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A Sourcebook for the Worldwide Discovery of a Creative Organic Universe
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A. A Familiar Ecode: An Ecosmome to Geonome Complementary Endowment is Found Everywhere

Katsnelson, Mikhail, et al. Self-Organized Criticality in Neural Networks. arXiv:2107.03402. As MK and Tom Westerhout, Radboud University and Vitality Vanchurin, NIH, Bethesda (search VV and MK) continue to propose that such cognitive connectivities have a common natural prevalence, they advance that this SOC optimum condition ought to be appreciated for its definitive advantage. If taken to a farthest implication, the whole ecosmic uniVerse might take on the cerebral semblance of a neural net learning process. See also Emergent Quantumness in Neural Networks at 2012.05082 for another entry by the authors.

We demonstrate, both analytically and numerically, that learning dynamics of neural networks is generically attracted towards a self-organized critical state. The effect can be modeled with quartic interactions between non-trainable variables (e.g. states of neurons) and trainable variables (e.g. weight matrix). Non-trainable variables are rapidly driven towards stochastic equilibrium and trainable variables are slowly driven towards learning equilibrium described by a scale-invariant distribution on a wide range of scales. Our results suggest that the scale invariance observed in many physical and biological systems might be due to some kind of learning dynamics and support the claim that the universe might be a neural network. (Abstract)

Kauffman, Stuart, et al, eds.. The Principle of Dynamical Criticality.. Entropy. December, 2022. This is a special issue to collect a current flow of evident findings about nature’s deep propensity across the universe to seek and reside at this optimum resolve. It is edited by SK, Roberto Serra, University of Modena, Italy, and Ilya Shmulevich and Sui Huang, Institute of Systems Biology, Seattle. Among the six papers so far are Emergent Criticality in Coupled Boolean Networks by Chris Kang, et al, and Robustness and Flexibility of Neural Function through Dynamical Criticality by Marcel Magnasco (see review herein).

While life, as Darwin noted, displays “endless forms most beautiful” at a macroscopic scale, it appears much more uniform at a microscopic level, where living systems share many common structural and functional features. There are, however, few “operating principles” at a macroscale that seem to hold for large classes of organisms. A promising candidate is the “criticality” principle, whereby evolution would have driven living beings towards critical states, since they are should be favorably selected over those that are chaotic or ordered. Moreover, since dynamically critical states are endowed with computational properties, they are interesting outside the domain of biology, such as artificial designs. (Excerpt)

Li, Xiu-Juan and Yu-Peng Yang. Signatures of the Self-organized Criticality Phenomenon in Precursors of Gamma-ray bursts. arXiv:2308.14281. Qufu Normal University and Nanking University astro-cybernetics researchers describe still another instance of nature's common avail of this optimum balance.

Precursors provide important clues to the nature of gamma-ray burst (GRB) central engines and can be used to contain GRB physical processes. In this letter, we study the self-organized criticality in precursors of long GRBs in the third Swift/BAT Catalog. We investigate the differential and cumulative size distributions with the Monte Carlo method. All of the distributions can be well described by power-law models within the physical framework of a self-organized criticality. The results show that both precursors and main bursts can be attributed to an self-organized criticality system.

Li, Xiu-Juan, et al. Evidence for Self-Organized Criticality Phenomena in Prompt Phase of Short Gamma-Ray Bursts. arXiv:2303.06667. Qufu Normal University, China physicists report a further notice of how this insistent propensity distinguishes all manner of atomic activities.

The prompt phase of gamma-ray burst (GRB) contains essential information about the physical nature and central engine, which is yet unknown. In this paper, we investigate the self-organized criticality (SOC) in GRBs as done in X-ray flares of GRBs, which can be well described by power-law models. Our findings show that GRB prompt phases and X-ray flares possess the very same magnetically dominated stochastic process and mechanism. (Excerpt)

Lopez, Roberto, et al.. The Excitatory-Inhibitory Branching Process: Cortical Asynchronous States, Excitability, and Criticality.. arXiv:2203.16374. RL and Miguel Munoz, University of Granada, Spain and Victor Buendia, University of Tubingen provide a current update on the widening evidence and propensity for an optimum cerebral and maybe “cosmobral” self-organized balance between activity and sedentary.

