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IV. Ecosmomics: An Independent, UniVersal, Source Code-Script of Generative Complex Network Systems

Changizi, Mark and Darren He. Four Correlates of Complex Behavioral Networks: Differentiation, Behavior, Connectivity, and Compartmentalization. Complexity. 10/6, 2005. A hierarchical universality of these features is reported across a wide range of phenomena such as nervous systems, organisms, social groups, economies, and ecosystems.

Chen, Yanguang. Zipf’s Law, l/f Noise, and Fractal Hierarchy. Chaos, Solitons, & Fractals. 45/1, 2012. As the extended Abstract conveys, a Peking University, College of Urban and Environmental Sciences, systems geographer contributes to the growing realizations of nature’s universally invariant, scalar repetition of the same structural and processual phenomena everywhere.

Fractals, 1/f noise, and Zipf’s laws are frequently observed within the natural living world as well as in social institutions, representing three signatures of complex systems. All these observations are associated with scaling laws and therefore have created much research interest in many diverse scientific circles. However, the inherent relationships between these scaling phenomena are not yet clear. In this paper, theoretical demonstration and mathematical experiments based on urban studies are employed to reveal the analogy between fractal patterns, 1/f spectra, and the Zipf distribution. First, the multifractal process empirically suggests the Zipf distribution. Second, a 1/f spectrum is mathematically identical to Zipf’s law. Third, both 1/f spectra and Zipf’s law can be converted into a self-similar hierarchy. Fourth, fractals, 1/f spectra, Zipf’s law can be rescaled with similar exponential laws and power laws. The self-similar hierarchy is a more general scaling method which can be used to unify different scaling phenomena and rules in both physical and social systems such as cities, rivers, earthquakes, fractals, 1/f noise, and rank-size distributions. The mathematical laws of this hierarchical structure can provide us with a holistic perspective of looking at complexity and complex systems. (Abstract)

Christensen, Kim and Nicholas Moloney. Complexity and Criticality. London: Imperial College Press, 2005. A technical work rooted in statistical mechanics that implies in part that self-organization in non-equilibrium systems may be a unifying concept for a emergent natural complexity.

For our purposes, complexity refers to the repeated application of simple rules in systems with many degrees of freedom that gives rise to emergent behavior not encoded in the rules themselves. (vii) Criticality refers to the behavior of extended systems at a phase transition where observables are scale free, that is, no characteristic scales exist for these observables. (vii) Criticality is therefore a cooperative feature emerging from the repeated application of the microscopic laws of a system of interacting ‘parts.’ (vii)

The science of complexity is highly interdisciplinary. It deals with dynamical systems composed of many interacting units, for example grains in granular media, rocks in the crust of the Earth, water droplets in the atmosphere, networks of organisms in biology or agents in economics, etc. (253)

Chua, Leon. Local Activity is the Origin of Complexity. International Journal of Bifurcation and Chaos. 15/11, 2005. Another example of growing efforts to identify a common complex system, but with dense mathematics it is hard to see how this feature can fit the bill. But the universality concept – that the same complex dynamics recurs everywhere throughout a nested nature –has long been the payoff.

Many scientists have struggled to uncover the elusive origin of “complexity,” and its many equivalent jargons, such as emergence, self-organization, synergetics, collective behaviors, nonequilibrium phenomena, etc…..The purpose of this paper is to show that all the jargons and issues cited above are mere manifestations of a new fundamental principle called local activity, which is mathematically precise and testable. (3435)

Chua, Leon, et al. A Nonlinear Dynamics Perspective of Wolfram’s New Kind of Science. Part V: Fractals Everywhere. International Journal of Bifurcation and Chaos. 15/12, 2005. The other four parts appeared over the last two years in this publication. A highly technical meditation on a “universal computation” by cellular automata and neural networks which manifests a self-similarity throughout an emergent world.

Cilliers, Paul. Difference, Identity, and Complexity. Philosophy Today. Spring, 2010. A synopsis of Cilliers and Rika Preiser’s edited work next in search of workable ways to understand nature’s self-organizing interplay of creative diversity and essential unity.

