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

4. Universality Affirmations: A Critical Complementarity

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)

Garcia-Seisdedos, Hector, et al. Proteins Evolve on the Edge of Supramolecular Self-Assembly. Nature. 548/244, 2017. As life becomes quantified across the biomolecular physiologies of every species, Weizmann Institute of Science structural biologists discern a common cellular dynamics. Nature again repeats the same phenomena for each creature and scale. A companion paper is Emergence and Function of Complex Form in Self-Assembly and Biological Cells by Stephen Hyde, et al in Interface Focus (7/20170035).

The self-association of proteins into symmetric complexes is ubiquitous in all kingdoms of life. Symmetric complexes possess unique geometric and functional properties, but their internal symmetry can pose a risk. In sickle-cell disease, the symmetry of haemoglobin exacerbates the effect of a mutation, triggering assembly into harmful fibrils. Here we examine the universality of this mechanism and its relation to protein structure geometry.

Goblot, Valentin, et al. Emergence of Criticality through a Cascade of Delocalization Transitions in Quasiperiodic Chains. Nature Physics. August, 2020. We cite this entry by thirteen Université Paris-Saclay, CNRS and ETH Zurich nanotechnologists to report and convey that even nature’s complex materiality seems to adopt and exhibit this common dynamic duality of more or less orderly phases.

Conduction through materials crucially depends on how ordered the materials are. Periodically ordered systems exhibit extended Bloch waves that generate metallic bands, whereas disorder is known to limit conduction and localize the motion of particles in a medium. In this context, quasiperiodic systems, which are neither periodic nor disordered, demonstrate exotic conduction properties, self-similar wavefunctions and critical phenomena. Here, we explore the localization properties of waves in a novel family of quasiperiodic chains obtained when continuously interpolating between two paradigmatic limits: the Aubry–André model, and the Fibonacci chain, known for its critical nature. We discover that the Aubry–André model evolves into criticality through a cascade of band-selective localization/delocalization transitions that iteratively shape the self-similar critical wavefunctions of the Fibonacci chain. (Abstract excerpts)

Godoy-Lorite, Antonia, et al. Long-Term Evolution of Techno-Social Networks: Statistical Regularities, Predictability and Stability of Social Behaviors. arXiv:1506.01516. As the quotes express, with Roger Guimera and Marta Sales-Pardo, scientists with postings at the Universitat Rovira I Virgili, Spain, and Northwestern University, USA, apply statistical physics to complex networks such as social media to reach remarkable findings. While individual events, as we well know, can be fraught with chaotic caprice, constant, reliable patterns emerge when averaged over large populations. Circa 2015, could this historic, default source of human hope be at last confirmed?

In social networks, individuals constantly drop ties and replace them by new ones in a highly unpredictable fashion. This highly dynamical nature of social ties has important implications for processes such as the spread of information or of epidemics. Several studies have demonstrated the influence of a number of factors on the intricate microscopic process of tie replacement, but the macroscopic long-term effects of such changes remain largely unexplored. Here we investigate whether, despite the inherent randomness at the microscopic level, there are macroscopic statistical regularities in the long-term evolution of social networks. In particular, we analyze the email network of a large organization with over 1,000 individuals throughout four consecutive years. We find that, although the evolution of individual ties is highly unpredictable, the macro-evolution of social communication networks follows well-defined statistical laws, characterized by exponentially decaying log-variations of the weight of social ties and of individuals' social strength. At the same time, we find that individuals have social signatures and communication strategies that are remarkably stable over the scale of several years. (Abstract)

We have shown that the long-term macro-evolution of email networks follows well-defined statistical laws, characterized by exponentially decaying log-variations of the weight of social ties and of individuals’ social strength. Therefore, the intricate processes of tie formation and decay at the micro-level give rise to macroscopic evolution patterns that are similar to those observed in other complex networks (such as air-transportation or financial networks), as well as in the growth and decay of human organizations. The fact that so diverse systems display similar stationary statistical patterns at a macroscopic level (and that these are stable over long periods of time) hints at the existence of universal mechanisms underlying all these processes (such as, for instance, multiplicative processes). Remarkably, together with these statistical regularities, we also observe that individuals have long-lasting social signatures and communication strategies, which have a psychological origin, and are unlikely to have a parallel in other systems. Reconciling the universality of the macroscopic evolutionary patterns with the importance of the psychological/microscopic processes should be one of the central aims of future studies about the evolution of social networks. (5)

Gonda, Tomas, et al. A Framework for Universality in Physics, Computer Science, and Beyond.. arXiv:2307.06851. This is a specific notice to date by University of Innsbruck and Technical University of Munich mathematicians including Gemma De les Coves as our 21st century worldly scientific revolution comes to realize a common evidential occurrence across the atomic, cosmic and personal infinities. A main emphasis on computational methods is then found to hold for quantum spin models, linguistic grammar, neural networks, and elsewhere. See also an introductory overview by this group at arXiv:2406.16607.

Turing machines and spin models share a notion of universality according to which some simulate all others. Is there a theory of universality that captures this notion? We set up a categorical framework for universality which includes as instances universal Turing machines, universal spin models, NP completeness, top of a preorder, denseness of a subset, and more. By identifying necessary conditions for universality, we show that universal spin models cannot be finite. We also characterize when universality can be distinguished from a trivial one and use it to show that universal Turing machines are non-trivial in this sense. Our framework allows not only to compare universalities within each instance, but also instances themselves.

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