The branching process is the minimal model for propagation dynamics, avalanches and criticality, broadly used in neuroscience. Adding inhibitory nodes then induces a richer phenomenology, including between quiescence and saturation to reveal the features of "asynchronous states" in cortical networks which allows us to rationalize striking empirical findings within a common and parsimonious framework. (Excerpt)

The idea that information-processing systems, both biological and artificial, can extract important functional advantages from operating near the edge of a phase transition was already suggested by A. Turing in 1950. Beggs and Plenz, pioneering the experimental search for signatures of criticality in neural systems in the 2010s, found scale-free outbursts of neuronal activity occurring in between consecutive periods of quiescence, i.e.neuronal avalanches. These avalanches have sizes and durations distributed as power laws with exponents consistent with those of a critical branching process and often exhibit a parabolic shape on average [1)

Magnasco, Marcelo. Robustness and Flexibility of Neural Function through Dynamical Criticality. Entropy. 24/5, 2022. In a special issue on this title subject into the 2020s, a Rockefeller University integrative neuroscientist (view his RU website) writes one of the strongest theoretical confirmations of this common phenomena to date. After an extensive review of earlier notices back to Stuart Kauffman in 1970s and Leo Szilard before, as this site section reports, it has lately become well known that this preferred poise actually occurs from celestial, quantum and material phases all through life’s cellular and communal development. A natural propensity thus seems to seek, prefer and reside at an optimum middle way via a reciprocity of more or less order, conserve or create, tradition and innovation options, and so on. Into 2023, after decades and years of complexity studies, by a combined virtue of structural and vitality features our Earthuman acumen may at last have reached a true discovery which can be affirmed and announced. As a horrific war rage close to the lands of Mendel and Galileo, this grand fulfillment need take on a guise as an epochal, crucial, revolutionary realization.

In theoretical biology, robustness refers to the ability of a biological system to function even under a stress of basic parameters (temperature or pH); flexibility refers to the ability of a system to switch functions or behaviors easily when necessary. While there are extensive explorations of the concept of robustness and what it requires mathematically, understanding flexibility has proven elusive, as well as also elucidating the opposite mathematical models for either mode. In this paper we consider a numberof neuroscience theories that show both robustness and flexibility can be attained by systems that poise themselves at the onset of dynamical bifurcations, which can influence the integration of information processing and function. (Abstract)

Long-term survival requires surviving many short terms. Thus species need to do “well enough” in the short term, but able ability to change when the niche shifts. In physiology, these two conflicting demands are identified with “robustness”, the ability of a physiological system to perform the same task correctly, and “flexibility”, so to adjust when as conditions change. While studies have explored robustness most often in molecular cell biology, the theoretical bases of biological flexibility are still obscure. One of the most striking forms of flexibility in neural function is integration. This phenomenon occurs at various scales, from the input-dependent changes in the range of intracortical functional connectivity, all the way up to entire brain areas working together to form associations. (1, 2)

Conclusion A large number of biological systems have shown dynamics that are linked to a system state which spontaneously poises itself at the boundary of dynamical transitions. We have reviewed the evolution of these ideas over many years and their firm rootings in experimental evidence. We have derived from this a family of models, the critically coupled map lattices. We have here shown the direct similarity and many connections to a related notion of criticality, that of “edge of chaos” dynamics, which altogether become a cellular automaton Turing universality. (15)

Marcelo Magnasco’s neuropsychology group uses living beings as a source of inspiration for creating new mathematical descriptions of nature. The lab’s focus is on computational and experimental methods to model the complexity, organization, and information-processing properties of living organisms. A primary interest is auditory function along with studies of vision, memory, olfaction, and sensory processing. Human beings are the main subject but dolphin communication in aquaria and the wild is also undertaken. (RU synopsis)

Mondal, Suman, et al. Self-Organized Criticality of Magnetic Avalanches in Disordered Ferrimagentic Material. arXiv:2210.05183. Indian Association for the Cultivation of Science researchers posted in Kolkata and Bangalore proceed to report the universal presence of this “golden mean” optimum state even across these substantial domains. (Once again, our intent is to document SOC occurrences everywhere across a genesis nature so that public politics might finally also become healed by a bicameral complementarity.)

