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

4. Universality Affirmations: A Critical Complementarity

Kossio, Felipe, et al. Growing Critical: Self-Organized Criticality in a Developing Neural System. arXiv:1811.02861. As it becomes well known that brains seek and best perform in a state of mutual balance between more or less orderly complements, University of Bonn, Radboud University and King Juan Carlos University, Madrid neuroinformatic researchers describe experimental evidence that developmental brain maturations likewise proceed toward this optimum condition.

Experiments in various neural systems found avalanches: bursts of activity with characteristics typical for critical dynamics. A possible explanation for their occurrence is an underlying network that self-organizes into a critical state. We propose a simple spiking model for developing neural networks, showing how these may "grow into" criticality. Avalanches generated by our model correspond to clusters of widely applied Hawkes processes. We analytically derive the cluster size and duration distributions and find that they agree with those of experimentally observed neuronal avalanches. (Abstract)

Laurent, Hebert-Dufresne, et al. Complex Networks as an Emerging Property of Hierarchical Preferential Attachment. Physical Review E. 92/6, 2015. University of Laval, Quebec and University of Barcelona physicists open this survey on the state of complexity science by tracing its advent to a 1962 paper The Architecture of Complexity by the pioneer theorist Herbert Simon in the Proceedings of the American Philosophical Society (106/467). Some half century later, as this 2015 section documents, the Grail goal of one, same, infinitely iterated, self-organizing system has been proven from quantum to human to cosmic realms, so as to imply a common, independent, universally manifest, source.

Real complex systems are not rigidly structured; no clear rules or blueprints exist for their construction. Yet, amidst their apparent randomness, complex structural properties universally emerge. We propose that an important class of complex systems can be modeled as an organization of many embedded levels (potentially infinite in number), all of them following the same universal growth principle known as preferential attachment. More importantly, we show how real complex networks can be interpreted as a projection of our model, from which their scale independence, their clustering, their hierarchy, their fractality and their navigability naturally emerge. Our results suggest that complex networks, viewed as growing systems, can be quite simple, and that the apparent complexity of their structure is largely a reflection of their unobserved hierarchical nature. (Abstract)

A number of proposals have been advanced in recent years for the development of “general systems theory” which, abstracting from properties peculiar to physical, biological, or social systems, would be applicable to all of them. (Simon)

Lin, Henry and Max Tegmark. Critical Behavior from Deep Dynamics: A Hidden Dimension in Natural Language. arXiv:1606.06737. A Harvard University prodigy and a MIT polymath (Google names) team up to propose in mid 2016 a theoretical union across the expanse of uniVerse and humanVerse. Again, as the sections Universality Affirmations, Rosetta Cosmos, and others lately attest, this scientific verification from an array of technical finesses finds these same physical principles at work in cultural literature, which in turn implies an intrinsic textual essence. In regard, “close analogies” are cited between recursive grammars and statistical physics, which can be tracked by an informational quality. Wikipedia postings, human genomes and cosmic materiality are thus written in and convey the same linguistic script.

We show that although many important data sequences - from texts in different languages to melodies and genomes - exhibit critical behavior, where the mutual information between symbols decays roughly like a power law with separation, Markov processes generically do not, their mutual information instead decaying exponentially. This explains why natural languages are very poorly approximated by Markov processes. We also present a broad class of models that naturally produce critical behavior. They all involve deep dynamics of a recursive nature, as can be implemented by tree-like or recurrent deep neural networks. This model class captures the essence of recursive universal grammar as well as recursive self-reproduction in physical phenomena such as turbulence and cosmological inflation. We derive an analytic formula for the asymptotic power law and elucidate our results in a statistical physics context: 1-dimensional models (such as a Markov models) will always fail to model natural language, because they cannot exhibit phase transitions, whereas models with one or more "hidden" dimensions representing levels of abstraction or scale can potentially succeed. (Abstract)

Lin, Henry and Max Tegmark. Critical Behavior in Physics and Probabilistic Formal Languages. Entropy. 19/7, 2017. Harvard and MIT polymath physicists offer a good instance of a late 2010s universality whence this same complexity trace is seen to occur from music compositions, Wikipedia text, human genomes to physical dynamics. Such common phenomena can then be given a grammatical linguistic character, which is affine to neural net and computational learning processes. The article is included in an Information Theory collection of the prolific online journal, which along with many similar efforts, tries to express this deepest quality of a universe to human articulation.

