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IV. Ecosmomics: An Independent Source Script of Generative, Self-Similar, Complex Network Systems

Sole, Ricard and Jordi Bascompte. Self-Organization in Complex Ecosystems. Princeton: Princeton University Press, 2006. A synoptic contribution reviewed more in Dynamic Ecosystems.

Sole, Ricard and Sergei Valverde. Evolving Complexity: How Tinkering Shapes Cells, Software and Ecological Networks. Philosophical Transactions of the Royal Society B. February, 2020. Barcelona systems theorists (search) provide a 21st century retrospective survey of their studies and this revolutionary witness by a worldwide faculty of a cosmos to creature to cognition proto-evolution which is suffused by a common multiplex anatomy and physiology. In 2019 this phenomenal animate reality is set within a scenario that implies a dynamic interplay of endemic self-organizing principles and constraints, along with many candidates subject to chancy selective forces. The main gist draws upon Francois Jacob’s 1977 Evolution and Tinkering paper (French Nobel geneticist, see Science 196/1161) to emphasize how nature seems to constantly repurpose organelle components as life strives to develop and emerge. Some four decades later, by way of novel network connectivities a balanced synthesis of non-random rules and working adaptations can be broached.

AA major finding of late is that complex systems can be represented by a network of interacting parts. The network organization (more than the parts) that conditions most higher-level properties, which are not reducible. Can the topology of these webs provide some insight into their evolutionary origins? Both biological and artificial networks share common architectural traits. They often exhibit correlations such as nestedness, modularity or hierarchical patterns which give rise to heterogeneous, scale-free and modular architectures. Here, we examine the evidence for tinkering in cellular, technological and ecological webs how it shapes them. (Abstract)

Sornette, Didier. Dragon-Kings, Black Swans and the Prediction of Crises. arXiv:0907.4290. A July 2009 paper where the Swiss systems theorist introduces his concept that apparently extreme events can in fact be found to have an intrinsic mathematical basis, which when properly understood can foster a modicum of predictability. This critical insight, embellished in Sornette and Ouillon 2012, is gaining currency such as “The Origins of Dragon-Kings and their Occurrence in Society” by Artemy Malkov, et al, Russian Academy of Sciences, in Physica A, online May 2012.

We develop the concept of “dragon-kings” corresponding to meaningful outliers, which are found to coexist with power laws in the distributions of event sizes under a broad range of conditions in a large variety of systems. These dragon-kings reveal the existence of mechanisms of self-organization that are not apparent otherwise from the distribution of their smaller siblings. We present a generic phase diagram to explain the generation of dragon-kings and document their presence in six different examples (distribution of city sizes, distribution of acoustic emissions associated with material failure, distribution of velocity increments in hydrodynamic turbulence, distribution of financial drawdowns, distribution of the energies of epileptic seizures in humans and in model animals, distribution of the earthquake energies). We emphasize the importance of understanding dragon-kings as being often associated with a neighborhood of what can be called equivalently a phase transition, a bifurcation, a catastrophe, or a tipping point. (Abstract)

One of the most remarkable emergent properties of natural and social sciences is that they are punctuated by rare large events, which often dominate their organization and lead to huge losses. This statement is usually quantified by heavy-tailed distributions of event sizes. Here, we present evidence that there is “life” beyond power laws: we introduce the concept of dragon-kings to refer to the existence of transient organization into extreme events that are statistically and mechanistically different from the rest of their smaller siblings. This realization opens the way for a systematic theory of predictability of catastrophes, which is outlined here and illustrated. (1)

Sornette, Didier. Why Stock Markets Crash: Critical Events in Complex Financial Systems. Princeton: Princeton University Press, 2003. The book is also a good primer on complex system dynamics with an emphasis on their power-law “discrete scale invariance.” Life’s evolution is likewise seen to possess an iterative self-similarity. The expansive work goes on to explore a necessary transition to sustainability by an informed symbiosis with nature, lest our host planet Earth die from ecological insults.

