IV. Ecosmomics: Independent Complex Network Systems, Computational Programs, Genetic Ecode Scripts

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)

Strogatz, Steven. Sync: The Emerging Science of Spontaneous Order. New York: Hyperion, 2003. A Cornell University mathematician explains the newly found tendency in nature to form a synchronous order. This effect occurs from the quantum realm to fireflies, heartbeats, and consciousness within an innately sympathetic universe.

All the examples are variations on the same mathematical theme: self-organization, the spontaneous emergence of order out of chaos. (14) It (sync) is grounded in rigorous mathematical ideas; it has passed the test of experiment; and it describes and unifies a remarkably wide range of cooperative behavior in living and nonliving matter, at every scale of length from the subatomic to the cosmic. (286)

Strogatz, Steven, et al. Fifty Years of “More is Different.”. Nature Reviews Physics. April, 2022. As a response to this anniversary (Science 177/393,1972), the veteran Cornell University systems theorist asks eight complexity thinkers such as Sara Walker, Corina Tarnita, and Oriol Artime for their views going forward. Some responses cite emerging patterns, broken symmetry, information flows, and new singularities. So into the 2020s, Anderson’s complexity prescience has now become a revolutionary florescence undertaken by a vast worldwise faculty.

August 1972 saw the publication of Philip Anderson’s essay ‘More is different’. In it, he crystallized the idea of emergence, arguing that “at each level of complexity entirely new properties appear” — that is, although, for example, chemistry is subject to the laws of physics, we cannot infer the field of chemistry from our knowledge of physics. Fifty years on from this landmark publication, eight scientists describe the most interesting phenomena that emerge in their fields.

Many emergent phenomena are sustained through networks of interactions. Focussing, for instance, on biophysical phenomena, we have biomolecular interactions emerging from the human interactome, or electrochemical neural connectivity patterns emerging from the human connectome. In general, though, these networks do not operate in isolation: they are coupled to each other by means of structural or functional interdependencies, and they are organized in multiple contexts of interactions, also knownas layers. These layers may include links that are spatial, temporal, informational or combinations thereof. (Oriol Artime, Manlio de Domenico)

Tadic, Bosiljka and Roderick Melnik. Fundamental interactions in self-organized critical dynamics on higher-order networks. arXiv:2404.06175.. Jozef Stefan Institute, Ljubljana, Slovenia and Wilfrid Laurier University; Waterloo, Canada (search each) contribute further theoretic findings of how pervasive nature’s propensity to reside at this synchronous optimum title state seems to be. In this case they discern its self-similar presence in multiplex connectivities such as cerebral phenomena. See also Self-organized dynamics beyond scaling of avalanches by Bosiljka Tadic, et al at arXiv:2403.15859.

In complex systems, higher-order connectivity is often revealed in the geometry of networked units. Such systems show signatures of self-organized criticality, a non-equilibrium collective behaviour associated with long-range correlations and scale invariance. Here, we intertwine features of higher-order geometry and self-organized critical dynamics as responsible for the emergence of new properties on a larger scale as occurs in brains. We provide an overview of collective dynamics phenomena, such as the synchronization of phase oscillators. (Excerpt)

Taran, Somayeh. Complex Network in Solar Features. arXiv:2410.09814. Into late this year, a University of Tabriz, Iran astrophysicist, building on her prior collegial studies along with full access to the global research cyber-literature, can proceed to analyze and find that even sunshine will hold to and exemplify nature’s universal dynamic patterns. See also Complex network view to solar flare asymmetric activity by S. Taran, et al in Advances in Space Research 70/8, 2022.

This paper is an overview of studying the solar features in a complex network approach. We introduce their structural features and important parameters such as detrended fluctuation, range analysis and power-law distributions. Using the HEALPix pixelization, as well as applying centrality (the nodes with the highest connectivity, closeness, betweenness, and Pagerank) we showed that the active areas on the solar surface were correctly identified. The complex network of sunspots has also shown that their appearance is formed through complex nonlinear dynamics.

