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

4. Universality Affirmations: A Critical Complementarity

Del Papa, Bruno, et al. Criticality Meets Learning: Criticality Signatures in a Self-Organizing Recurrent Neural Network. PLoS One. May 26, 2017. Computational neuroscientists BDP and Jochen Triesch, Goethe University, Frankfurt, and Viola Priesemann, MPI Dynamics and Self-Organization press on with studies of a neural propensity to seek and reside at a preferred, simultaneous poise of more or less orderly states.

Many experiments suggest that the brain operates close to a critical state, based on signatures such as power-law distributed neuronal avalanches. In neural network models, criticality is a dynamical state that maximizes information processing capacities, e.g. sensitivity to input, dynamical range and storage capacity. Although models that self-organize towards a critical state have been proposed, the relation between criticality signatures and learning is still unclear. Here, we investigate criticality in a self-organizing recurrent neural network (SORN). We show that, after a transient, the SORN spontaneously self-organizes into a dynamical state that shows criticality signatures comparable to those found in experiments. Overall, our work shows that the biologically inspired plasticity and homeostasis mechanisms responsible for the SORN’s spatio-temporal learning abilities can give rise to criticality signatures in its activity. (Abstract excerpt)

Dobrovolska, Olena. Interrelationship Between Fractal Ornament and Multilevel Selection Theory. Biosemiotics. Online May, 2018. A Kharkiv National University of Radioelectronics, Ukraine philosopher achieves a unique synthesis across the sciences and the cultural ages. From an ancient land beset by internecine conflict, a woman scholar is able to cast an intellectual survey to broach an animate natural iteration. If to allow and consider, it promises to fulfill perennial wisdom as it reveals a universally recurrent pattern and process. As our worldwide sapience finds a cosmic biosemiosis via an informational agency, such a self-similarity and reference in kind can be noticed at each and every scale and instance. See also a 2018 paper by O. Mryglod for more an Ukranian uniVerse.

Interdisciplinarity is one of the features of modern science, defined as blurring the boundaries of disciplines and overcoming their limitations or excessive specialization by borrowing methods from one discipline into another, integrating different theoretical assumptions, and using the same concepts and terms. Biosemiotics, a field that arose at the crossroads of biology, semiotics, linguistics, and philosophy, enables scientists to borrow theoretical assumptions from semiotics and extend them to different biological theories. In the present research, the semiotic system of Ukrainian folk ornament is analyzed through the theory of fractals, key features of which are recursion and self-similarity. What follows is a discussion of how this assumption can contribute to the multilevel selection theory, one of the foundations of extended synthesis, which employs the concept of self-similarity at all levels of the biological hierarchy. (Abstract)

In the present research, the semiotic system of Ukranian folk ornament is analyzed through the theory of fractals, key features of which are recursion and self-similarity. As a result, an assumption is made about the fractal structure of culture and social life on a conceptual level. What follows is a discussion of how this assumption can contribute to the multilevel selection theory, one of the foundations of extended synthesis, which employs the concept of self-similarity at all levels of the biological hierarchy. (2)

Another typical fractal symbol is the Tree of Life, which is self-similar in two dimensions. First, the tree-shape is itself fractal, since every branch is a small, virtually identical copy of the whole tree. Second, self-repetition is evident in the structure of trees. The Tree of Life, which holds a special place in Ukranian culture, representing as it does the Universe and nature on one hand and the family on another. This symbol crops uo in many areas of Ukranian folk art, since the Tree represents the universe and the diversity of life forms, uniting the underworld (roots), the Earth (trunk), and heaven (branches). At the same time, it unites spirit (the growing parts during summertime: leaves, blossoms, and fruit) and matter (the bulk of the tree during the year). The other meaning is the family, consisting of many generations linking past, present, and future. Roots would be a family’s ancestors, while branches with leaves and blossoms would represent present and future generations. The tree of life emphasizes the similarity between humankind and family, the Universe and the individual. (12-13)

Dodig-Crnkovic, Gordana. Information, Computation, Cognition: Agent-Based Hierarchies of Levels. Muller, Vincent, ed. Fundamental Issues of Artificial Intelligence. Switzerland: Springer, 2016. In this select collection from a Philosophy and Theory of AI conference at Oxford University, the Chalmers University theorist, among her many writings (search) again offers a cogent recitation of life’s emergent, nested, repetitive iteration from atomic and biomolecular origins to our aware collective cognizance. This cosmic and Earthly evolution is seen to proceed by an interplay of agent entities in relational communication. As many concurrent papers herein attest, a fractal self- similarity is thus said to repeat in kind from universe to humanity.

