomy. Abstract Measuring complexity is fast becoming a key instrument to compare different ecosystems at various scales in ecology. To date there has been little agreement on how to properly describe complexity in terms of ecology. In this regard, this manuscript assesses the significance of using a set of proposed measures based on information theory. These measures are as follows: emergence, self-organization, complexity, homeostasis and autopoiesis. A combination of quantitative and qualitative approaches was used in the data analysis with the aim to apply these proposed measures. This study system...

To improve the efficiency of peer-to-peer (P2P) systems while adapting to changing environmental conditions, static peer-to-peer protocols can be replaced by adaptive plans. The resulting systems are inherently complex, which makes their development and characterization a challenge for traditional methods. Here we propose the design and analysis of adaptive P2P systems using measures of complexity, emergence, self-organization, and homeostasis based on information theory. These measures allow the evaluation of adaptive P2P systems and thus can be used to guide their design. We evaluate the proposal with a P2P computing system provided with adaptation mechanisms. We show the evolution of the system with static and also changing workload, using different fitness functions. When the adaptive plan forces the system to converge to a predefined performance level, the nodes may result in highly unstable configurations, which correspond to a high variance in time of the measured complexity. Co...

The slower is faster (SIF) effect occurs when a system performs worse when its components try to be better. Thus, a moderate individual efficiency actually leads to a better systemic performance. The SIF effect takes place in a variety of phenomena. We review studies and examples of the SIF effect in pedestrian dynamics, vehicle traffic, traffic light control, logistics, public transport, social dynamics, ecological systems, and adaptation. Drawing on these examples we generalize common features of the SIF effect and suggest possible future lines of research. When slower is faster Carlos Gershenson, Dirk Helbing http://arxiv.org/abs/1506.06796 Update : paper was published in Complexity : http://onlinelibrary.wiley.com/doi/10.1002/cplx.21736/abstract

Self-organisation occurs in natural phenomena when a spontaneous increase inorder is produced by the interactions of elements of a complex system. Thermodynamically,this increase must be offset by production of entropy which, broadly speaking, can beunderstood as a decrease in order. Ideally, self-organisation can be used to guide the systemtowards a desired regime or state, while “exporting” the entropy to the system’s exterior. Thus, Guided Self-Organisation (GSO) attempts to harness the order-inducing potentialof self-organisation for specific purposes. Not surprisingly, general methods developed tostudy entropy can also be applied to guided self-organisation. This special issue covers a broad diversity of GSO approaches which can be classified in three categories: informationtheory, intelligent agents, and collective behavior. The proposals make another step towardsa unifying theory of GSO which promises to impact numerous research fields. Entropy Methods in Guided Self-Organisat...

Ashby's law of requisite variety states that a controller must have at least as much variety (complexity) as the controlled. Maturana and Varela proposed autopoiesis (self-production) to define living systems. Living systems also require to fulfill the law of requisite variety. A measure of autopoiesis has been proposed as the ratio between the complexity of a system and the complexity of its environment. Self-organization can be used as a concept to guide the design of systems towards higher values of autopoiesis, with the potential of making technology more "living", i.e. adaptive and robust. Requisite Variety, Autopoiesis, and Self-organization Carlos Gershenson Invited keynote at WOSC 2014 http://arxiv.org/abs/1409.7475

We 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. Zubillaga, Darío; Cruz, Geovany; Aguilar, Luis D.; Zapotécatl, Jorge; Fernández, Nelson; Aguilar, José; Rosenblueth, David A.; Gershenson, Carlos. 2014. "Measuring the Complexit...

We compared entropy for texts written in natural languages (English, Spanish) and artificial languages (computer software) based on a simple expression for the entropy as a function of message length and specific word diversity. Code text written in artificial languages showed higher entropy than text of similar length expressed in natural languages. Spanish texts exhibit more symbolic diversity than English ones. Results showed that algorithms based on complexity measures differentiate artificial from natural languages, and that text analysis based on complexity measures allows the unveiling of important aspects of their nature. We propose specific expressions to examine entropy related aspects of tests and estimate the values of entropy, emergence, self-organization, and complexity based on specific diversity and message length. Complexity measurement of natural and artificial languages Gerardo Febres, Klaus Jaffé and Carlos Gershenson Complexity , Early View http://dx.doi.org/...

Upshot : The limitations of materialism for studying cognition have motivated alternative epistemologies based on information and computation. I argue that these alternatives are also inherently limited and that these limits can only be overcome by considering materialism, info-computationalism, and cognition at the same time. Open peer commentary on the article “ Info-computational Constructivism and Cognition ” by Gordana Dodig-Crnkovic. Gershenson C. (2014) Info-computationalism or Materialism? Neither and Both. Constructivist Foundations 9(2) : 241–242. Available at  http://www.univie.ac.at/constructivism/journal/9/2/241.gershenson

We apply measures of complexity, emergence and self-organization to an abstract city traffic model for comparing a traditional traffic 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 traffic is a non-stationary problem, which requires controllers to adapt constantly. Controllers must also change drastically the complexity of their behavior depending on the demand. Based on our measures, we can say that the self-organizing method achieves an adaptability level comparable to a living system. Measuring the Complexity of Self-organizing Traffic Lights Dario Zubillaga, Geovany Cruz, Luis Daniel Aguilar, Jorge Zapotecatl, Nelson Fernandez, Jose Aguilar, David A. Rosenblueth, Carlos Gershenson http://arxiv.org/abs/1402.01...