Sunspots Complex Networks Sunspots are a phenomenon that clearly shows the complexity of the solar magnetic field. Studying the sunspot time series generally reveals the periodicity of solar activities, although the amplitude of sunspot activity differs in various periods. Sunspots with different numbers and sizes appear on the solar surface, and observations show that large spots are divided into tiny spots, which is a sign of the self-organization of the sunspot system. (24)

Thurner, Stefan, et al. Introduction to the Theory of Complex Systems. Oxford: Oxford University Press, 2018. Senior Medical University of Vienna system physicists Stefan Thurner, Peter Klimek and Rudolf Hamel provide a wide-ranging technical survey to date which covers scaling, networks, evolutionary processes, self-organized criticality, non-equilibrium statistical mechanics, information theory, and future advances, see next quote.

The chapter is a mini outlook on the field. The classic achievenments in complexity science are mentioned, and we summarize how the new directions might open new doors into a twenty-first-century science of complex systems. We do that by clarifying the origin of scaling laws, in particular for driven non-equilibrium systems, deriving the statistics of driven systems, categorizing probabilistic complex systems into universality classes, by meaningful generalizations of statistical mechanics and information theory, and finally, by unifying approaches to evolution and co-evolution into a single mathematical framework. We comment on our view of the role of artificial intelligence and our opinion on the future of science of complex systems. (Future of Complex Systems Science excerpt)

Tsallis, Constantino, Murray Gell-Mann, and Yuzuru Sato. Special Scale-Invariant Occupancy of Phase Space Makes the Entropy Sq Additive. Santa Fe Institute Working Paper. 05-03-005, 2005. Available at www.santafe.edu where its authors present technical nonequilibrium thermodynamic reasons why nature exhibits a universal, nested self-similarity.

We conjecture that this mechanism is deeply related to the nearly ubiquitous emergence, in natural and artificial complex systems, of scale-free structures.

Turcotte, Donald and John Rundle. Self-Organized Complexity in the Physical, Biological, and Social Sciences. Proceedings of the National Academy of Sciences. 99/Supp. 1, 2002. This Supplement contains papers from a 2001 NAS meeting to glimpse precocious theories as they may express dynamic relations between the previously found separate parts and objects. Authorities such as Eugene Stanley, Luis Amaral, Geoffrey West, Per Bak, Mark Newman, Stephen Strogatz and Didier Sornette spoke on topics like Allometric Scaling of Metabolic Rate from Molecules and Mitochondria to Cells and Mammals, Fractal Dynamics in Physiology, Unified Scaling Law for Earthquakes, Self-organized Complexity in Economics and Finance, and Scaling Phenomena in the Internet. But today’s worldwide web where these papers can be readily accessed was not yet in place. Circa 2018, as we seek to document and convey, the project is now reaching a convergent universality phase and accomplishment. A decade and a half is all it takes for a our global brain via instant communications to achieve this on her/his own.

The National Academy of Sciences convened an Arthur M. Sackler Colloquium on “Self-organized complexity in the physical, biological, and social sciences” at the NAS Beckman Center, Irvine, CA, on March 23–24, 2001. The organizers were D.L.T. (Cornell), J.B.R. (Colorado), and Hans Frauenfelder (Los Alamos National Laboratory, Los Alamos, NM). The organizers had no difficulty in finding many examples of complexity in subjects ranging from fluid turbulence to social networks. However, an acceptable definition for self-organizing complexity is much more elusive. Symptoms of systems that exhibit self-organizing complexity include fractal statistics and chaotic behavior. Some examples of such systems are completely deterministic (i.e., fluid turbulence), whereas others have a large stochastic component (i.e., exchange rates). The governing equations (if they exist) are generally nonlinear and may also have a stochastic driver. Many of the concepts that have evolved in statistical physics are applicable (i.e., renormalization group theory and self-organized criticality). As a brief introduction, we consider a few of the symptoms that are associated with self-organizing complexity.

Turnbull, Laura, et al. Connectivity and Complex Systems: Learning from a Multi-Disciplinary Perspective. Applied Network Science. 3/11, 2018. As an example of our present integrative phase after years of special studies, eleven generalists from the UK, Germany, the Netherlands, Cyprus, and Sweden proceed to identify and describe a common feature, as the Abstract cites, which plays a formative role from geology to ecology. The paper first describes this fundamental associative property being found to join the prior pieces, as underway in genomic relations and neural networks. In this necessary turn isolate parts are brought into an actual unitary whole. Six subject areas as below are then reviewed to show how the same lineaments are in similar effect everywhere. With this in place, basic “toolbox” methods are specified to define connective features from the biosphere to cultures going forward. Several reference pages over the past decades document the research divergence and convergence.

