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

1. Network Physics: A Vital Interlinked Anatomy and Physiology

Cajic, Pavle, et al. On the information-theoretic formulation of network participation. arXiv:2307.12556. University of Sydney systems theorists including Joseph Lizier describe an improved finesse of a method by which to parse relative multiples meanings.

The participation coefficient is a measure of the diversity of a node's connections with respect to a modular partition. While diversity metrics have been studied in other fields such as ecology, they have not been applied to networks. Here we show that the distinction is an approximation to participation entropy and use the additive properties of entropy to develop new metrics of connection diversity. Our information-theoretic formalism developed allows new and more subtle connection patterns in complex networks to be studied.

Caldarelli, Guido. Scale-Free Networks. Oxford: Oxford University Press, 2007. In some ten years since their discovery, this class of ‘real world,’ self-organized, interconnected systems distinguished by preferred nodes and links whose structure and dynamics repeat at any level have been studied both with regard to an independent universality, and to their manifest presence throughout in nature and society. As a result, a work such as this by the University of Rome complexity scientist can now describe their common properties, and as the quote notes, how an iterative invariance is evident from molecules to a metropolis.

The structure of this book…starts with some basic notions of graph theory. After that we spend some time in explaining (mainly by use of fractals) why scale-free behavior is so interesting. After the theory we present an overview of the application of the above concepts. The areas selected are those of natural sciences (protein interactions, metabolic and gene regulatory networks, food webs, taxonomies, and river networks), information technology (Inter and WWW), and socio-economic sciences (collaboration, cognitive networks, and financial systems). (4)

Caldarelli, Guido, et al. Progress in the Physics of Complex Networks. European Physical Journal Special Topics. 212/1, 2012. Italian and British scientists introduce a topical issue on this growing interdisciplinary synthesis of statistical physics and nonlinear systems. A typical technical paper is “Von Neumann’s Growth Model: Statistical Mechanics and Biological Applications” by Andrea De Martino, Enzo Marinari, and Andrea Romualdi. At what point, by what means, might it then dawn and be availed that beyond all the theories, a profoundly phenomenal genesis uniVerse is being discovered?

The presence of self-similar phenomena in Statistical Physics has a long tradition. From the classical studies of critical phenomena and renormalization group, we moved in the seventies and eighties of the last century to the analysis of scale-invariance in the geometrical features of self-similar phenomena. A further evolution of this approach resulted in the analysis of scale-invariance in the time dynamics of these systems with concepts such as Self-Organized Criticality and studies of the so-called “sandpile models”, an example of which is present in this issue. Most of the activity is now focussed on the search for scale-invariance in the topology, that is, in the way things are connected to each other. (1)

Carletti, Timoteo, et al. Global Topological Synchronization on Simplical and Cell Complexes. arXiv:2208.14783. TC, Lorenzo Giambagli, University of Namur, Belgium and Ginestra Bianconi, Queen Mary University, London theorists press their studies of network phenomena, which as an ecosmic anatomy and physiology seems ever graced by such innate facilities. See also Solitary States in Complex Networks: Impact of Topology by Anna Zakharova, et al (2208.14911).

Chavalarias, David. From Inert Matter to the Global Society: Life as Multi-level Networks of Processes. Philosophical Transactions of the Royal Society B. February, 2020. In this Unifying the Essential Concepts of Biological Networks issue, a Parisian cognitive scientist (bio below) illumes a cosmic to congress synthesis due to the generative activity of self-organization, autopoiesis, biocatalysis, recurrent scales, and more. This view leads a “triple closure” (see Abstract) made up of member components, active relations, and an integral unity. Life’s evolutionary basis and intent is then seen as a constant fulfillment of this iconic, triune whole. A consequentl rise of cerebral cognition, collective intelligence, and cultural learning can also be observed. As this universe to human course proceeds, our global phase is seen to be emerging into a “humanity-organism.” In closing, it is noted that this worldwide advance must not be left to chance, rather a common, informed, popular, concerted effort is imperative to bring to fruition.

