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A Sourcebook for the Worldwide Discovery of a Creative Organic Universe
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IV. Ecosmomics: Independent, UniVersal, Complex Network Systems and a Generative Code-Script Source

4. Universality Affirmations: A Critical Complementarity

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)

Guszejnov, David, et al. Universal Scaling Relations in Scale-Free Structure Formation. arXiv:1707.05799. As a good example of the sophistication of mid 2017 cosmic science compared with a decade ago, Cal Tech astrophysicists including Philip Hopkins proceed to affirm a pervasive, natural interstellar self-similarity. And in regard, here is worldwide proof of the perennial tradition of a macrocosm and microcosm correspondence, by which both universe and human realms could be known. See also Star Cluster Structure from Hierarchical Star Formation by this extended group at arXiv:1708.09065.

A large number of astronomical phenomena exhibit remarkably similar scaling relations. The most well-known of these is the mass distribution dN/dlnM∝M−2 which (to first order) describes stars, protostellar cores, clumps, giant molecular clouds, star clusters and even dark matter halos. In this paper we propose that this ubiquity is not a coincidence and that it is the generic result of scale-free structure formation where the different scales are uncorrelated. We show that all such systems produce a mass function proportional to M−2 and a column density distribution with a power law tail of dA/dlnΣ∝Σ−1. Furthermore, structures formed by such processes (e.g. young star clusters, DM halos) tend to a ρ∝R−3 density profile. We compare these predictions with observations, analytical fragmentation cascade models, semi-analytical models of gravito-turbulent fragmentation and detailed "full physics" hydrodynamical simulations. We find that these power-laws are good first order descriptions in all cases. (Abstract)

Finally, in a somewhat different approach, one can notice that the apparent similarity in the slopes of the mass functions could be explained by a fractal-like, self-similar ISM out of which structures like stars, cores and GMCs form. An important property of these models is that they tie structures of different sizes together (stars, cores, clumps) as their mass distribution is the result of the same fractal ISM structure. The density structure predicted by these fractal ISM models is in agreement with simulations of supersonic turbulence. In general these inherently imply an underlying self-similar process, which serves as the main motivation for this paper. (2)

In this paper we showed that there are universal scaling relations that generally arise in scale-free models of structure formation with a large but finite dynamic range and no correlation between scales. These relations are shared between very different phenomena, including the formation of stars, protostellar cores, clumps, giant molecular clouds, star clusters and even dark matter halos. Despite their differences all these processes can be approximately described by the dimensionless version of the pressure-free Euler equation with self-gravity. Thus a hierarchical structure building process would follow the same equation for all these systems on a wide range of scales. This means that (to first order) the formation of these (very different) gravitationally bound structures produces the same scaling relations for a wide range of physical quantities. (8)

Hastings, Harold, et al. Challenges in the Analysis of Complex Systems. European Physical Journal Special Topics. 226/15, 2017. For some context, I have been tracking nonlinear CS sciences since the 1980s, e.g. visiting the Santa Fe Institute in August 1987. As this large chapter and sections report, the past decades were an intense phase of technical studies which widely fanned out, ramified, clarified, and lately are melding into a common synthesis. In this special issue introduction, Bard College and University of Calgary theorists affirm that the same far-from-equilibrium patterns and processes have been found to occur from astronomy to seismology, chemistry, neural and cardiac dynamics, and even climatology. Since the 2000s, network phenomena, as affine with statistical physics and phase transitions, has become a significant addition. Similar to Jordi Vallverdu, et al 2017, it is noted that nature’s mathematical source is in generative play prior to and “in the absence of selection.”

One of the main challenges of modern physics is to provide a systematic understanding of systems far from equilibrium exhibiting emergent behavior. Prominent examples of such complex systems include, but are not limited to the cardiac electrical system, the brain, the power grid, social systems, material failure and earthquakes, and the climate system. Due to the technological advances over the last decade, the amount of observations and data available to characterize complex systems and their dynamics, as well as the capability to process that data, has increased substantially. The present issue discusses a cross section of the current research on complex systems, with a focus on novel experimental and data-driven approaches to complex systems that provide the necessary platform to model the behavior of such systems. (Abstract)

Helmrich, Stephan, et al. Signatures of Self-Organized Criticality in an Ultracold Atomic Gas. Nature. 577/481, 2020. In a paper appropriately published in the first month of this binocular year, University of Heidelberg, Cal Tech, and University of Koln physicists contribute to the ubiquitous occurrence of self-similar, critically poised states everywhere. The subject case here is elemental gases where such exemplary features appear even at these frigid, quantum extremes. See also Singular Charge Fluctuations at a Magnetic Quantum Critical Point and Quantum Spin Liquids in Science for January 17, 2020. Two decades into the 21st century, a Worldwide Discovery of a Organic, Procreative UniVerse does seem well underway, if we might be of a mind to ask and see.