We show that the mutual information between two symbols, as a function of the number of symbols between the two, decays exponentially in any probabilistic regular grammar, but can decay like a power law for a context-free grammar. This result about formal languages is closely related to a well-known result in classical statistical mechanics that there are no phase transitions in dimensions fewer than two. It is also related to the emergence of power law correlations in turbulence and cosmological inflation through recursive generative processes. We elucidate these physics connections and comment on potential applications of our results to machine learning tasks like training artificial recurrent neural networks. (Abstract)

Critical behavior, where long-range correlations decay as a power law with distance, has many important physics applications ranging from phase transitions in condensed matter experiments to turbulence and inflationary fluctuations in our early Universe. It has important applications beyond the traditional purview of physics, as well [1–5], including applications to music [4,6], genomics [7,8] and human languages [9–12]. (1)

Lorenzo, Salvatore, et al. Quantum Critical Scaling under Periodic Driving. Nature Scientific Reports. 7/5672, 2017. (arXiv:1612.02259) Into these later 2010s, University of Palermo, Milan, Calabria, and Cologne physicists distill the presence of universally recurrent phenomena, for example a propensity of quantum systems to seek and reach a critically poised state.

Universality is key to the theory of phase transitions, stating that the equilibrium properties of observables near a phase transition can be classified according to few critical exponents. These exponents rule an universal scaling behaviour that witnesses the irrelevance of the model’s microscopic details at criticality. Here we discuss the persistence of such a scaling in a one-dimensional quantum Ising model under sinusoidal modulation in time of its transverse magnetic field. We show that scaling of various quantities (concurrence, entanglement entropy, magnetic and fidelity susceptibility) endures up to a stroboscopic time proportional to the size of the system. Our results suggest that relevant features of the universality do hold also when the system is brought out-of-equilibrium by a periodic driving. (Abstract)

Lugo, Haydee, et al. Chimera and Anticoordination States in Learning Dynamics. arXiv:1812.05603. We cite this entry by Spanish economists because they go on to suggest ways that this recently realized tendency of physical, electronic and neural systems to become poised between more or less order could be similarly evident in personal and social activities. Its early on, but we add that by perceptive extensions like this, its traditional version best known as yin/yang dynamics can at last gain a modern, 21st century scientific confirmation.

In many real-life situations, individuals are motivated to achieve both social acceptance or approval and strategic objectives of coordination. Since these modes may take place in different environments, a two-layer network works well for its analysis. From an evolutionary approach, we focus on asymptotic solutions for all-to-all interactions across and inside the layers and for initial distributions of strategies. We report the existence of chimera states in which two collective states coexist in the same network. We trace back the emergence of chimera states and global anticoordination states to the agents inertia against social pressure. (Abstract excerpt)

The coexistence of coherent and incoherent states has received much attention as an intriguing manifestation of collective behaviour. This interesting behaviour was first observed by Kuramoto et al. and then named it as chimera state. Although the literature about chimera states started with the study of interacting populations of oscillators in dynamical systems, it has been dizzily expanded to many fields in physics, chemistry, biology, etc. Also in social systems, situations of two interacting populations in which one exhibits a coherent or synchronized behaviour while the other is incoherent or desynchronized are commonly observed. This phenomena has also been addressed from the conceptual framework of chimera states. (1)

In the context of coordination in social systems, our contribution brings a more realistic insight about the consequences of a collective behavior that makes a distinction between social and strategic objectives. This collective behavior may lead herding societies to chimera states and skeptical societies to polarized states of anti-coordination. (12)

Mac Carron, Padraig and Ralph Kenna. Universal Properties of Mythological Networks. Europhysics Letters EPL. 99/28002, 2012. As the quotes describe, Coventry University physicists apply condensed matter theories in the form of complex systems to the historic corpus of epic fabled and storied mythic literatures. The second quote is a also exemplifies how such papers now open as the range and reach of nonlinear phenomena extends across every natural and social domain. As a result, a true cosmos to culture “universality” is at last becoming evident and proven.