A central property of a complex system is the possible occurrence of coherent large-scale collective behaviors with a very rich structure, resulting from the repeated nonlinear interactions among its constituents: the whole turns out to be much more than the sum of its parts. (16)

Sornette, Didier and Guy Ouillon. Dragon-Kings: Mechanisms, Statistical Methods and Empirical Evidence. European Physical Journal Special Topics. 205/1, 2012. To introduce a special issue, ETH Zurich systems scientists advocate an overdue and important course correction for the complexity sciences and their implied worldview. A pessimistic, defeatist attitude holds that extreme, unpredictable “black swan” events result from a nature and society bereft any fundamental mathematical regularity. By keen theoretical insights presented here, this is not the actual case. While the term may not be ideal, by ‘dragon’ is meant an extraordinary outlier, and ‘king’ stands for wealth out of proportion to the realm. As introduced in a 2009 posting below, ‘dragon-kings’ are “coherent collective events in the synchronized regime of systems of interacting threshold oscillation.” As noted in the second quote, despair over an ultimately unknowable, capricious reality can be repealed by such a perceptive finesse of self-organizing, power law phenomena.

Many phenomena in the physical, natural, economic and social sciences can be characterized by power-law statistics, for which there are many different mechanisms. Power-law (i.e. self-similar) distributions of the sizes of events suggest that mechanisms of nucleation and growth dynamics remain the same over the whole spectrum of relevant spatial and temporal scales. According to this paradigm, small, large and extreme events belong to the same population, the same distribution, and reflect the same underlying mechanism(s). Major catastrophes are just events that started small and did not stop growing to develop into large or extreme sizes. (1)

Following that reasoning, a majority of the scientific community considers those events as unpredictable, in the sense that the final size of a future event cannot be forecasted in advance. This concept has become popular since Nassim Taleb’s book “The Black Swan” (2007). This view is particularly pessimistic, and even alarming if true, as it casts a strong doubt on possibilities of precise hazard prediction, with all the societal consequences. In our mind, it is even dangerous as it promotes an attitude of irresponsibility: in a world where catastrophes (in human-controlled activities, for instance) are pure surprises, no one can be responsible. In contrast, the concept of dragon-kings, if their occurrences can be diagnosed ex-ante, brings back responsibility and accountability. (1)

Stanisz, Tomasz, et al. Linguistic Data Mining with Complex Networks. arXiv:1808.05439. Polish Academy of Sciences system physicists Stanisz, Jaroslaw Kwapien, and Stanislaw Drozdz (search latter names) continue their project to theorize and describe a dynamic nonlinear nature which appears to be manifestly evident and exemplified even in literary script and conversation. Into the 2010s, the second quote conveys a typical opening paragraph for entries like this (see F. Rosas above) that says just as being found in every other cosmic to cultural stage and instance, these universally recurrent forms can equally be seen to grace our human textual phase.

By representing a text by a set of words and their co-occurrences, one obtains a word-adjacency network as a reduced representation of the given language sample. In this paper, the possibility of using network representation in order to extract information about individual language styles of literary texts is studied. By determining selected quantitative characteristics of the networks and applying machine learning algorithms, it is made possible to distinguish between texts of different authors. It turns out that within the studied set of texts in English and Polish, the properly rescaled weighted clustering coefficients and weighted degrees of only a few nodes in the word-adjacency networks are sufficient to obtain the accuracy of authorship attribution over 90%. The presented approach can be viewed as a generalization of the authorship attribution methods based on simplest lexical features. (Abstract)

Many systems studied in contemporary science, from the standpoint of their structure, can be viewed as the ensembles of large number of elements interacting with each other. Such systems can often be conveniently represented by networks, consisting of nodes and links between these nodes. As nodes and links are abstract concepts, they may refer to many different objects and types of interactions, respectively. Therefore, a rapid development of the so-called network science has found application in studies on a great variety of systems, like social networks, biological networks, networks representing financial dependencies, the structure of the Internet, or the organization of transportation systems. (1)

Stankowski, Tomislav, et al. Coupling Functions: Universal Insights into Dynamical Interaction. Reviews of Modern Physics. 89/4, 2017. As complexity sciences gain a substantial credence, Lancaster University, UK, and Imperial College London physicists point out and elucidate still another relational attribute and propensity which appears to be in constant play everywhere.

