But if I were to try to explain in a paragraph, I would say this - it is like when water, at just the right pressure, changes into steam. For a moment it is both a flowing liquid and individual molecules zipping around in the air. Neurons can act this way too, firing synchronously then breaking of to improvise by themselves. Just at this transition. They are both independent and interdependent with all other neurons. Right here at what we will call the critical point, information flows easily, computations are most facile, and the brain is very sensitive to inputs. Here intricate patterns of waves, oscillations, and avalanches of activity arise most readily. (1)

Most broadly, there are two main consequences for a neural network that operates near the critical point. First, it will have scale-free properties which are linked to optimal information processing. Second it will exhibit universality, as we explored in this chapter. (105)

Over the last few decades, an idea called the critical brain hypothesis has been helping neuroscientists understand how the human brain operates as an information-processing powerhouse. It posits that the brain always teeters between two phases of activity: a relative quiet, less orderly side, and a more active, attentive mode,. The hypothesis predicts that between these conditions, at a “sweet spot” known as the critical point, the brain has an ideal balance of variety and structure so as to produce the most complex and information-rich patterns. (Beggs, Quanta)

Chen, Luyao, et al. AI of Brain and Cognitive Sciences: From the Perspective of First Principles. arXiv:2301.08382. Sixteen Chinese length scholars under the auspices of the AI of Brain and Cognitive Sciences Research Group, Beijing Academy of Artificial Intelligence, and Beijing University post an array of chapters, per the first quote, in an effort to advance AI abilities by better appreciations of how our own cerebral faculties have actually formed and well function. Our main interest is Criticality: Bringing New Perspectives to the Brain and AI, which gathers and presents an extensive, latest survey as this realization lately gains a wide, quantified acceptance. The two longer quotes are from this section.

This paper collects six such first principles summarized by the research team, “AI of Brain and Cognitive Sciences”, in the Beijing Academy of Artificial Intelligence (BAAI). They are attractor network, criticality, random network, sparse coding, relational memory, and perceptual learning. On each topic, we review its biological background, fundamental property, potential application to AI, and future development.

The framework of criticality is a powerful tool to understand and analyze complex systems because many systems in physics and nature are in a critical state. In the past 20 years, researchers found that biological neural networks in the brain operate close to a critical state, which provides a new perspective on studying brain dynamics. It is known that the critical state is important for brain activities/functions because it optimizes numerous aspects of information transmission, storage, and processing. In addition, some brain diseases are believed to be related to the deviation from the critical state, which also opens a new window for diagnosing and treating these diseases. In the field of artificial intelligence, the framework of the critical state is used to analyze and guide both the structural design and weight initialization of deep neural networks, suggesting that operating close to a critical state may be considered one of the fundamental principles governing computations in neural networks. (9)

The critical state gives us a new perspective to study biological and artificial neural networks. At present, the framework of criticality has not only been used to understand neural dynamics and brain diseases but also to analyze the operation of deep neural networks and guide the design for further improvement. Through theoretical analysis and numerical simulations, we know that the critical state of the network can be controlled by some simple control parameters, such as branching ratio, spectral radius, and input-output Jacobian singular values. This makes it possible to analyze or tune the overall behavior of complex networks through statistics that are easy to observe. We believe that the framework of criticality will play an even more important role in helping us better understand the constraints applied to artificial neural networks and to design better architectures as well as dynamical rules to improve its performance in complex information processing. (14)

Ciss, Mamadou, et al. Description of the Cattle and Small Ruminants Trade Network in Senegal.. arXiv:2301.11784. We cite as another instance by Senegalese, French and British system veterinaries of how a mature awareness of common, implicate nonlinear lineaments in universal effect can provide an implicate guidance even for the distribution and maintenance of indigenous herd animals.

