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A Sourcebook for the Worldwide Discovery of a Creative Organic Universe
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A. An Ecode Endowment: A Universal, Independent, Exemplary, Ecosmome to Geomome Complementarity

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.

Ortez, Ronaldo and John Rundle. Correlated Avalanche-Burst Invasion Percolation: Multifractal Origins of a Characteristic Self-Organized Critical System.. arXiv:2303.10272. UC Davis system physicists continue to deftly tease out another presence of a consistent, self-similar dynamic balance as a deep distinction of nature’s optimum preference.

We extend our previous avalanche-burst invasion percolation (AIP) model by adding long-range correlations between sites described by fractional Brownian statistics. In this way, we are able to produce a family of critical exponents characterized by the local long-range correlations inherent to host sediment. As a result, we show how multiple cluster scaling power laws gives rise to a truly multifractal system. (Excerpt)

Pereverzev, Sergey. Dark Matter Searches and Energy Accumulation and Release in Materials. arXiv:2212.13964. This presentation at the 14th International Conference on Identification of Dark Matter (Vienna 2022) by a Lawrence Livermore experimental physicist describes highly complex, diverse experiments which show how self-organized critical phenomena is inherently pervasive all manner of material and energetic phases.

This presentation at the 14th International Conference on Identification of Dark Matter (Vienna 2022) by a Lawrence Livermore experimental physicist describes highly complex, diverse experiments which show how self-organized critical phenomena is inherently pervasive all manner of material and energetic phases.

Provata, Astero.. From Turing Patterns to Chimera States in the 2D Brusselator Model. arXiv:2212.01297. A National Center for Scientific Research, Athens (bio below) physicist contributes a latest explanation about these spatial and temporal conditions which appear across a widening array of life’s natural and social phenomena. A novel contribution is their aptness to shift from a morphogenetic phase to a self-organized critical activity. On a personal note, I had lunch with Ilya Prigogine in a group in 1987 at a conference. Some 35 years on, into these 2020s the complexity sciences have come to and settled on this common non-equilibrium occasion, a true universality in kind.

The Brusselator has been used as a prototype model for autocatalytic reactions, and for the Belouzov-Zhabotinsky reaction. When coupled at the diffusive limit, the it undergoes a bifurcation resulting in the formation of classical Turing patterns such as spots, stripes and spirals. In the present study we use generic nonlocally coupled Brusselators and show that in the diffuse limit of the coupling range, the Turing effects are recovered, while for intermediate coupling ranges and appropriate parameter values chimera states are produced. This study demonstrates how the parameters of a typical nonlinear oscillator can be tuned so that the coupled system passes from spatially stable structures to dynamical spatiotemporal chimera modes. (Abstract)

A decade after the first theoretical prediction of chimera states, experimental evidence has been reported in mechanical, physical and chemical lsystems consisting of interacting oscillatory units. Some examples are optical systems, in electronic circuits, in mechanics, in biomedicine, and reaction diffusion systems. Beyond experimental findings in the laboratory, chimera states have been associated with the uni-hemispheric sleep in mammals and birds, with the onset of epileptic seizures and other biomedical conditions. (2)
The Brusselator is a theoretical model for a type of autocatalytic reaction. It was proposed by Ilya Prigogine and collaborators at the Université Libre de Bruxelle A Belousov–Zhabotinsky reaction servse as a classic example of non-equilibrium thermodynamics, resulting in the establishment of a nonlinear chemical oscillator.

Astero Provata received her B.Sc. degree in physics from the University of Athens in 1985 and Ph.D. degree from Boston University, USA, in 1991. She is currently Research Director of Nanoscience and Nanotechnology, Greece. Her interests include neural networks, nonlinear dynamical systems, statistical physics, fractals, and complex systems.

Proverbio, Daniele, et al. Buffering in Cell Regulation Motifs Close to Criticality. arXiv:2212.08600. As late 2022 scientific studies proceed to find a widening propensity across life’s metabolic, and cerebral phases to achieve and benefit from dynamic sensitivities, University of Luxembourg theorists show how these a these nuanced responses can also foster a ecological resilience.