As in statistical physics, the concept of universality plays an important, albeit qualitative, role in the field of comparative mythology. Here we apply statistical mechanical tools to analyse the networks underlying three iconic mythological narratives with a view to identifying common and distinguishing quantitative features. Of the three narratives, an Anglo-Saxon and a Greek text are mostly believed by antiquarians to be partly historically based while the third, an Irish epic, is often considered to be fictional. Here we use network analysis in an attempt to discriminate real from imaginary social networks and place mythological narratives on the spectrum between them. (Abstract)

Over the past decades many statistical physicists have turned their attention to other disciplines in attempts to understand how properties of complex systems emerge from the interactions between component parts in a non-trivial manner. Applications include the analysis of complex networks in the natural, social and technological sciences as well as in the humanities. One of the notions intrinsic to statistical physics is universality, and attempts have been made to classify complex networks from a variety of areas to facilitate comparison amongst them. Universality is also an important, albeit hitherto qualitative, notion in the field of comparative mythology. (Joseph) Campbell maintained that mythological narratives from a variety of cultures essentially share the same fundamental structure, called the monomyth. Here we statistically compare networks underlying mythological narratives from three different cultures to each other as well as to real, imaginary and random networks. In this way we quantitatively explore universality in mythology and attempt to place mythological narratives on the spectrum from the real to the imaginary. (1)

Mandal, Abhijit, et al. Phase Transition and Critical Phenomena of Black Holes. arXiv:1608.04176. As our worldwise sapiensphere proceeds to explore any breadth and depth of a self-realizing creative cosmos, Jadavpur University, Narasinha Dutt College, and Indian Institute of Technology astrophysicists quantify the presence of thermodynamic transformations in these extreme gravitational fields. And we wish to reflect how fantastic is it that we human beings can altogether achieve such knowledge, surely there must be some grand cosmic reason and purpose for it.

We present a general framework to study the phase transition of a black hole. Assuming that there is a phase transition, it is shown that without invoking any specific black hole, the critical exponents and the scaling powers can be obtained. We find that the values are exactly same which were calculated by taking explicit forms of different black hole spacetimes. The reason for this universality is also explained. The implication of the analysis is -- one does not need to investigate this problem case by case, what the people are doing right now. We also observe that these, except two such quantities, are independent of the details of the spacetime dimensions. (Abstract)

Manicka, Santosh, et al. Effective Connectivity Determines the Critical Dynamics of Biochemical Networks. arXiv:2101.08111. Into 2021, Indiana University, Center for Social and Biomedical Complexity theorists including Luis Rocha (see his website at IU) advance understandings of the phenomena of self-organized criticality which is seen to naturally mediate life’s need to conserve and preserve, along with an openness to creative change. And if this golden middle way might ever at be confirmed and comprehended, it could revise our awful politics which now pits one mode vs. the other.

Living systems operate in a critical dynamical regime between order and chaos where they are both resilient to perturbation, and flexible enough to evolve. To characterize such critical dynamics, the present method uses automata network connectivity and node bias (to be on or off) as tuning parameters, which can lead to uncertain predictions. We derive a more accurate approach by way of canalization, a redundancy that buffers response to inputs and traits keeping them close to optimal states despite genetic and environmental perturbations. The new 'canalization theory' of criticality is based on a measure of effective connectivity, which resolves how to find precise ways to design or control network models of biochemical regulation. (Abstract excerpt)

Markovic, Dimitrije and Claudius Gros. Power Laws and Self-Organized Criticality in Theory and Nature. Physics Reports. 536/2, 2014. In a 21st century tutorial that would please Johann Wolfgang, Goethe University, Frankfurt, physicists can quantify via sophisticated mathematics the presence of a natural vitality that repeats in constant sequential and structural kind everywhere. Its essence is a dynamic balance of order and disorder, form and fracture, separate entities and integral wholes, as found via a scale-invariance from solar flares to neural cognition and Internet sites. By these propensities, it is proposed that a good way to understand life’s evolution is an on-going endeavor toward states of “highly optimized tolerance,” i.e. an optimizing process. In regard, a true “universality” of the same pattern and process from cosmos to civilization can be now affirmed. We cite its long Abstract.