A billion years have passed since the first life forms appeared. Since then, life has continued to form complex associations between emergent levels of interconnection. Advances in molecular chemistry and theoretical biology based on a systems view can now conceptualize life’s origins and complexity from three notions of closure: processes, autocatalysis and constraints. This integral paradigm can then trace the physical levels of the organization of matter from physics to biology and society without resorting to reductionism. The phenomenon of life thus becomes a contingent complexification until life emerges as a network of auto-catalytic process networks, organized in a multi-level manner. A living systems approach inevitably reflects on cognition; and on the deep changes that affects humanity by way of our cultural evolution. (Abstract Excerpt)

Humanity, by becoming an ‘organism’, is becoming de facto mortal. Cultural evolution as we used to think of it, is over. It will become more similar to a process of adaptation and learning at the level of humanity that can lead to its disappearance at any time. The new humanity – organism is alone on its evolutionary path and we can ask ourselves if we can afford to have it guided by random trials and errors. The kinds of collective cognition and behaviours that humanity will adopt in this new phase of its existence will determine its chances of survival in the future. (9)

David Chavalarias is the director of the Complex Systems Institute of Paris and Vice-President of the Complex Systems Society. He holds a PhD from the Ecole Polytechnique in cognitive sciences and attended the Ecole Normale Supérieure de Cachan in Mathematics and Computer Sciences. Currently permanent researcher at the National Center for Scientific Research (CNRS) in France, he studies the social and cognitive dynamics, both. His interdisciplinary research includes: quantitative epistemology, information visualization, modelling of the cultural dynamics, socio-semantic networks modelling, scientific discovery processes and cognitive economics.

Cimini, Giulio, et al. The Statistical Physics of Real-World Networks. arXiv:1810.05095. In a paper to appear in the new Nature Reviews Physics (2019), IMT School for Advanced Studies, Lucca, Italy researchers including Guido Caldarelli expand appreciations of nature’s universal complex nodal and relational networks. A widely separate yet integral rooting of our global civilization into physical condensed matter can then be achieved. An illustration displays how the same multiplex phenomena arises from a independent source which is exemplified from agriculture and industry to travel and trade. See also The Dynamics of Knowledge Acquisition via Self-Learning in Complex Networks by this team at 1802.09337.

Statistical physics is the natural framework to model complex networks. In the last twenty years, it has brought novel physical insights on a variety of emergent phenomena, such as self-organization, scale invariance, mixed distributions and ensemble non-equivalence, which cannot be deduced from individual constituents, along with information theory and the principle of maximum entropy. We review the statistical physics approach for complex networks and the null models for the various physical problems, focusing on the analytic frameworks reproducing the local features of the network. We show how these models have been used to detect statistically significant and predictive structural patterns in real-world networks. We further survey the statistical physics frameworks that reproduce more complex, semi-local network features using Markov chain Monte Carlo sampling, and the models of generalised network structures such as multiplex networks, interacting networks and simplicial complexes. (Abstract edits)

Cinardi, Nicola, et al. Quantum Statistics in Network Geometry with Fractional Flavor. arXiv:1902.10035. Systems physicists NC and Andrea Rapisarda, University of Catania, and Ginestra Bianconi, Queen Mary University of London continue to finely season nature’s true anatomy and physiology as it ever arrays in similar kinds from quantum to neuronal realms.

Growing network models have been shown to display emergent quantum statistics when nodes are associated to a fitness value describing the intrinsic ability of a node to acquire new links. Recently it has been shown that quantum statistics emerge also in a growing simplicial complex model called Network Geometry with Flavor which allow for the description of many-body interaction between the nodes. In this case the faces of the simplicial complex are naturally described by the Bose-Einstein, Boltzmann and Fermi-Dirac distribution depending on their dimension. We show that in this case the statistical properties of the faces of the simplicial complex are described by the Bose-Einstein or the Fermi-Dirac distribution only. (Abstract flavor)

Cohen, Reuven and Shlomo Havlin. Complex Networks: Structure, Robustness and Function.. Cambridge: Cambridge University Press;, 2010. A Bar-Ilan University, Israel mathematician and a physicist provide a comprehensive survey of ever growing realizations of an innately interconnected nature, organisms, and societies.