We compared entropy for texts written in natural languages (English, Spanish) and artificial languages (computer software) based on a simple expression for the entropy as a function of message length and specific word diversity. Code text written in artificial languages showed higher entropy than text of similar length expressed in natural languages. Spanish texts exhibit more symbolic diversity than English ones. Results showed that algorithms based on complexity measures differentiate artificial from natural languages, and that text analysis based on complexity measures allows the unveiling of important aspects of their nature. We propose specific expressions to examine entropy related aspects of tests and estimate the values of entropy, emergence, self-organization and complexity based on specific diversity and message length. Complexity measurement of natural and artificial languages Gerardo Febres, Klaus Jaffe, Carlos Gershenson http://arxiv.org/abs/1311.5427  

In recent years, we have heard more and more about complexity. However, it seems that given the increasing discourse divergence on this topic, instead of generating knowledge we are generating confusion. This paper offers a perspective to speak clearly about complexity from an epistemological point of view. En años recientes hemos escuchado hablar más y más sobre complejidad. Pero pareciera que al haber una diversidad creciente de discursos sobre el tema, en lugar de generar conocimiento estamos generando confusión. En este artículo se ofrece una perspectiva para hablar claramente sobre la complejidad desde un punto de vista epistemológico. En els últims anys s'ha sentit parlar cada cop més de complexitat. Tot i això, com que hi ha una diversitat creixent de discursos sobre aquest tema, en lloc de generar coneixement, estem generant confusió. En aquest article s'ofereix una perspectiva per parlar clarament sobre complexitat des d'un punt de vista epistemològic. Gershe...

The extended mind hypothesis has stimulated much interest in cognitive science. However, its core claim, i.e. that the process of cognition can extend beyond the brain via the body and into the environment, has been heavily criticized. A prominent critique of this claim holds that when some part of the world is coupled to a cognitive system this does not necessarily entail that the part is also constitutive of that cognitive system. This critique is known as the "coupling-constitution fallacy". In this paper we respond to this reductionist challenge by using an evolutionary robotics approach to create a minimal model of two acoustically coupled agents. We demonstrate how the interaction process as a whole has properties that cannot be reduced to the contributions of the isolated agents. We also show that the neural dynamics of the coupled agents has formal properties that are inherently impossible for those neural networks in isolation. By keeping the complexity of the model ...

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

Gershenson, C. (2013). Facing complexity: Predition vs. adaptation . In A. Massip and A. Bastardas (eds),  Complexity Perspectives on Language, Communication and Society . One of the presuppositions of science since the times of Galileo, Newton, Laplace, and Descartes has been the predictability of the world. This idea has strongly influenced scientific and technological models. However, in recent decades, chaos and complexity have shown that not every phenomenon is predictable, even if it is deterministic. If a problem space is predictable, in theory we can find a solution via optimization. Nevertheless, if a problem space is not predictable, or it changes too fast, very probably optimization will offer obsolete solutions. This occurs often when the immediate solution affects the problem itself. An alternative is found in adaptation. An adaptive system will be able to find by itself new solutions for unforeseen situations.

From today's seminar [in Spanish] Your browser does not support iframes. http://bambuser.com/v/3140519 Based on: Gershenson, C. (In Press) The Implications of Interactions for Science and Philosophy. Foundations of Science. http://dx.doi.org/10.1007/s10699-012-9305-8

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 ...

Butterflies have four wings. Can they fly with only two? This question arose this week. My wife and daughter had picked up a butterfly cocoon to see how the butterfly emerged and later free her. But our naughty/lovely cat bit on the cocoon. So when the butterfly came out, her right wings were damaged. She couldn't fly. Still, to answer the question of this post, if the hind wings are missing, butterflies can fly, their flight is amazingly robust. This is a nice example of how reductionism fails to see the function of systems by ignoring their interactions. You can have two out of four wings, but a butterfly will fly or not, live or die, depending on how the remaining wings interact . Looking only at individual wings will not tell you much about the capabilities of the insect.

Ultra-large scale (ULS) systems are becoming pervasive. They are inherently complex, which makes their design and control a challenge for traditional methods. Here we propose the design and analysis of ULS systems using measures of complexity, emergence, self-organization, and homeostasis based on information theory. We evaluate the proposal with a ULS computing system provided with genetic adaptation mechanisms. We show the evolution of the system with stable and also changing workload, using different fitness functions. When the adaptive plan forces the system to converge to a predefined performance level, the nodes may result in highly unstable configurations, that correspond to a high variance in time of the measured complexity. Conversely, if the adaptive plan is less "aggressive", the system may be more stable, but the optimal performance may not be achieved. Measuring the Complexity of Ultra-Large-Scale Evolutionary Systems, Michele Amoretti, Carlos Gershenson. Subm...

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