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

Bornholdt, Stefan and Stuart Kauffman. Ensembles, Dynamics, and Cell Types: Revisiting the Statistical Mechanics Perspective on Cellular Regulation. arXiv:1902.00483. University of Bremen and Institute for Systems Biology, Seattle senior theorists look back 50 years to review Kauffman’s 1969 paper Metabolic Stability and Epigenesis in Randomly Constructed Genetic Nets (Journal of Theoretical Biology, 22/3, Abstract below). His 1993 work The Origins of Order played a major part in establishing the field of complex system studies. This posting continues its Self-Organization and Selection in Evolution subtitle by adding a statistical mechanics basis for biological regulation, along with selective effects. Into 2019 his prescient glimpses are well proven as we now know that gene regulatory networks do seek a self-organized criticality (search Bryan Daniels, Universality, Autocatalytic sections and elsewhere).

Genetic regulatory networks control ontogeny. For fifty years Boolean networks have served as models of such systems, ranging from ensembles of random Boolean networks as models for generic properties of gene regulation to working dynamical models of a growing number of sub-networks of real cells. At the same time, their statistical mechanics has been thoroughly studied. Here we recapitulate their original motivation in the context of current theoretical and empirical research. We discuss ensembles of random Boolean networks whose dynamical attractors model cell types. There is now strong evidence that genetic regulatory networks are dynamically critical, and that evolution is exploring the critical sub-ensemble. The generic properties of this sub-ensemble predict essential features of cell differentiation. Thus, the theory correctly predicts a power law relationship between the number of cell types and the DNA contents per cell, and a comparable slope. (2019 Abstract excerpt)

Proto-organisms probably were randomly aggregated nets of chemical reactions. The hypothesis that contemporary organisms are also randomly constructed molecular automata is examined by modeling the gene as a binary (on-off) device and studying the behavior of large, randomly constructed nets of these binary “genes”. The results suggest that, if each “gene” is directly affected by two or three other “genes”, then such random nets behave with great order and stability; undergo behavior cycles whose length predicts cell replication time as a function of the number of genes per cell; and under the stimulus of noise are capable of differentiating directly from any mode of behavior to at most a few other modes of behavior. The possibility of a general theory of metabolic behavior is suggested. (1969 SK Abstract excerpt)

Bountis, Tassos, et al. The Science of Complexity and the Role of Mathematics. European Physical Journal Special Topics. 225/883, 2016. Greek and British systems theorists introduce a special issue on this title subject. As the quotes say, and this site documents, as these endeavors reach a broad veracity, we ought to avail their wider natural, social and global benefit. And how appropriate that some two millennia later, such a scientific and philosophical advance comes from mainly Greece. If this robust 21st century natural knowledge can be translated, understood, and put to practical service, we might be able to resolve a local and global free-fall into economic, political, and internecine chaos. Sadly their own country is a prime example. Some papers are Regular and Chaotic Orbits in the Dynamics of Exoplanets, Hypernetworks, and Controlled Aggregation in Complex Systems. See also Bridging the Gaps at the Physics-Chemistry-Biology Interface in Philosophical Transactions of the Royal Society A (374/2080, 2016) for a similar edition.

In the middle of the second decade of the 21st century, Complexity Science has reached a turning point. Its rapid advancement over the last 30 years has led to remarkable new concepts, methods and techniques, whose applications to complex systems of the physical, biological and social sciences has produced a great number of exciting results. The approach has so far depended almost exclusively on the solution of a wide variety of mathematical models by sophisticated numerical techniques and extensive simulations that have inspired a new generation of researchers interested in complex systems. Still, the impact of Complexity beyond the natural sciences, its applications to Medicine, Technology, Economics, Society and Policy are only now beginning to be explored. Furthermore, its basic principles and methods have so far remained within the realm of high level research institutions, out of reach of society’s urgent need for practical applications. (Abstract excerpt)

“Complexity” is the Latin version of the Greek word, which refers to a multitude of twisting and folding structures similar to what one finds in the braids of a lady’s hair, the foliages of a tree or the flocking behavior of birds. At first sight, an object, or natural phenomenon characterized as complex (or “polyplokon”) evokes feelings of confusion and perplexity. When expressed in mathematical terms, however, it often reveals deep geometrical, dynamical and statistical properties and global unifying features that allow us to associate it with some particular universality class. (884) In this regard, we are no longer interested in the trajectories of individual particles, but wish to analyze the statistical behavior of the particular ensemble. We thus discover that the most interesting systems of natural, biological and social sciences are far from equilibrium, and exhibit self organization and emergence of patterns and coherent structures that cannot be explained by the behaviour of individual components. These are known as complex systems. (884)