Bistable biological regulatory systems need to cope with stochastic noise to fine-tune their function close to bifurcation points. Here, we study stability properties of this regime in generic systems to demonstrate that cooperative interactions buffer noise-induced regime shifts. Our generic framework, based on minimal models, can be used to extract robustness and variability properties of more complex models and empirical data close to criticality. (Abstract)

Overall, our study characterised fundamental dynamical mechanisms to buffer systems’ variability in critical regimes. We determined parameter ranges, corresponding to plausible cooperativity values for the positive feedback loop motif, where both variance and autocorrelation display low relative sensitivity to additive noise. (5)

Rao, Ankit, et al. Self-Assembled Meuromorphic Networks at Self-Organized Criticality in Ag-hBN Platform. arXiv:2301.01619. Eight India Institute of Science and University of Groningen researchers describe an involved physical material method by which to attain, demonstrate and explain this optimum performance condition.

Networks and systems which exhibit brain-like behavior can analyze information from noisy data with low power consumption due to the critical nature and complex interconnectivity of their neuronal-like network. We show that a system comprised of hexagonal Boron Nitride (hBN) films contacted with Silver (Ag), that can uniquely host two different self-assembled networks, which are self-organized at criticality (SOC). This system shows bipolar resistive switching between high resistance (HRS) and low resistance states (LRS). The temporal avalanche dynamics in both these states exhibit power-law scaling,
The temporal avalanche dynamics in both these states exhibit power-law scaling, long-range temporal correlation, and SOC. (Abstract excerpt)

Rispoli, Matthew, et al. Quantum Critical Behavior at the Many-Body Localization Transition. arXiv:1812.06959. We cite this 2018 entry by Harvard physicists in Spring 2023 as an example of how some five years later their early witness of this phenomenal behavior has become robustly evident, as this section documents. As the PediaPedia Earthica section next continues, as the spiral of science to a global sapiensphere with her/his own findings and knowledge, the present moment and advance can be appreciated as convergent synthesis and discovery.

Phase transitions are driven by collective fluctuations of a system's constituents that emerge at a critical point. This mechanism has been extensively explored for classical and quantum systems in equilibrium, whose critical behavior is described by a general theory of phase transitions. Our results unify the system's microscopic structure with its macroscopic quantum critical behavior, and they provide an essential step towards understanding criticality and universality in non-equilibrium systems. (Excerpt)

Romanczuk, Pawel and Bryan Daniels. Phase Transitions and Criticality in the Collective Behavior of Animals. arXiv:2211.03879. Humboldt University and Arizona State University (see websites) post a chapter for the 2023 Volume VII of the World Scientific series Order, Disorder, and Criticality. An especial notice is that it is edited by Yuri Holovatch (search) at the Laboratory for Statistical Physics of Complex Systems (, National Academy of Science in Ukraine, see notes below. This subject entry has its own distinction as an early integral synthesis of 21st century nonlinear science which proceeds to join an older complex adaptive system format with newly-realized, consequent self-organized criticalities. After these novel appreciations are described as they exemplify across every natural and social domain, the paper goes on to trace their deep rootings in active statistical physics phenomena.

Collective behaviors exhibited by animal groups, such as fish schools, bird flocks, or insect swarms are valid examples of self-organization in biology. Concepts and methods from statistical physics have lately been used as a theoretic reason for such collective effects in living systems. In addition, it has been implied that animal groupings should operate close to a phase transition as a (pseudo-)critical point to optimize their capability for collective computation. In this chapter, we will discuss the current state of research on the "criticality hypothesis", along with how to measure distance from criticality. We highlight the emerging view that explores the benefits of living systems being able to tune to an optimal distance from criticality. (Abstract)

Collective behavior exhibited by large animal aggregations such as swarms of insects, schools of fish, and flocks of birds are ubiquitous examples of biological self-organization. Physicists now investigate parallels between large animal collectives and statistical phenomena where local interactions between simpler components can lead to adaptive macroscopic properties. This functional behavior relies on distributed information available to entities within complex biological systems such as proteins in cells, neurons in brains onto animal and human groups. (2)

As laid out in this chapter, phase transition and criticality theories are highly relevant for understanding the interplay of self-organization and active organism behaviors. The “criticality hypothesis", whence complex biological system seek to optimize their collective computation capabilities, can provide a unifying principle across life’s life’s nested scales. Our consideration aligns with recent calls within evolutionary biology and ecology for novel ideas that can be grounded in a theoretical physics perspective. A truly bidirectional exchange between physics and biology thus opens new avenues of research for better fundamental understandings. (21)