We observe multiple step-like jumps in a Dy-Fe-Ga-based ferrimagnetic alloy in its magnetic hysteresis curve. The observed jumps have a stochastic character with respect to their magnitude and critical field of occurrence.. The jump size distribution follows a power law indicating the scale invariance nature of the jumps. The flipping of coupled Dy and Fe clusters is responsible for the observed discrete avalanche-like features in the hysteresis loop. These characteristics indicate that the present phenomenon can be well described within the realm of self-organized criticality. (Abstract)

Morales, Guillermo and Miguel Munoz. Optimal Input Representation in Neural Systems at the Edge of Chaos. arXiv:2107.05709. University of Granada, Spain complexity theorists (search Munoz) contribute to the latest articulations of nature’s insistent preference for an active balance and poise composed of more or less conserve and create, fixed or flexible, closed or open, modes. Here this optimum occasion is shown to offer much benefit to active informational learning tasks. As such entries typically say nowadays, it is noted that many other physical, biological, cerebral and societal phases are similarly distinguished by this “sweet spot” fittest condition.

Shedding light onto how biological systems represent, process and store information in noisy environments is a key and challenging goal. An innovative hypothesis in the making poses that operating in dynamical regimes near the edge of a phase transition, i.e. at criticality, can provide information-processing living systems with operational advantages as poised between robustness and flexibility. Our contribution in this regard will be to construct an artificial neural network and train it to classify images. Indeed, we find that the best performance is obtained when the network operates near the critical point, at which the eigenspectrum of its covariance matrix follows the same statistics as actual neurons do. Thus, we conclude that operating near criticality can also have the benefit of allowing for flexible, robust and efficient input representations. (Abstract excerpt)

A popular concept from artificial neural networks is that information-processing complex systems, which are composed of many individual interacting units, are best suited to encode, respond, process, and store information if they operate in the dynamical critical point regime of a phase transition, i.e. at the edge between "order" and "disorder.” In regard, there needs to be some trade-off between order and disorder that can be stated in a number of ways, e.g., between "stability and responsiveness" or "robustness and flexibility". The criticality hypothesis poses that such a contrast is resolved near criticality. (1-2)

Muolo, Riccardo, et al. Persistence of Chimera States and the Challenge for Synchronization in Real-World Networks. arXiv:2306.00237. University of Namur, Belgium, University of Limerick and Florida State University provide further theoretical reasons for nature’s broad and deep propensity to seek and reside in this optimum complementary balance.

Orderly phases emerge in nature with synchronization modes as a representative example. In this regard, the role played by interactions between the constituting parts of a complex system is a prime research subject bridging network science and dynamic phenomena. An especial interest is the presence of chimera states whereby synchronized oscillations coexist with asynchronous ones. Such alternate states of coherence and incoherence exemplify how order and disorder can coexist over a long time. Our concern is their presence in real-world networks. By way of a symmetry-breaking mechanism, we describe how non-normality, a ubiquitous structural property, can cause this bilateral occasion. (Excerpt)

Nettuno, Beatrice, et al. The role of mobility in epidemics near criticality. arXiv:2402.06505. Four years into the pandemic, a team of biophysicists at Ludwig-Maximilians-University including Erwin Frey achieve a host sophisticated mathematical formulation which draws upon and widely applies both physical principles and complexity science. Renormalization group theory and self-organized phase transitions are found to independently underline and channel this dynamic public malady wherever it occurs.