Bourgine, Paul, et al, eds. The CSS Roadmap for Complex Systems Science and its Applications 2012 – 2020. http://unitwin-cs.org/documents.html. A mission guide for the European based UniTwin UNESCO Complex Systems Digital Campus, a network of research and teaching institutions. CSS is Complex Systems Society, Director Bourgine is a CREA-Ecole Polytechnique, Paris, senior researcher. Publications on the webpage appear in four languages – French, English, Spanish, and Portuguese. Scroll down and click on this title, other Brochures are also available, along with an “African Roadmap” in French. The text, and burgeoning project, is another sign of the broad historical shift to better understand and guide human societies by way of these palliative organic vitalities.

The new science of complex systems is providing radical new ways of understanding, modeling, predicting, managing the physical, biological, ecological, and social universe. Complex systems are characterised by emergent structures that occur in many domains and questions that apply across the domains in the modern world. Radical new strategies of research and teaching are necessary for all the previous transversal questions through all kind of complex systems, from atoms to complex matter, from the molecules to organisms, from organisms to the ecosphere, from neurotransmitters to the individual and social cognition, from individuals to human society. This huge effort is necessary for reconstructing the observed multi-scale dynamics relevant for the “human scales” in between the physics of the two infinites, the nuclear physics in one side and the cosmology in the other side.

The Science of Complex Systems will develop in the same way that physics has developed during the three last centuries through a constant process of reconstructing models from constantly improving data. The reconstruction of the multi-level dynamics of complex systems, i.e. integrated models, presents a major challenge to modern science but it is becoming more and more accessible through ubiquitous cloud computing. (3) The science of complex system is therefore different to any other particular science because it focuses on the methods of reconstructing the dynamics of systems of heterogeneous systems across the traditional domains. This methodological perspective and the trans-disciplinary nature of complex systems science make it unique in that it is an integrative science that strives to combine the methods, knowledge and theory of other domain-based science. (5)

As an example for a social system consider the people evacuating a building in an emergency. The motion of people in crowds is observed and a phenomenological model is created of the ways people move with respect to each other. Using this phenomenological model, an agent-based computer simulation can be used to create an augmented phenomenology for this system. A theoretical model of pedestrian flows can be proposed and permit spatio-temporal simulations to create another augmented phenomenology. In fact this new science can assist the authorities to redesign Mecca for the Hajj pilgrimage which hitherto was subject to fatal accidents with large numbers of people being trampled as the dynamics of the crowd changed. This is one of the major success stories of complex systems science. (5-6)

Brauns, Fridtjof, et al. Phase-Space Geometry of Reaction-Diffusion Dynamics. arXiv:1812.08684. In a densely technical, tightly composed 55 page paper, Ludwig-Maximilians University system physicists FB, Jacob Halatek and Erwin Frey (search) continue their decadal project to explain by way of nonequilibrium thermodynamics, structural formations, Turing-like morphogenesis, self-organized critical complexities, computational biology, and more how life proceeds to develop and maintain its physiological vitality. With 158 references, in these later 2010s a collaborative sense of a realistic model is evident. It is proposed in closing that such cellular coherence is an generalization which could apply to other natural systems. See also Rethinking Pattern Formation in Reaction-Diffusion Systems by Halatek and Frey in Nature Physics (14/5, 2018) and for example Guiding Self-Organized Pattern Formation in Cell Polarity Establishment by Peter Gross, et al (NP December 2018)

Experimental studies of protein pattern formation have stimulated new interest in the dynamics of reaction--diffusion systems. However, a comprehensive theoretical understanding of the dynamics of such highly nonlinear, spatially extended systems is still missing. Here we show how a description in phase space, which has proven invaluable in shaping our intuition about the dynamics of nonlinear ordinary differential equations, can be generalized to mass-conserving reaction--diffusion (McRD) systems. We present a comprehensive theory for two-component McRD systems, which serve as paradigmatic minimal systems. The fundamental elements of the theory presented suggest ways of experimentally characterizing pattern-forming systems on a mesoscopic level and are generalizable to a broad class of spatially extended non-equilibrium systems, and thereby pave the way toward an overarching theoretical framework. (Abstract excerpt)

Brown, Barton, et al. Dynamically Generated Hierarchies in Games of Competition. arXiv.1906.01383. By way of our philoSophia approach, Virginia Tech physicists and a Jacobs University, Bremen physicist (Hildegard Meyer-Ortmanns) can be seen to achieve a quantified description of intrinsic natural “spontaneities” which evidently form on into complex, interactive, beneficial groupings.