In order to study within one framework cognition in living organisms (including humans) and machines (including cognitive software), this article is generalizing some common ideas, thus using extended concepts of , , , , , , , and . The basis is the idea of nature as a network of networks of that exchange information. This generalized type of exist on the level of fundamental particles, then on the higher level of atoms as composed of networks of elementary particles, then higher still there are molecules consisting of atoms as . Up in hierarchy of levels of organization of agents there are cells as networks of molecules, organisms as networks of cells, ecologies as networks of organisms, etc. In short there is a fractal structure with recurrent pattern of agents within agents on a variety of levels of organization. (142)

This volume offers a look at the fundamental issues of present and future AI, especially from cognitive science, computer science, neuroscience and philosophy. This work examines the conditions for artificial intelligence, how these relate to the conditions for intelligence in humans and other natural agents, as well as ethical and societal problems that artificial intelligence raises or will raise. The key issues this volume investigates include the relation of AI and cognitive science, ethics of AI and robotics, brain emulation and simulation, hybrid systems and cyborgs, intelligence and intelligence testing, interactive systems, multi-agent systems, and super intelligence. (Publisher)

Dunham, Christopher, et al. Nanoscale Neuromorphic Networks and Criticality. Journal of Physics: Complexity. 2/4 December, 2021. We record this entry by nine UCLA, University of Sydney, and UnLAB, Savannah, GA researchers as a latest example of many wide and deep areas where critical point behavior is being found. Its dynamic distinction is to become situated and balanced between more or less orderly or coherent phases. (As chimera theory notes, often in both states at once.) The paper reviews these phenomenal findings and goes on to describe how cerebral activity is seen as an archetypal instance.

Numerous studies suggest critical dynamics may play a role in information processing and task performance in biological systems. However, studying these systems can be challenging due to many biological variables that limit access to underlying physical processes. Here we offer a perspective on the use of abiotic, neuromorphic nanowire networks as a means to investigate critical dynamics in complex adaptive systems. Neuromorphic nanowire networks are composed of metallic nanowires and metal-insulator-metal junctions. They self-assemble into interconnected, variable-density forms and exhibit nonlinear electrical switching properties and information processing capabilities. We posit that such neuromorphic networks can function as abiotic physical systems for studying critical dynamics and computation. (Abstract excerpt)

Ermann, Leonardo, et al. Google Matrix Analysis (GMA) of Directed Networks. Reviews of Modern Physics. 87/4, 2015. Theoretical physicists Ermann, CNEA Argentina, with Klaus Frahm and Dima Shepelyansky (search), University of Toulouse, write a lengthy tutorial on such scale-free mathematical and topological methods including Markov chains, which are found to similarly apply from genomes to economies. But searching the title phrases does not result in a simple definition. As a gloss, a meld of directed graphs with weighted, oriented edges and the PageRank algorithms, topics considered in initial pages. This generic pattern is seen to appear in software architecture, the worldwide web, Wikipedia, social media, global trade, scientific citations, neural nets, gene regulation, and more. An allusion is made to Jorge Borges’ The Library of Babel that such a common recurrence could begin to bring some organizational sense across nature and society. See also prior papers GMA of DNA Sequences (1301.1626), and GMA of C.elegans Neural Network (1311.2013), and GMA of the World Network of Economic Activities (1504.06773) by these authors and colleagues. A further surmise might be that the constant system is much akin to a genome, a semblance of a universe to human genetic code.