The first volume of Order, Disorder and Criticality was published by World Scientific in 2004 and, over time, it gave rise to this book series. Its chapter content originated from the Ising (Ernst 1900-1998) Lectures workshops that occurred annually in Lviv in the Ukraine. The volumes initially aimed to provide topical surveys related to phase transitions and criticality in theoretical studies. As they appeared, it grew to natural phenomena beyond statistical physics such as complex biological systems composed of many interacting components that display collective behavior above their individual parts. (Yuri Holovatch)

Schaposnik, Laura, et al. Animal Synchrony and Agent’s Segregation. arXiv:2212.07505. Into late 2022, a paper by University of Chicago, Illinois and Oxford University (Robin Dunbar) biobehavior researchers to appear in the Proceedings A of the Royal Society proceeds to add a a further causal mathematic basis whereby creaturely activities in diverse assemblies can be well modeled as reciprocal, self-organized critical, relations. By our notice, this is the first time (on schedule) that Kuramoto (cited), chimera-like oscillations have been applied to and seen in formative effect across to life’s multi-organism phase. See also Relating Size and Functionality in Human Social Networks through Complexity by Bruce West, Robin Dunbar, et al in PNAS (117/31, 2022) for another approach which can perceive and quantify critical behaviors of active groups.

In recent years it has become evident that a lack of coordination imposes constraints on the size of stable groups that highly social mammals can live in. Here we examine the forces that keep animals together as a herd and others that drive them apart. For example, different phenotypes (e.g. genders) have various rates of gut fill, causing them to spend more or less time performing activities. By modeling a group as a set of semi-coupled oscillators, we show that its members may become decoupled until the group breaks apart. We show that when social bonding creates a stickiness, or gravitational pull, between pairs of individuals, fragmentation is reduced. (Abstract)

Shpurov, Ivan and Tom Froese. Evidence of Critical Dynamics in Movements of Bees inside a Hive. Entropy. 24/12, 2022. As scientific realizations in later 2022 report an increasing notice of a vital self-organized critically from quantum to neural and social realms, as this new section reports, for a Statistical Physics of Collective Behavior issue edited by Bryan Daniels (see below), Okinawa Institute of Science and Technology cognitive theorists (search Froese) even perceive and report how this optimum behavioral phenomena is present in insect activities.

Social insects such as honey bees exhibit complex behavioral patterns whose distributed coordination enables decision-making at the colony level. It has been proposed that a high-level description of their collective behavior might share commonalities with the dynamics of neural processes in brains. Here, we investigated this proposal by focusing on how brains are poised at the edge of a critical phase transition which fosters increased computational power and adaptability. We found that certain characteristics of the activity of the bee hive system are consistent with the Ising model when it operates at a critical temperature, and that the system’s behavioral dynamics share features with the human brain in the resting state. (Abstract)

Understanding how the adaptive behavior of groups is controlled by the individuals within them is a major challenge for 21st century science. From proteins in a cell to neurons in a brain, and from fish in a school to people in society, we know how most entities perform and interact, but mapping this to adaptive behavior at the aggregate scale is difficult. Statistical physics has long approached similar problems in non-living systems, connecting macroscopic theories to the microscopic details. This Special Issue will explore these themes using concepts such as coarse graining, renormalization, scaling, phase transitions, collective instabilities, broken symmetries, dynamical modes, free energy, critical phenomena, and more. Our aim is to build predictive theories o describe the collective behavior of proteins, bacteria, neurons, insects, mammals, fish, robots, computers, artificial neural networks, species, people, societies, and ideas. (Byron Daniels Entropy)

Smyth, William, et al. Self-Organized Criticality in Geophysical Turbulence. Nature Scientific Reports. 9/3747, 2019. Into 2019, it is becoming strongly evident that a genesis universe evolves and develops by repetitions and iterations of the same dynamic phenomena in kind everywhere. Here Oregon State University oceanographers describe such a tendency to reach a critical balance even in these geologic and atmospheric phases.

Turbulence in geophysical flows tends to organize itself so that the mean flow remains close to a stability boundary in parameter space. That characteristic suggests self-organized criticality (SOC), a statistical property that has been identified in a range of complex phenomena including earthquakes, forest fires and solar flares. This note explores the relationship between forced, sheared, stratified turbulence in oceans, atmospheres and other geophysical fluids and those of SOC. Self-organization to the critical state is demonstrated in a wide range of ocean turbulence, which also follows a power-law distribution indicating self-similarity. (Abstract capsule)

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