Spatial many-species predator-prey systems have been shown to yield very rich space-time patterns. This observation begs the question whether there exist universal mechanisms for generating such emerging complex patterns in non-equilibrium systems. In this work we investigate the possibility of dynamically generated hierarchies in predator-prey systems. We analyze a nine-species model with competing interactions and show that the situation results in the spontaneous formation of spirals within spirals. As cyclic interactions occur spontaneously in systems with competing strategies, the mechanism discussed in this work should contribute to our understanding of various social and biological systems. (Abstract excerpt)

Non-equilibrium growth processes provide well known examples of emerging space-time patterns in a variety of fields, ranging from magnets to social systems and from bacterial colonies to ecosystems. In such far from equilibrium conditions, rich space-time patterns can emerge spontaneously. (2)

Brown, James and Geoffery West, eds. Scaling in Biology. New York: Oxford University Press, 2000. Papers from a Santa Fe Institute conference which explore the fractal and allometric scaling and self-similarity present in Metazoan anatomy and physiology, ecosystems and evolution.

Life is amazing. Even the smallest bacterium is far more complex in its structure and function than any known physical system. The largest, most complex organisms, large mammals and giant trees, weigh more than 21 orders of magnitude more than the simplest microbes, yet they use basically the same molecular structures and biochemical pathways to sustain and reproduce themselves. (1)

Brown, James, et al. The Fractal Nature of Nature: Power Laws, Ecological Complexity and Biodiversity. Philosophical Transactions of the Royal Society of London B. 357/619, 2002. Further insights into an intricate, tangled but knowable natural kingdom by virtue of its universally recurring principles.

The Earth’s surface and the living things that inhabit it are incredibly diverse….Underlying this enormous physical and biological diversity, however, are emergent patterns that are precise, quantitative, and universal or nearly so. (619)

Buchanan, Mark. Ubiquity: Why the World Is Simpler Than We Think. London: Weidenfeld & Nicolson, 2000. An accessible introduction to how the nonlinear sciences reveal a “universality” in nature and history. The same patterns and processes are in evidence from cosmic origins to world civilization and economic society because they spring from an independent dynamics of power laws and self-organized criticality.

Cavalcante, Hugo, et al. Predictability and Control of Extreme Events in Complex Systems. arXiv:1301.0244. In this January 2013 posting, systems physicists Cavalcante and Marcos Oria, Universidade Federal da Paraiba, Brazil, Didier Sornette, ETH Zurich, and Daniel Gauthier, Duke University, provide further quantitative support for the theories of Sornette (search) and colleagues that warning signs of impending catastrophic calamities can in fact be limned from hyper-complexities such as climates and economies, contrary to many denials. These significance insights are also well explained by mathematician James Weatherall in his fine The Physics of Wall Street: A Brief History of Predicting the Unpredictable (Houghton Mifflin Harcourt, 2013)

In many complex systems, large events are believed to follow power-law, scale-free probability distributions, so that the extreme, catastrophic events are unpredictable. Here, we study coupled chaotic oscillators that display extreme events. The mechanism responsible for the rare, largest events makes them distinct and their distribution deviates from a power-law. Based on this mechanism identification, we show that it is possible to forecast in real time an impending extreme event. Once forecasted, we also show that extreme events can be suppressed by applying tiny perturbations to the system. (Abstract)

Chandler, Jerry and Gertrudis Van de Vijver, eds. Closure: Emergent Organizations and Their Dynamics. New York: New York Academy of Sciences. Volume 901, 2000. Many articles consider autopoietic processes with regard to their property of constantly forming, describing and "closing" their “biosemiotic” identity. This is a sign-based organic viability which pervades the natural realm as living systems refer to and enhance their own internal definition and individuality.

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)

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