In past ten years, modern societies developed enormous communication and social networks. Their classification and information retrieval processing become a formidable task for the society. Due to the rapid growth of World Wide Web, social and communication networks, new mathematical methods have been invented to characterize the properties of these networks on a more detailed and precise level. Various search engines are essentially using such methods. It is highly important to develop new tools to classify and rank enormous amount of network information in a way adapted to internal network structures and characteristics. This review describes the Google matrix analysis of directed complex networks demonstrating its efficiency on various examples including World Wide Web, Wikipedia, software architecture, world trade, social and citation networks, brain neural networks, DNA sequences and Ulam networks. The analytical and numerical matrix methods used in this analysis originate from the fields of Markov chains, quantum chaos and Random Matrix theory. (Article Abstract)

For DNA sequences of various species we construct the Google matrix G of Markov transitions between nearby words composed of several letters. The statistical distribution of matrix elements of this matrix is shown to be described by a power law with the exponent being close to those of outgoing links in such scale-free networks as the World Wide Web (WWW). At the same time the sum of ingoing matrix elements is characterized by the exponent being significantly larger than those typical for WWW networks. This results in a slow algebraic decay of the PageRank probability determined by the distribution of ingoing elements. The spectrum of G is characterized by a large gap leading to a rapid relaxation process on the DNA sequence networks. We introduce the PageRank proximity correlator between different species which determines their statistical similarity from the view point of Markov chains. The properties of other eigenstates of the Google matrix are also discussed. Our results establish scale-free features of DNA sequence networks showing their similarities and distinctions with the WWW and linguistic networks. (1301.1626 Abstract)

Fan, Jingfang, et al. Universal Gap Scaling in Percolation. Nature Physics. April, 2020. We cite this technical entry by JF, Jun Meng, Yang Liu, Abbas Saberi, and Jurgen Kurths, Potsdam Institute for Climate Impact Research, along with Jan Nagler, Deep Dynamics Group, Frankfurt School of Finance as another current finding about the universal presence, so it seems, from physical networks to everywhere else such as cells, brains, hearts, genomes, and onto to linguistic information. Cosmic to cultural nature can now indeed be found to draw upon and express a single, infinitely recurrent, critical condition.

Universality is a principle that underlies many critical phenomena from epidemic spreading to the emergence of connectivities in networks. Percolation, the transition to global connectedness on gradual addition of links, may exhibit substantial gaps in the size of the largest connected network component. We uncover that the largest gap statistics is governed by extreme-value theory. This allows us to unify continuous and discontinuous percolation by virtue of universal critical scaling functions. This links extreme-value statistics to universality and criticality in percolation. (Abstract)

Filatov, Denis and Alexey Lyubushin. Stochastic Dynamical Systems Always Undergo Trending Mechanisms of Transition to Criticality. Physica A. Volume 521, 2019. Sceptica Science, UK and Russian Academy of Sciences physicists post a theoretical affirmation as to why and how nature’s active phenomena has an intrinsic attraction to reach a critically poised state. See also A Method for Identification of Critical States of Open Stochastic Dynamical Systems by D. Filatov in Journal of Statistical Physics (165/4, 2016).

We study the transition of stochastic dynamical systems to critical states. We begin from employing two independent quantitative methods of time series analysis, first-order detrended fluctuation analysis and multivariate canonical coherence analysis. We find out that there are two different mechanisms of the transition to criticality: the first mechanism is consistent with that observed in some biological dynamical systems and associated with a growth of the energies at low frequencies in the power spectrum, whereas the second mechanism is new and governed by a decay of the energies at high frequencies. Despite this difference, we show that both mechanisms lead to a loss of chaoticity in the system’s behavior and result in a more deterministic evolution of the system as a whole. The obtained results allow hypothesis that in stochastic dynamical systems of any nature the transition to a critical state is always realized through a trending nonlinear process. (Abstract)

Frank, Steven A.. The Price Equation Program: Simple Invariances Unify Population Dynamics, Thermodynamics, Probability, Information and Inference. arXiv:1810.09262. The UC Irvine biologist continues his project (search SAF website) to finesse and expand evolutionary and selective theories by way of affinities with and rootings in physical, mathematical, energetic, and communicative domains. Into the 2010s by contributions as this, it is increasingly apparent that a universal recurrence in kind of a common iconic source code is in independent, procreative effect. See also Universal Expressions of Population Change by the Price Equation by SAF in Ecology and Evolution (7/3381, 2017).