Power laws and distributions with heavy tails are common features of many complex systems. Examples are the distribution of earthquake magnitudes, solar flare intensities and the sizes of neuronal avalanches. Previously, researchers surmised that a single general concept may act as an underlying generative mechanism, with the theory of self organized criticality being a weighty contender. The power-law scaling observed in the primary statistical analysis is an important, but by far not the only feature characterizing experimental data. The scaling function, the distribution of energy fluctuations, the distribution of inter-event waiting times, and other higher order spatial and temporal correlations, have seen increased consideration over the last years. Leading to realization that basic models, like the original sandpile model, are often insufficient to adequately describe the complexity of real-world systems with power-law distribution.

Consequently, a substantial amount of effort has gone into developing new and extended models and, hitherto, three classes of models have emerged. The first line of models is based on a separation between the time scales of an external drive and a an internal dissipation, and includes the original sandpile model and its extensions, like the dissipative earthquake model. Within this approach the steady state is close to criticality in terms of an absorbing phase transition. The second line of models is based on external drives and internal dynamics competing on similar time scales and includes the coherent noise model, which has a non-critical steady state characterized by heavy-tailed distributions. The third line of models proposes a non-critical self-organizing state, being guided by an optimization principle, such as the concept of highly optimized tolerance.

We present a comparative overview regarding distinct modeling approaches together with a discussion of their potential relevance as underlying generative models for real-world phenomena. The complexity of physical and biological scaling phenomena has been found to transcend the explanatory power of individual paradigmal concepts. The interaction between theoretical development and experimental observations has been very fruitful, leading to a series of novel concepts and insights. (Abstract)

Munoz, Miguel. Colloquium: Criticality and Dynamical Scaling in Living Systems. Reviews of Modern Physics. 90/031001, 2018. This entry by the veteran University of Granada complexity theorist is reviewed more in Chap. IV Ecosmomics. It has since become considered as a premier exposition of the 21st century vivifying revolution.

Nagata, Shintaro and Macoto Kikuchi. Emergence of Cooperative Bistability and Robustness of Gene Regulatory Networks. . An Osaka University biochemist and a biophysicist report that the common bistability state (Wikipedia) of dynamical systems can likewise be recognized in this genomic mode, whence GRNs reside in two coordinated, genes on and off, positions at once. See also a slide presentation Simultaneous emergence of Cooperative Response and Mutational Robustness in Gene Regulatory Networks by the authors at www.cp.cmc.osaka-u.ac.jp/~kikuchi/presentation/CCS2018.

Gene regulatory networks (GRNs) are complex systems in which many genes mutually regulate their expressions for changing the cell state adaptively to environmental conditions. The GRNs utilized by living systems possess several kinds of robustness which here means that they do not lose their functions when exposed to mutation or noises. In this study, we explore the fitness landscape of GRNs and investigate how the robust feature emerges in the "well-fitted" GRNs. Thus the more sensitively a GRN responds to the input, the fitter it is. To do this, they exhibit bistability, which necessarily emerges as the fitness becomes high. These properties are universal irrespective of the evolutionary pathway, because we did not perform evolutionary simulations. (Abstract excerpt)

The emergence of the new fixed points can be considered as an innovation or a big evolutionary jump. Then, what can we infer about the evolution based on them? The cooperative bistability and the robustness against noises are the consequence of the high fitness. Thus, we can say that this evolutional jump occurs inevitably as the fitness increases irrespective of the evolutionary pathway. We may identify this as the universality of evolution. (9)

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