Self organisation provides an elegant explanation for how complex structures emerge and persist throughout nature with remarkably similar scale-invariant properties. While this can be captured by simple models, the connection to real-world systems is difficult to test. Here we identify three key signatures of self-organised criticality in the dynamics of a dissipative gas of ultracold atoms and provide a first characterisation of its universal properties. We show that population decay drives the system to a stationary state that is independent of the initial conditions and exhibits scale invariance and a strong response to perturbations. This establishes a practical platform for investigating self-organisation phenomena and non-equilibrium universality with much experimental access to the microscopic details of the system. (Abstract)

Hidalgo, Jorge, et al. Cooperation, Competition and the Emergence of Criticality in Communities of Adaptive Systems. arXiv:1510.05941. The Spanish, Italian, and American team including Jayanth Banavar and Amos Maritan follow up their 2014 paper (search) with further theoretical explanations for nature’s propensity to seek and reach a balance between relative order or conflict. This “metastable” state (Kelso) is lately being verified from many quarters, for example At the Edge of Chaos by Christian Rossert, et al, (PLoS One October 2015) and Adaptation to Sensory Input Tunes Visual Cortex to Criticality by Woodrow Shew, et al (Nature Physics 11/8, 2015).

The hypothesis that living systems can benefit from operating at the vicinity of critical points has gained momentum in recent years. Criticality may confer an optimal balance between exceedingly ordered and too noisy states. We here present a model, based on information theory and statistical mechanics, illustrating how and why a community of agents aimed at understanding and communicating with each other converges to a globally coherent state in which all individuals are close to an internal critical state, i.e. at the borderline between order and disorder. We study --both analytically and computationally-- the circumstances under which criticality is the best possible outcome of the dynamical process, confirming the convergence to critical points under very generic conditions. Finally, we analyze the effect of cooperation (agents try to enhance not only their fitness, but also that of other individuals) and competition (agents try to improve their own fitness and to diminish those of competitors) within our setting. (Abstract)

Hidalgo, Jorge, et al. Information-based Fitness and the Emergence of Criticality in Living Systems. Proceedings of the National Academy of Sciences. 111/10095, 2014. We cite this entry by senior system theorists JH, Jacopo Grilli, Samir Suweis, Miguel Munoz, Jayanth Banavar and Amos Maritan (search each) as an early perception of life’s universal propensity to seek and reside at an optimum self-organized criticality. By 2020, a few years later, this section can now document its robust worldwide affirmation. In this time of great need, if we might mindfully allow and witness, here is a vital finding that a phenomenal nature prefers an active reciprocity of conserve/create, person/group and ever so on. Rather than totalitarian or anarchic extremes, me individual vs. We together politics, a salutary resolve going forward would be a middle way complementarity.

Recently, evidence has been mounting that biological systems might operate at the borderline between order and disorder, i.e., near a critical point. A general mathematical framework for understanding this common pattern, explaining the possible origin and role of criticality in living adaptive and evolutionary systems, is still missing. We rationalize this apparently ubiquitous criticality in terms of adaptive and evolutionary functional advantages. We provide an analytical framework, which demonstrates that the optimal response to broadly different changing environments occurs in systems organizing spontaneously—through adaptation or evolution—to the vicinity of a critical point. Furthermore, criticality turns out to be the evolutionary stable outcome of a community of individuals aimed at communicating with each other to create a collective entity. (Significance)

Horstmeyer, Leonhard, et al. Network Topology near Criticality in Adaptive Epidemics. arXiv:1805.09358. Just as every other area from quantum to neural has become defined by the universally prevalent self-organized complex network systems, here LH and Stefan Thurner, Medical University of Vienna and Christian Kuehn, Technical University of Munich theorists describe how even human disease vectors among variegated populations similarly hold, as they mathematically must,Just as every other area from quantum to neural has become defined by the universally prevalent self-organized complex network systems, here LH and Stefan Thurner, Medical University of Vienna and Christian Kuehn, Technical University of Munich theorists describe how even human disease vectors among variegated populations similarly hold and exhibit, as they mathematically must, to predictable, critical principles.

We study structural changes of adaptive networks in the co-evolutionary susceptible-infected-susceptible (SIS) network model along its phase transition. We clarify to what extent these changes can be used as early-warning signs for the transition at the critical infection rate λc at which the network collapses and the system disintegrates. We analyze the interplay between topology and node-state dynamics near criticality. Several network measures exhibit clear maxima or minima close to the critical threshold that could potentially serve as early-warning signs. For the SI link density and triplet densities the maximum is found to originate from the co-existence of two power laws. (Abstract)

Iyer-Biswas, Srividya, et al. Universality in Stochastic Exponential Growth. Physical Review Letters. 113/028101, 2014. University of Chicago and LBNL (Gavin Crooks) physicists consider a common mathematical recurrence for ecosmos to economic developments. See also 1409.7068 for more work by the authors on bacterial cells.

Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth. (Abstract)

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