The fundamental equations of various disciplines often seem to share the same basic structure. Natural selection increases information in the same way that Bayesian updating does. Thermodynamics and probability distributions express maximum increase in entropy, which appears mathematically as loss of information. Physical mechanics follows paths of change that maximize Fisher information. This web of vague analogies hints at a deeper common mathematical structure. I suggest that the abstract Price equation expresses that underlying universal structure as it describes dynamics as the change between two sets. One component of dynamics expresses the change in the frequency of things, holding constant the values associated with things. The other component of dynamics expresses the change in the values of things, holding constant the frequency of things. From that perspective, interpretations such as selection, information, entropy, force, acceleration, and physical work arise from the same underlying geometry expressed by the Price equation. (Abstract excerpts)

My goal has been to reveal the common mathematical structure that unifies seemingly disparate results from different subjects. The common mathematical structure arises primarily through simple invariances and their expression in geometry. (15)

In the theory of evolution and natural selection, the Price equation (George R. 1922-1975) describes how a trait or gene changes in frequency over time. The equation uses a covariance between a trait and fitness to give a mathematical description of evolution and natural selection. It provides a way to understand the effects that gene transmission and natural selection have on the proportion of genes within each new generation of a population. (Wikipedia)

Frey, Nathan, et al. Universal Fluctuations in Growth Dynamics of Economic Systems. arXiv:1712.02003. After some two decades of explaining economic behaviors by way of physics principles, Boston University theorists including Eugene Stanley, a prime founder of this endeavor, affirm how industrial commerce and finance is quite distinguished by the same complex structures and dynamics everywhere else in nature and society. Once more a recurrent, iterative universality from cosmos to culture becomes filled in and confirmed.

After some two decades of explaining economic behaviors by way of physics principles, Boston University theorists including Eugene Stanley, a prime founder of this endeavor, affirm how industrial commerce and finance is quite distinguished by the same complex structures and dynamics everywhere else in nature and society. Once more a recurrent, iterative universality from cosmos to culture becomes filled in and confirmed.

Friston, Karl, et al. Parcels and Particles: Markov Blankets in the Brain. arXiv:2007.09704. We cite this entry from researchers based at University College London Wellcome Centre along with a companion posting Is the Free-energy Principle a Formal Theory of Semantics? by Maxwell Ramstead, et al (2007.09291). While cast in technical jargon they emphasize an active complementarity of neuronal parts and modular wholes, aka reciprocal segregation and integration, or separate and come together dynamic phases. As these cerebral processes empower a predictive brain, they are seen to reside in a far-from-equilibrium, self-organized critical state.

Ganaie, Mudasir, et al. Identification of Chimera using Machine Learning. arXiv:2001.08985. We cite this entry by Indian Institute of Technology complexity scientists as an example of how new AI techniques with their basis in cerebral cognition can now reveal the propensity of all manner of natural systems to be attracted to and perform best at an active poise of a more or less orderly balance. A notable feature is that any instance can be seen to exist in both states at the same moment.

Coupled dynamics on network models have provided much insight into complex spatiotemporal patterns from many large-scale real-world complex systems. Chimera, a state of coexistence of incoherence and coherence, is one such pattern which has drawn attention due to its common presence, especially in neuroscience. We describe an approach to characterize chimeras using machine learning techniques, namely random forest, oblique random forests via multi-surface proximal support vector machines. We demonstrate high accuracy in identifying the coherent/incoherent chimera states from given spatial profiles. (Abstract excerpt)

Garcia-Perez, Guille, Maciej and Zohar Ringel. Mutual Information, Neural Networks and the Renormalization Group. Nature Physics. 14/6, 2018. ETH Zurich and Hebrew University of Jerusalem physicists post another, deeply technical approach to qualify cosmic nature’s seemingly infinite yet reliable repetition in kind of common, iconic topologies and activities. Might one add a phrase “Methinks whatever we are trying to explain has properties like these?”

Physical systems differing in their microscopic details often display strikingly similar behaviour when probed at macroscopic scales. Those universal properties, largely determining their physical characteristics, are revealed by the powerful renormalization group (RG) procedure, which systematically retains ‘slow’ degrees of freedom and integrates out the rest. However, the important degrees of freedom may be difficult to identify. Here we demonstrate a machine-learning algorithm capable of identifying the relevant degrees of freedom and executing RG steps iteratively without any prior knowledge about the system. Our results demonstrate that machine-learning techniques can extract abstract physical concepts and consequently become an integral part of theory- and model-building. (Abstract)

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