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

4. Universality Affirmations: A Critical Complementarity

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)

Nicolaides, Christos, et al. Self-Organization of Network Dynamics into Local Quantized States. Nature Scientific Reports. 6/21360, 2016. In a contribution that typifies how such papers can be written nowadays, MIT engineers distill and describe a general, mechanism by which an interaction of many nodes, entities, or components in heterogeneous networks results in a spontaneous, emergent self-organization. We cite the Abstract, and the first two paragraphs where many references are listed that describe this same, archetypal phenomena from biology and brains to ecologies and societies.

Self-organization and pattern formation in network-organized systems emerges from the collective activation and interaction of many interconnected units. A striking feature of these non-equilibrium structures is that they are often localized and robust: only a small subset of the nodes, or cell assembly, is activated. Understanding the role of cell assemblies as basic functional units in neural networks and socio-technical systems emerges as a fundamental challenge in network theory. A key open question is how these elementary building blocks emerge, and how they operate, linking structure and function in complex networks. Here we show that a network analogue of the Swift-Hohenberg continuum model—a minimal-ingredients model of nodal activation and interaction within a complex network—is able to produce a complex suite of localized patterns. Hence, the spontaneous formation of robust operational cell assemblies in complex networks can be explained as the result of self-organization, even in the absence of synaptic reinforcements. (Abstract)

Pattern formation in reaction-diffusion systems has emerged as a mathematical paradigm to understand the connection between pattern and process in natural and sociotechnical systems. The basic mechanisms of pattern formation by local self-activation and lateral inhibition, or short-range positive feedback and long-range negative feedback are ubiquitous in ecological and biological spatial systems, from morphogenesis and developmental biology to adaptive strategies in living organisms and spatial heterogeneity in predator-prey systems. Heterogeneity and patchiness associated with Turing patterns in vegetation dynamics have been proposed as a connection between pattern and process in ecosystems, suggesting a link between spatial vegetation patterns and vulnerability to catastrophic shifts in water-stressed ecosystems. The theory of non-equilibrium self-organization and Turing patterns has been recently extended to network-organized natural and socio-technical systems, including complex topological structures such as multiplex, directed and Cartesian product networks. Self-organization is rapidly emerging as a central paradigm to understand neural computation. (1)

Self-organized activation has been shown to emerge spontaneously from the heterogenous interaction among neurons, and is often described as pattern formation in two-population networks. Localization of neural activation patterns is a conceptually challenging feature in neuroscience. Cell assemblies, or small subsets of neurons that fire synchronously, are the functional unit of the cerebral cortex in the Hebbian theory of mental representation and learning. Associative learning forms the basis of our current understanding of the structure and function of neural systems. It is also the modeling paradigm for information-processing artificial neural networks. The emergence of cell assemblies in complex neural networks is a fascinating example of pattern formation arising from the collective dynamics of interconnected units. Understanding the mechanisms leading to pattern localization remains a long-standing problem in neuroscience. Here we show that simple mechanisms of nodal interaction in heterogeneous networks allow for the emergence of robust local activation patterns through self-organization. (1)

Nicolas-Carlock, J., et al. Universal Fractality of Morphological Transitions in Stochastic Growth Processes. Nature Scientific Reports. 7/3523, 2017. Benemérita Universidad Autónoma de Puebla, Mexico theorists cleverly quantify the presence of common, ever repetitive dynamic forms across organismic nature. We note that over the course of this website chronicle since 2000 and before, it was not possible until just now to assert and mathematically prove such a whole scale recurrence. See also the cited paper Global Optimization, Local Adaptation, and the Role of Growth in Distribution Networks in Physical Review Letters (117/138301, 2016) and Angular and Radial Correlation Scaling in Stochastic Growth Morphodynamics at arXiv:1803.03715.

Stochastic growth processes give rise to diverse and intricate structures everywhere in nature, often referred to as fractals. In general, these complex structures reflect the non-trivial competition among the interactions that generate them. In particular, the paradigmatic Laplacian-growth model exhibits a characteristic fractal to non-fractal morphological transition as the non-linear effects of its growth dynamics increase. So far, a complete scaling theory for this type of transitions, as well as a general analytical description for their fractal dimensions has been lacking. In this work, we show that despite the enormous variety of shapes, these morphological transitions have clear universal scaling characteristics. Using a statistical approach to fundamental particle-cluster aggregation, we introduce two non-trivial fractal to non-fractal transitions that capture all the main features of fractal growth. (Abstract excerpt)

Found everywhere in nature, the intricate structures generated by fractal growth usually emerge from non-trivial self-organizing and self-assembling pattern formation. One striking feature of these systems is the morphological transition they undergo as a result of the interplay between entropic and energetic processes in their growth dynamics, that ultimately manifest themselves in the geometry of their structure. It is here where, despite their complexity, great insight can be obtained into the fundamental elements of their dynamics from the powerful concepts of fractal geometry. (1)

Norrman, Andreas and Lukasz Rudnicki. Quantum Correlations and Complementarity of Vectorial Light Fields. arXiv:1904.07533. We review this entry by MPI Science of Light researchers much more in Quantum Organics, especially for its introduction of a “triality” concept to join and unite complements.

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