Dynamical systems in science with examples ranging from physics, chemistry, and biology up to population dynamics, communication, and climate are rarely isolated but generally interact with each other. One particular way of characterizing the interactions is to use coupling functions which possess the property of enabling one not only to understand but also to control and predict the underlying interaction dynamics. This article demonstrates the usefulness of coupling functions for studying the interaction mechanisms of dynamical systems in different research fields. (Summary)

Stanley, Eugene. Universality and Scale Invariance: Organizing Principles that Transcend Disciplines. www.societyforchaostheory.org/conf2003/abstracts.html. A keynote paper presented at the annual Society for Chaos Theory and Psychology Conference. The Boston University systems physicist describes how the same power-law behavior is being found in widely diverse realms from statistical physics to the “econophysics” of financial markets.

Stanley, Eugene, et al. Scaling and Universality in Animate and Inanimate Systems. Physica A. 231/1, 1996. (Also in Fractals. 4/3, 1996.) An earlier glimpse of mathematical reasons why nature is characterized at every phase by the same self-organized critical system from crystalline lattices to DNA base pairs, heartbeat intervals, neighborhood geometries and economic markets.

Stauffer, Dietrich, et al. From Newton to Mandelbrot. Berlin: Springer, 2017. Senior theoretical physicists Stauffer, Eugene Stanley and Annick Lesne post the third edition since 1990 of a tutorial volume all about the natural persistence of self-similar fractal forms and movements from quantum mechanics, statistical physics, and broadly conceived dynamical systems

Stavroglou, Stavros, et al. Unveiling Causal Interactions in Complex Systems. Proceedings of the National Academy of Sciences. 117/7599, 2020. Complexity theorists SS, University of Liverpool, A. A. Pantelous, Monash University, Eugene Stanley, Boston University and K. M. Zuev, CalTech contribute to current realizations of how universally manifest these iconic complex dynamics truly are.

Patterns in nature and society are described as complex systems due to their complicated, highly interconnected properties. Capturing the ebb and flow of their structures can aid better understandings of nature’s rules and social integrity. In this context, a methodology is proposed that unveils important operations and components of complex systems. Its wide utility is demonstrated by reconstructing a desert ecosystem, describing features of the alcoholic brain, and locating key assets in financial markets. (Significance)

Strogatz, Steven. Math and the City. http://judson.blogs.nytimes.com/2009/05/19/math-and-the-city/?em. A May 19, 2009 guest posting by the Cornell University systems scientist on evolutionary biologist Olivia Judson’s New York Times blog, which would surely please Galileo. By virtue of 21st century worldwide computer capabilities, from galaxies to Gaia this natural creation is newly becoming legible and explained via an underlying realm of mathematical dynamics. Moreover, of much import for human comprehension, the same patterns and processes of network self-organization are found to recur at every stage and instance. (See also a new video course “Chaos” by Prof. Strogatz offered by The Teaching Company, along with its online description at http://www.teach12.com/ttcx/coursedesclong2.aspx?cid=1333.)

One of the pleasures of looking at the world through mathematical eyes is that you can see certain patterns that would otherwise be hidden. This week’s column is about one such pattern. It’s a beautiful law of collective organization that links urban studies to zoology. It reveals Manhattan and a mouse to be variations on a single structural theme. (1)

These numerical coincidences seem to be telling us something profound. It appears that Aristotle’s metaphor of a city as a living thing is more than merely poetic. There may be deep laws of collective organization at work here, the same laws for aggregates of people and cells. (3)

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