I. Our WumanWise Edition: A 21st Century, philoSophia, eLibrary of eCosmos, PediaPedia Resource

C. Our 2022 Earthuman Convergent Discovery of a UniVerse to WumanVerse ProCreation

Tadic, Bosiljka and Roderick Melnik. Self-Organized Critical Dynamics as a Key to Fundamental Features of Complexity in Physical, Biological and Social Networks. Dynamics. 2/2, 2022. Senior theorists in Solvenia and Canada (see bio’s below and home websites) provide a select, consummate survey of 21st century worldwise multiplex non-equilibrium system studies as they may reach their current convergent, integrative syntheses across every spatial and temporal, uniVerse to humanVerse, domain. We pair the entry with On the Biological Complexity of Brain Dynamics by N. Shettigar, et al in this issue so as prime instances of a epochal discovery event in our midst. Herein the emphasis is on novel findings about nature’s consistent propensity to seek and reside at an optimum mid-point balance between more or less relative coherence. The paper reviews technical attributes such as self-similarity, power laws, multifractal landscapes, simplicial networks, collective behaviors and all else. As one reads along, the text reiterates the cerebral descriptions in the other paper. That is to say, our Earthropocene sapience, as it learns and thinks on its own, can has well found and defined the presence of a familial genetic-like code which universally recurs in kind everywhere.

Studies of many complex systems have revealed new collective behaviours that emerge through the mechanisms of self-organised critical fluctuations. These collective states with long-range spatial and temporal correlations often arise from an external dynamic drive with an intrinsic nonlinearity and geometric interactions. The self-similarity of critical fluctuations enables us to describe natural systems using fewer parameters and universal functions that can then simplify the computational and information complexity. Current research on self-organised critical systems across many scales strives to formulate a unifying mathematical framework by way of critical universal properties in information theory. Through physical, biological, and social network exemplars, we show how a constant self-organised criticality occurs at the interplay of the complex topology and driving mode. (Abstract excerpt)

This feature article has two goals. Firstly, we give a brief survey of a diversity of current research trends of SOC systems across different scales and types of interactions. Secondly, we present new results on the field-driven spin dynamics in complex nano-networks, an appearing prominent example of SOC behaviour induced by the substrate’s geometry. Using several representative examples of SOC systems of different nature and interaction patterns, we highlight some fundamental aspects of the dynamic complexity. (3)

The SOC occurs in many complex systems and networks at various scales, types of interactions, and intrinsic dynamics. They all obey some universal behaviours that can be captured by the properties of the emergent critical states. These are the long-range correlations, fractality, avalanching dynamics and scale invariance. It has been understood that these properties of the critical states can provide a deeper understanding of different aspects of complexity. In particular, recent research on various SPA models and real-world systems strives to underpin self-organised critical behaviour in the mechanisms underlying the emergence of new collective features, essential for the physical and biological complexity. They also provide a more transparent structure of information stored in the critical state and reduced computational complexity. In the context of complexity, understanding the role of various geometrical constraints in the critical dynamics and hidden geometry features that enable competing interactions at different scales are of paramount importance. (13-14)

Bosiljka Tadic is a theoretical physicist at the Jozef Stefan Institute, Ljubljana who researches the intrinsic nature of complex systems and networks. Her studies involve the statistical physics of cooperative phenomena from functional brain networks to emotional behaviors in Internet societies. In regard, she has published over 120 technical papers.

Roderick Melnik is internationally regarded for his work in applied mathematics, and numerical analysis and a Canada Research Chair in Mathematical Modeling and Professor at Wilfrid Laurier University. He was born in the Ukraine and earned his doctorate at the National University of Kyiv. (I was unaware of his bio as I chose to highlight the paper, which is so appropriate for this knowledge vs. madness moment.)

Teuscher, Christof. Revisiting the Edge of Chaos: Again?.. Biosystems. May, 2022. The veteran Portland State University systems theorist looks back over the course of this perception all the way to Stuart Kauffman’s autocatalysis whereof life prefers to seek and reside at an active poise between more or less order. Albeit along the way there were doubts, problems and variations, but it can indeed once more be affirmed that this optimum balance does seem to be in prevalent effect across much natural and social phenomena. Which into 2022, with L. da Costa and myriad other confirmations, would constitute an epochal, salutary discovery.