The general epidemic process (GEP) describes its spread within a population of susceptible individuals. We investigate the impact of mobility on disease spreading threshold by two generalizations of GEP, where the mobility of susceptible and recovered individuals is examined independently. The critical dynamics are studied through a perturbative renormalization group approach and large-scale stochastic simulations. This analysis predicts that both models belong to the same universality class which describe the critical epidemic dynamics. At the associated renormalization group fixed point, the immobile species decouples from the dynamics of the infected species due to coupling with the diffusive species.. Numerical simulations in two dimensions affirm our renormalization group results by identifying the same set of critical exponents for both models. (Excerpt)

Notarmuzi, Daniele, et al. Universality, Criticality and Complexity of Information Propagation in Social Media. arXiv:2109.00116. Indiana University systems theorists including Filippo Radicchi post a strong exposition to date of how all manner of dynamic self-organizing systems can be seen to spring from and express an iconic array of similar forms and behaviors. As a result, it is noted that all this disparate phenomena quite implies an independent generative source which seems to be in eternal effect. Into these 2020s, a natural propensity to seek and reside at an active bilateral poise from galaxies to Google becomes evident. For later work by this group see Critical avalanches of Susceptible-Infected-Susceptible dynamics in finite networks at 2301.06939.

Information avalanches in social media are typically studied in a similar fashion as avalanches of neuronal activity in the brain. Whereas much literature reveals a substantial agreement about a unique process that characterizes neuronal activity across organisms, the dynamics of information in online social media is far less understood. Here, we analyze almost 1 billion time-stamped events collected from a multitude of platforms (Telegram, Twitter and Weibo) over some 10 years to show that the propagation of information in social media is a universal and critical process. Universality arises from the observation of identical macroscopic patterns, irrespective of the specific system. Critical behavior is deduced from the power-law distributions, and their hyperscaling relations, which control the size and duration of avalanches of information. (Abstract excerpt)

For example, there is large agreement on the fact that neuronal activity in the brain is universal and critical. Universality is the notion that nearly identical avalanche statistics are observed for a multitude of organisms. Criticality instead refers to the fact that avalanche statistics are characterized by algebraic distributions. (4)

We speculate that our results extend beyond the six platforms considered here. If so, there must be a mechanism that explains the universality shown by the data, involving a critical dynamics that is independent of the peculiarities implemented in the individual platforms. Understanding where this mechanism is rooted in and how to exploit it for the prediction of the propagation of information in online social media remain open challenges for future research. (10)

Ohler, Simon, et al. Towards Learning Self-Organized Criticality of Rydberg Atoms using Graph Neural Networks. arXiv:2207.08927. University of Kaiserslautern, Germany and Merantix Momentum, AI Campus, Berlin researchers including Johannes Otterbach at once testify to nature’s universal preference for this optimum state and describe an avail of deep machine algorithmic methods by which to advance their latest studies.

Self-Organized Criticality (SOC) is a ubiquitous dynamical phenomenon believed to be responsible for the emergence of universal scale-invariant behavior in many disparate systems such as forest fires, viral epidemics or atomic excitation. SOC is found across large-scale and long-range spatio-temporal correlations as a result of local interactions. We investigate Graph Neural Networks (GNNs) as an effective way to model a physical system of driven Rydberg atoms as a typical SOC occasion. While inspired by active Rydberg atoms, the approach could readily be applied to many other cases. (Abstract excerpt)

Deep Learning methods deliver impact for many applications ranging from Computer Vision, Natural Language, Processing, Audio and Speech Processing to Optimal Control. In recent years we also see these methods drive innovation in areas of scientific interest, such as drug discovery, protein folding, molecule dynamics, as well as classic multi-particle systems and many more. In the context of particle dynamics the class of Graph Neural Networks (GNNs) are particularly successful. We build up on this success and investigate the application of GNNs to learn the time-evolution of a complex many-body system in the regime of so-called self-organized criticality (SOC). (1)

A Rydberg atom is an excited atom with one or more electrons that have a very high principal quantum number. The higher the value of n, the farther the electron is from the nucleus, on average. Rydberg atoms have certain properties including a response to electric and magnetic fields, long decay periods and electron wavefunctions.

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