Examining important results and analytical techniques, this graduate-level textbook is a step-by-step presentation of the structure and function of complex networks. Using a range of examples, from the stability of the internet to efficient methods of immunizing populations, and from epidemic spreading to how one might efficiently search for individuals, this textbook explains the theoretical methods that can be used, and the experimental and analytical results obtained in the study and research of complex networks. Giving detailed derivations of many results in complex networks theory, this is an ideal text to be used by graduate students entering the field.

Costa, Luciano da Fontoura, et al. Analyzing and Modeling Real-World Phenomena with Complex Networks. Advances in Physics. 60/3, 2011. Drawing upon a departmental focus on this field, eight University of Sao Paulo physicists provide a 108 page survey, with 565 references, of this real dynamic materiality across nature and society. After noting Basic Concepts, topical areas are Social, Communications, Economy, Finance, Computers, Internet, World Wide Web, Citations, Transportation Power Grids, Biomolecular, Medicine, Ecology, Neuroscience, Linguistics, Earthquakes, Physics, Chemistry, Mathematics, Climate, and Epidemics – that is everywhere. From these many exemplars can be distilled a common, independent, complex system topology. Circa 2012, how could it dawn upon international collaborative science that this ubiquitous discovery is actually revealing a procreative genesis universe? In such regard, other such citations lately weigh in, e.g., Li and Peng in Complex Human Societies, Dorogovtsev, the Nature Physics Insight review, all herein, boding a critical credence. We append extended quotes.

Drawing upon a departmental focus on this field, eight University of Sao Paulo physicists provide a 108 page survey, with 565 references, of this real dynamic materiality across nature and society. After noting Basic Concepts, topical areas are Social, Communications, Economy, Finance, Computers, Internet, World Wide Web, Citations, Transportation Power Grids, Biomolecular, Medicine, Ecology, Neuroscience, Linguistics, Earthquakes, Physics, Chemistry, Mathematics, Climate, and Epidemics – that is everywhere. From these many exemplars can be distilled a common, independent, complex system topology. Circa 2012, how could it dawn upon international collaborative science that this ubiquitous discovery is actually revealing a procreative genesis universe? In such regard, other such citations lately weigh in, e.g., Li and Peng in Complex Human Societies, Dorogovtsev, the Nature Physics Insight review, all herein, boding a critical credence. We append extended quotes.

Courtney, Owen and Ginestra Bianconi. Generalized Network Structures: The Configuration Model and the Canonical Ensemble of Simplicial Complexes. arXiv:1602.04110. Queen Mary University, London mathematicians employ this topological phrase for their perception of connective patterns commonly found across networks. After technicalities, generic, repetitive webs are defined which form and flow everywhere. See also such later postings as Centralities of Nodes and Influences of Layers in Large Multiplex Networks at 1703.05833, Weighted Growing Simplicial Complexes. 1703.01187, and Emergent Hyperbolic Network Geometry in Nature Scientific Reports (7/41974, 2017) which each have GB as a coauthor. Altogether these distinct, recurrent features would seem to imply and arise from a natural propensity.

Simplicial complexes are generalized network structures able to encode interactions occurring between more than two nodes. Simplicial complexes describe a large variety of complex interacting systems ranging from brain networks, to social and collaboration networks. Here we characterize the structure of simplicial complexes using their generalized degrees that capture fundamental properties of one, two, three or more linked nodes. We evaluate the entropy of these ensembles, finding the asymptotic expression for the number of simplicial complexes in the configuration model. We provide the algorithms for the construction of simplicial complexes belonging to the configuration model and the canonical ensemble of simplicial complexes. (Abstract)

A large variety of interacting complex systems are characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links, triangles, tetrahedra) that have a natural geometric interpretation. Here, by extending our knowledge of growing complex networks to growing simplicial complexes we investigate the nature of the emergent geometry of complex networks and explore whether this geometry is hyperbolic. Specifically we show that an hyperbolic network geometry emerges spontaneously from models of growing simplicial complexes that are purely combinatorial. The statistical and geometrical properties of the growing simplicial complexes strongly depend on their dimensionality and display the major universal properties of real complex networks (scale-free, small-world and communities) at the same time. (GB/Rahmede)