Does biological computation happen at some sort of “edge of chaos”, a dynamical regime somewhere between order and chaos? And if so, is this a fundamental principle that underlies self-organization, evolution, and complex natural and artificial systems that are subjected to adaptation? In this article, we will review the literature on the fundamental principles of computation in natural and artificial systems at the “edge of chaos”. The term was coined by Norman Packard in the late 1980s. Since then, the concept of “adaptation to the edge of chaos” was demonstrated and investigated in many fields where both simple and complex systems receive some sort of feedback. Besides reviewing both historic and recent literature, we will also review critical voices of the concept. (Excerpt)

Udrescu, Silviu-Marian, et al. AI Feynman 2.0: Pareto Optimal Symbolic Regression Exploiting Graph Modularity. arXiv:2006,10762. MIT and Stanford physicists including Max Tegmark conceive and employ further effective techniques that can inform and serve this global computational ascent.

We present an improved method for symbolic regression that seeks to fit data to formulas that are Pareto-optimal and have the best accuracy for a given complexity. We develop a method for discovering generalized symmetries (arbitrary modularity in the computational graph of a formula) from gradient properties of a neural network fit. We use normalizing flows to generalize and aid probability distributions for which we only have samples, along with statistical hypothesis testing. (Excerpt)

Wuppuluri, Shyam and Ian Stewart, eds. Electrons to Elephants to Elections. International: Springer Frontiers, 2022. An Indian editorial philosopher and and the British mathematician and author here gather and arrange some 45 chapters so as to illustrate and flesh out that from our late vantage nature’s evident course from universe to human can be as some manner of emergence. This broad theme unites essays from physical and biological to personal and social phases. whereby we need take leave of a bottomed-out reduction method. The entries variously agree on a scalar, recurrent hierarchy which frames an oriented ascent from quantum realms through life’s long, sentient evolution onto cultural behaviors. By this view, some manner of self-similar recurrence in sequential kind can be perceived. A paper which richly evinced was Shared Mathematical Content in the Context of Complex Systems by the Jacobs University physicist Hildegard Meyer-Ortmanns (search), whose Abstract is next. Overall, these intellectual endeavors do seem closer to an encoded natural genesis of complexity, awareness and persons.

We pursue reduction to mathematics rather than materiality which seems more likely to underlie universal phenomena in different contexts. We illustrate with examples of increasing complexity. Firstly, by way of a set of differential equations which apply to pattern formation in biology and to classical mechanics. We then refer to the asymptotics of singular behavior at criticality between various substances. Thirdly, a set of stochastic reactions gives rise to emergent ecological phenomena which corresponds to a transition from species coexistence to extinction.. The fourth case is about Tracy-Widom probability distributions which observes universality classes in wide occurrence. (H. Meyer-Ortmanns excerpt)

Zanin, Massimiliano and Johann Martinez. Analysing International Events through the Lens of Statistical Physics: The Case of Ukraine. arXiv:2203.07403. IFISC Institute for Cross-Disciplinary Physics and Complex Systems, University of the Balearic Islands, Spain theorists provide a timely and insightful application of 21st century complex network science advances, as these natural mathematics gain deeper roots in conducive physical phenomena. (Search Neil Johnson, Pedro Manrique, for more findings of how an independent dynamics can even underlie violent conflicts.) The paper was written before the invasion, but can convey a vital illumination. As our 2020s postings now confirm (A Naturome Code, Earthuman Integrations), an actual organic genesis is found to be animated and constrained by an independent source script in exemplary, genetic-like effect for each and every instance. So into this real March madness, maybe concurrent Earthwise Learnings can dispense such edifications we so need.

During the last years, statistical physics has received an increasing attention as a framework for the analysis of real complex systems. However, this is less clear in the case of international political events, partly due to a difficulty in securing relevant quantitative evidence. Here we consider a detailed data set of violent events that took place in Ukraine since January 2021, and analyse their temporal and spatial correlations through entropy and complexity metrics, and functional networks. Results depict an unstable scenario, with events occurring in a non-random fashion, but with eastern-most regions functionally disconnected from the remainder of the country. (Abstract)

During the last decades, statistical physics concepts and tools have ceased being exclusive of this scientific field, for becoming standard approaches used in the analysis of numerous and heterogeneous real-world problems. To illustrate but a few examples, complex networks have become an essential asset in epidemics spreading models, neuroscience, and climate; along with biomedical systems from brain to heart dynamic. The reason for such success is possibly rooted in statistical physics' ability for decoupling the dynamical and observational scales; while a system may only be observable at the macro-scale, conclusions about the underlying micro-scale source can still be drawn. (1)

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