In recent years, parallel developments in disparate disciplines have focused on what has come to be termed connectivity; a concept used in understanding and describing complex systems. Conceptualizations have evolved largely within their disciplinary boundaries, yet similarities in this concept and its application among disciplines are evident. This situation leads us to ask if there an approach to connectivity that might be applied to all disciplines. In this review we explore four ontological and epistemological challenges. These are: (i) defining the fundamental unit for the study of connectivity; (ii) separating structural connectivity from functional connectivity; (iii) understanding emergent behaviour; and (iv) measuring connectivity. We draw upon insights from Computational Neuroscience, Ecology, Geomorphology, Neuroscience, Social Network Science and Systems Biology to explore the use of connectivity among these disciplines. (Abstract excerpt)

Valverde, Sergi, et al. Emergent Behavior in Agent Networks. http://arxiv.org/abs/physics.0602003. A web posting of a paper accepted for a special issue of IEEE Intelligent Systems on Self-Management through Self-organization.

Villegas, Pablo, et al. Laplacian Renormalization Group for Heterogeneous Networks. arXiv:2203.07230. Into spring 2022, Four Enrico Fermi Research Center, Rome, IMT, Institute for Advanced Studies, Lucca, and University of Venice (Giudo Caldarelli) theorists put together still another way to quantify and discern nature’s common avail of complex, dynamic patterns and processes. The credible case for an intrinsic mathematical domain in universal keeps filling in as braced by these many approaches. By an attention to read the scientific literature as revealing such findings on its own, their content bodes well for a salutary mid 2020s discovery. See also Laplacian Paths in Complex Networks: Information Core Emerges from Entropic Transitions by this team at 2202.06669.

The renormalization group is the cornerstone of the modern theory of universality and phase transitions, a powerful tool to scrutinize symmetries and organizational scales in dynamical systems. However, its network counterpart is particularly challenging due to correlations between intertwined scales. To date, the explorations are based on hidden geometries hypotheses. Here, we propose a Laplacian RG diffusion-based picture in complex networks, defining both the Kadanoff supernodes' concept, the momentum space procedure, and applying this RG scheme to real networks in a natural and parsimonious way. (Abstract)

An open question is how to perform network reduction to generate replicas that connect internal scales above a microscopic phase. This scenario invites a powerful method of in modern physics, the Renormalization Group (RG). RG provides an elegant and precise theory of criticality and allows for connections across the varied spatiotemporal scales, so as to demonstrate a ubiquitous invariance. (1)

Volkening, Alexandria. Volkening, Alexandria. Methods for quantifying self-organization in biology: a forward-looking survey. arXiv:2407.10832. A Purdue University mathematician contributes a latest tutorial chapter for an interdisciplinary audience which presents various approaches for qualitative data studies across a range of applications. See a prior paper by AV, Linking discrete and continuous models of cell birth and migration, at arXiv:2308.16093.

rom flocking birds to schooling fish, organisms interact to form collective dynamics across the natural world. Self-organization is present at smaller scales as well: cells interact and move during development to produce patterns in fish skin. For all these examples, scientists are interested in the individual behaviors informing spatial group dynamics and the patterns that will emerge due to agent interactions. A current issue is that models of self-organization are qualitative and need pattern data to include quantitative information. In this tutorial chapter, I survey some methods for quantifying self-organization, including order parameters, pair correlation functions, and techniques from topological data analysis. (Abstract)

Pattern formation driven by the interactions of agents is found across the natural and social world, spanning the population scale to the intracellular scale. Large-scale examples include pedestrian movements, honeybee aggregation, schooling fish, and marching locusts. In the domain of cells and tissues, neural-crest cell migration, color in fish skin, and wound healing are examples of self-organization. At smaller scales, proteins and filaments regulate transport and shape within cells. Studying such complex systems often leads to qualitative pattern data in the form of images. Being able to quantify these spatial data opens the door to a broader perspective on self-organization and makes complex systems more amenable to interdisciplinary investigation. (1)

Andrea V. was a programme participant in the Mathematics of Movement: an interdisciplinary approach to mutual challenges in animal ecology and cell biology (Google) symposium at the Isaac Newton Institute for Mathematical Sciences, Cambridge, autumn 2023. She gratefully acknowledges a travel grant from the Association for Women in Mathematics.

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