The argument in this essay is primarily one which resists an interpretation of deconstruction, and a post-structural understanding of difference, as an absolute free-play. Deconstruction acknowledges the inevitability of structure, and of its transformation. This “double movement” should be central when we think of institutions and organizations. (63)

Cilliers, Paul and Rika Preiser, eds. Complexity, Difference and Identity: An Ethical Perspective. Berlin: Springer, 2010. University of Stellenbosch, RSA, systems philosophers gather papers to address a troublesome issue in nonlinear studies – how to square a prolific spontaneity with an implied steady source. Its sections of Complexity, Difference, Identity, Ethics of Complexity, and Consequences strive toward a necessary reciprocity. See chapters by Cilliers and Collier herein, also Cilliers’ synopsis in Philosophy Today, (Spring 2010).

Corning, Peter. Nature’s Magic: Synergy in Evolution and the Fate of Humankind. Cambridge: Cambridge University Press, 2003. A consummate volume to convey this biologist’s thesis that cooperative effects between, for example, genes or individuals, are equally as important as the components themselves. The theory posits that when cooperation produces beneficial functional effects or synergies (some are not beneficial), these may be favored or selected (synergistic selection). This propensity then plays a causal role in the evolution of emergent complexity from the origin of life to human societies.

Corominas-Murtra, Bernat, et al. Hierarchy in Complex Systems. arXiv:1303.2503. A March 2013 posting by Corominas-Murtra and Ricard Sole, Universitat Pompeu Fabra, with Joaquin Goni and Carlos Rodgiguez-Caso, Indiana University, which is seen as confirming a half century later, Herbert Simon’s advocacy that regnant nature relies on hierarchical modularities for its robust maintanence. Indeed this 21st century Barcelona-Bloomington team can avail theoretical computations to develop 3D visualizations, which reveals an implicate source from which these nested, evolutionary structures arise. Ricard Sole acknowledges conversations in regard at the Santa Fe Institute with Douglas Erwin, Eric Smith, Geoffrey West and Murray Gell-Mann. See for example, Colm Ryan, et al. “Hierarchical Modularity and the Evolution of Genetic Interactomes across Species” in Molecular Cell (46/691, 2012) which also cites “general design principles” at work.

Cowan, George, et al, eds. Complexity. Reading, MA: Addison Wesley, 1994. A compendium of papers in search of unifying themes in terms of complex adaptive systems. The pioneers are represented: Philip Anderson, Brian Arthur, Per Bak, Walter Fontana, Murray Gell-Mann, Brian Goodwin, John Holland, Erica Jen, Stuart Kauffman, Melanie Mitchel, Peter Schuster, along with many others.

De Florio, Vincenzo. Systems, Resilience, and Organization: Analogies and Points of Contact with Hierarchy Theory. arXiv:1411.0092. A citation for publications on this site and in journals by the University of Antwerp mathematician. The endeavor often casts back to Gottfried Leibniz to propose a 2010s synthesis by way of a fractal self-similarity from cells to communities that could fulfill his prescience of a universally recurrent code script.

De Marzo, Giordano, et al. Quantifying the Unexpected: A Scientific Approach to Black Swans. Physical Review Research. 4/033079, 2022. The prolific collaboration of these Centro Ricerche Enrico Fermi, Rome system physicists including Luciano Pietronero here continues to apply their innovative analyses from sidereal realms to, in this instance, the pesky problem of whether sudden complex bursty behaviors (wild weather, market crashes, tipping points) can be found to have a quantifiable basis. While many prior efforts were not satisfactory, by virtue of a better perception of endemic fractal affinities this endeavor allows that some manner of an actual mathematic basis seems to be discernible. See also Using Machine Learning to Anticipate Tipping Points and Extrapolate to Post-Tipping Dynamics of Non-Stationary Dynamical Systems by Dhruvit Patel and Edward Ott at arXiv:2207.00521 for another contribution.

Many natural and socio-economic systems are characterized by power-law distributions that make the occurrence of extreme events not negligible. Such events are sometimes referred to as Black Swans, but a quantitative definition is still lacking. By leveraging on the properties of Zipf-Mandelbrot law, we investigate the relations between such events and the dynamics of the upper cutoff of the inherent distribution. This analysis provides a method to classify White, Grey, or Black Swans. The systematic and quantitative methodology we developed allows a scientific and immediate categorization of rare events, along with new insights into their generative mechanism. (Abstract excerpt)

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