IV. Ecosmomics: Independent, UniVersal, Complex Network Systems and a Genetic Code-Script Source

4. Universality Affirmations: A Critical Complementarity

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)

Jagielski, Maciej, et al. Theory of Earthquakes Interevent Times Applied to Financial Markets. arXiv:1610.08921. With Ryszard Kutner and Didier Sornette, European theorists describe an inherent mathematical correspondence between these disparate geological and societal realms, which is then seen as a universal quality of abrupt dynamic phenomena.

We analyze the probability density function (PDF) of waiting times between financial loss exceedances. The empirical PDFs are fitted with the self-excited Hawkes conditional Poisson process with a long power law memory kernel. The Hawkes process is the simplest extension of the Poisson process that takes into account how past events influence the occurrence of future events. By analyzing the empirical data for 15 different financial assets, we show that the formalism of the Hawkes process used for earthquakes can successfully model the PDF of interevent times between successive market losses. (Abstract)

The activity of many complex systems in social and natural sciences can be characterized by sporadic bursts followed by long periods of low activity. To quantitatively describe this kind of dynamics, we can use the interevent times defined as times between two consecutive events of high (suitably defined) activity of the system. It was shown in many research papers that the probability density distribution (PDF) of interevent times plays the role of a universal characteristic of dynamical complex systems. Examples include anomalous transport, pattern discovery, earthquakes and rock fractures, extreme events and long-memory processes, email communications, web browsing, library visits, stock trading, human dynamics, social dynamics, finance risks, letter correspondences, and financial markets. (1, bold added)

Jofre, Paula, et al. Cosmic Phylogeny: Reconstructing the Chemical History of the Solar Neighborhood with an Evolutionary Tree. arXiv:1611.02575. Cambridge University, Universidad Diego Protales, Chile, and Oxford University scientists, including Robert Foley, explore promising ways to apply life’s developmental topologies across chemical and stellar realms. An allusion is made to an analogous celestial genome, whose resultant webworks suggest an “astrocladistics.”

Using 17 chemical elements as a proxy for stellar DNA, we present a full phylogenetic study of stars in the solar neighbourhood. This entails applying a clustering technique that is widely used in molecular biology to construct an evolutionary tree from which three branches emerge. These are interpreted as stellar populations which separate in age and kinematics and can be thus attributed to the thin disk, the thick disk, and an intermediate population of probable distinct origin. Combining the ages of the stars with their position on the tree, we are able to quantify the mean rate of chemical enrichment of each of the populations, and thus show in a purely empirical way that the star formation rate in the thick disk is much higher than in the thin disk. Our method offers an alternative approach to chemical tagging methods with the advantage of visualising the behaviour of chemical elements in evolutionary trees. This offers a new way to search for `common ancestors' that can reveal the origin of solar neighbourhood stars. (Abstract)

Kalinin, Nikita, et al. Self-organized Criticality and Pattern Emergence through the Lens of Tropical Geometry. Proceedings of the National Academy of Sciences. I115/E8135, 2018. National Research University, St. Petersburg, IBM Watson Research Center, University of Toulouse, Institute of Science and Technology, Austria, and CINVESTAV, Mexico system mathematicians provide another way to perceive and quantify nature’s constant propensity to reach an a balance beam of more or less relative order in every topological form and function. In actuality, each instantiated complement of the dual, reciprocal condition then resides in both modes at once (particle/wave). See also Introduction to Tropical Series by the authors at arXiv:1706.03062.

A simple geometric continuous model of self-organized criticality (SOC) is proposed. This model belongs to the field of tropical geometry and appears as a scaling limit of the classical sandpile model. We expect that our observation will connect the study of SOC and pattern formation to other fields (such as algebraic geometry, topology, string theory, and many practical applications) where tropical geometry has already been successfully used. (Significance)

Klamser, Pascal and Pawel Romanczuk. Collective Predator Evasion: Putting the Criticality Hypothesis to the Test. PLoS Computational Biology. March, 2021. Humboldt University, Berlin, computational neuroscientists conduct analytical studies of how and why animal groupings as they cope with survival issues seem to tend toward a dynamic critical state. Their work goes on to study the role that self-organizing forces play in facilitating this optimum viability.

Collective intelligence relies on efficient processing of information. Complex systems theory suggests that this activity is optimal at the border between order and disorder, i.e. at a critical point. However, for animal collectives fundamental questions remain open regarding self-organization towards criticality. Using a spatially explicit model of collective predator avoidance, we show that schooling prey performance is indeed optimal at criticality, but is not due to a collective response. Rather it occurs because of the emergent dynamical group structure. More importantly, this structural sensitivity makes the critical state evolutionary highly unstable in the context of predator-prey interactions, and demonstrates the decisive importance of spatial self-organization in collective animal behavior. (Author summary)

Kolodrubetz, Michael. Quenching Our Thirst for Universality. Nature. 563/191, 2018. A UT Dallas systems physicist introduces three papers in this issue: Observation of Universal Dynamics in a Spinor Bose Gas Far from Equilibrium (Prufer, 217), Universal Prethermal Dynamics of Bose Gases Quenched to Unitarity (Eiger, 221) and Universal Dynamics in an Isolated One-Dimensional Bose Gas Far from Equilibrium (Erne, 225), that verify in different places and ways the natural presence of ubiquitous, infinitely iterated, formative patterns and active processes.

Although we live in a world of constant motion, physicists have focused largely on systems in or near equilibrium. In the past few decades, interest in non-equilibrium systems has increased, spurred by developments that are taking quantum mechanics from fundamental science to practical technology. Physicists are therefore tasked with an important question: what organizing principles do non-equilibrium quantum systems obey? Herein Prüfer et al, Eigen et al, and Erne et al report experiments that provide a partial answer to this question. The studies show, for the first time, that ultracold atomic systems far from equilibrium exhibit universality, in which measurable experimental properties become independent of microscopic details. (MK)
While the evolution of a many-body system is in general intractable in all its details, relevant observables can become insensitive to microscopic system parameters and initial conditions. This is the basis of the phenomenon of universality. Far from equilibrium universality is identified through the scaling of the spatio-temporal evolution of the system. This has been studied in the reheating process in inflationary cosmology, the dynamics of nuclear collision described by quantum chromodynamics, and the post-quench dynamics in dilute quantum gases in non-relativistic field theory. Here we observe the emergence of universal dynamics by spatially resolved spin correlations in a quasi-one-dimensional spinor Bose–Einstein condensate. (Prufer)

Understanding the behaviour of isolated quantum systems far from equilibrium and their equilibration is one of the most pressing problems in quantum many-body physics. There is strong theoretical evidence that sufficiently far from equilibrium a wide variety of systems — including the early Universe after inflation, quark–gluon matter generated in heavy-ion collisions, and cold quantum gases — exhibit universal scaling in time and space during their evolution, independent of their initial state or microscale properties. (Erne)

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)

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