Csermely, Peter. Fast and Slow Thinking – of Networks. arXiv:1511.01238. As 2014 and 2015 additions to our Introduction convey, intensive research since the early 1990s to the mid 2010s has reached a phase of consolidation and universality. This posting by the Semmelweis University, Budapest, systems biochemist (search) is a synopsis of a book chapter Plasticity-Rigidity Cycles at arXiv:1511.01239, we both review together. In this contribution, the robust field of scale-free networks is shown to apply to these evolutionary and personal cognitive modes. The main reference is the popular 2011 book Thinking, Fast and Slow by Daniel Kahneman about the dual systems model, as reported in A Complementary Brain and Thought Process. A subtitle “The complementary ‘elite’ and ‘wisdom of crowds’ of amino acid, neuronal and social networks” cites a first rapid response core network that draws on past experiences. If inadequate for novel, unfamiliar inputs, a weakly linked cerebral periphery is activated, often with conflicting views.

The longer posting expands this model to “A general adaptation mechanism” applicable from protein folding and birdsong learning to financial markets and environments. As a result, a dynamic structural universality across natural and social realms can now be affirmed. And a further surmise presents itself. The first page of the summary depicts these archetypal complements as a yin-yang symbol. Yet while dual process attributes match left and right brain hemisphere qualities, this association is rarely made. If to think about it, what might be averred in late 2015 is the worldwide discovery, with similar bicameral modes, of an integral, iterative natural genome code.

Complex systems may have billion components making consensus formation slow and difficult. Recently several overlapping stories emerged from various disciplines, including protein structures, neuroscience and social networks, showing that fast responses to known stimuli involve a network core of few, strongly connected nodes. In unexpected situations the core may fail to provide a coherent response, thus the stimulus propagates to the periphery of the network. Here the final response is determined by a large number of weakly connected nodes mobilizing the collective memory and opinion, i.e. the slow democracy exercising the 'wisdom of crowds'. This mechanism resembles to Kahneman's "Thinking, Fast and Slow" discriminating fast, pattern-based and slow, contemplative decision making. The generality of the response also shows that democracy is neither only a moral stance nor only a decision making technique, but a very efficient general learning strategy developed by complex systems during evolution. The duality of fast core and slow majority may increase our understanding of metabolic, signaling, ecosystem, swarming or market processes, as well as may help to construct novel methods to explore unusual network responses, deep-learning neural network structures and core-periphery targeting drug design strategies. (Abstract: Fast and Slow Thinking)

Successful adaptation helped the emergence of complexity. Alternating plastic- and rigid-like states were recurrently considered to play a role in adaptive processes. However, this extensive knowledge remained fragmented. In this paper I describe plasticity-rigidity cycles as a general adaptation mechanism operating in molecular assemblies, assisted protein folding, cellular differentiation, learning, memory formation, creative thinking, as well as the organization of social groups and ecosystems. (Abstract: Plasticity-Rigidity Cycles)

Csermely, Peter. The Wisdom of Networks: A General Adaptation and Learning Mechanism of Complex Systems. BioEssays. Online November, 2017. The Semmelweis University, Budapest, medical chemist also advises that a salient feature of networks is their broad array into a faster, constrained detail, core area, (seeds or words), and a slower periphery (search term) capable of viewing a contextual field. While the rigid core keeps doing the same thing, the freer outliers are open to beneficial variations. Akin to Miguel Munoz and others, the paper cites many phases such as proteins, metabolic signaling, neural nets, ecosystems, and social media whence this independent, common trait is exemplified in kind. See also Structure and Dynamics of Core/Periphery Networks by P. Csermely, et al in Journal of Complex Networks (1/93, 2013).

I hypothesize that re-occurring prior experience of complex systems mobilizes a fast response, whose attractor is encoded by their strongly connected network core. In contrast, responses to novel stimuli are often slow and require the weakly connected network periphery. Upon repeated stimulus, peripheral network nodes remodel the network core that encodes the attractor of the new response. This “core-periphery learning” theory reviews and generalizes the heretofore fragmented knowledge on attractor formation by neural networks, periphery-driven innovation, and a number of recent reports on the adaptation of protein, neuronal, and social networks. Moreover, the power of network periphery-related “wisdom of crowds” inventing creative, novel responses indicates that deliberative democracy is a slow yet efficient learning strategy developed as the success of a billion-year evolution. (Abstract)

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