Livestock mobility of small and large ruminants, is a main pillar of production and trade in West Africa. These movements cover several thousand kilometers and connect the whole West African region. But this activity also leads to the diffusion of many animal and zoonotic diseases. In this paper, we present a procedure based on temporal network theory to identify possible sentinel locations using two indicators: vulnerability (i.e. the probability of being reached by the disease) and time of infection (i.e. the time of first arrival of the disease). (Excerpt)

corbetta, Alessandro and Federico Toschi. Physics of Human Crowds. Annual Review of Condensed Physics. 14/311, 2023. Eindhoven University of Technology system theorists provide a strong, exemplary illustration of how our public lives can also be seen to actually reflect the presence of an independent, common, mathematic program-like source. Yes, people indeed have their own wills, yet going forward, by our 21st century organic revolution it would serve us one and all to be aware of this deeper genetic-like guidance.

Understanding the behavior of human crowds is a key step toward a safer society and more livable cities. Despite the individual variability and will of single individuals, human crowds, from dilute to dense, invariably display a remarkable set of universal features and statistically reproducible behaviors. Here, we review ideas and recent progress in employing the language and tools from physics to develop a deeper understanding about the dynamics of pedestrians. (Abstract)

Dresp-Langley, Birgitta. The Grossberg Code: Universal Neural Network Signatures of Perceptual Experience. Information. 14/2, 2023. A Strasbourg University, Center for National Scientific Research neuroscholar (search) post a succinct review of Stephen Grossberg’s opus Conscious Mind, Resonant Brain (2022) along with a detailed, sequential expansion of its integral invariance from universe to us as we learn. See also her paper The Weaponization of Artificial Intelligence: What the Public Needs to be Aware Of in Frontiers in Artificial Intelligence (6/115484, 2023).

Two universal functional principles of Grossberg’s Adaptive Resonance Theory decipher the brain code of all biological learning and adaptive intelligence. Low-level representations of multisensory stimuli in their immediate environmental context are formed on the basis of bottom-up activation and under the control of top-down matching rules that integrate high-level, long-term traces of contextual configuration. These universal coding principles lead to the establishment of lasting brain signatures of perceptual experience in all living species, from aplysiae to primates. They are re-visited in this concept paper on the basis of examples drawn from the original code and from some of the most recent related empirical findings on contextual modulation in the brain, highlighting the potential of Grossberg’s pioneering insights and groundbreaking theoretical work for intelligent solutions in the domain of developmental and cognitive robotics. (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, 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)

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)

Tadic, Bosilijka. Cyclical Trends of Network Load Fluctuations in Traffic Jams. Dynamics. 2/4, 2022. We cite this entry by the veteran Solvenian complexity theorist (search) as an example into these 2020s of how a mathematical awareness of a separate domain that underlies and structures human social activities can provide natural (genetic-like) informed guidance for better results.

The transport of information packets in complex networks is a prototype system for the study of traffic jamming, a nonlinear dynamic phenomenon that arises with increased use and limited road capacity. An intrinsic framework helps to reveal how the macroscopic build-ups from microscopic forces, depending on the posting rate, navigation rules, and network form. We find that near congestion thresholds, traffic fluctuations show a temporal pattern described by cyclical trends with multifractal features. (Excerpt)

Tang, Xun and Huifang Ye. Xun and Huifang Ye. Metaphorical Language Change Change is Self-Organized Criticality. arXiv:2211.10709. Huazhong University of Science and Technology, Wuhan system linguists extend later 2022 perceptions of a ubiquitous SOC so to highlight its innate coherence of two complementary modes. Here linguistic domains are seen as distinguished by this universal scale-free form and facility. As the abstract states, the authors record an historic recognition of how even narrative writings and spoken conversation can equally be seen to avail these archetypal benefits.

One way to resolve the actuation problem of language change is to provide a statistical profile of metaphorical constructions and generative rules. Based the view of language as a complex system and the dynamic view of metaphor, this paper argues that language change qualifies as a self-organized criticality state and the linguistic expressions can be profiled as a fractal correlation. Synchronously, metaphorical usages self-organize into a self-similar, scale-invariance with a power-law distribution. We verify this by statistical analyses of twelve randomly selected Chinese lexicon in a large-scale diachronic corpus. (Abstract)

Tsakmakidis, Kosmos, et al. Quantum Coherence-driven Self-Organized Criticality and Nonequilibrium Light Localization. Science Advances. May, 2018. UC Berkeley research physicists discern one more actual presence of nature’s optimum dynamic phase ineven at this deepest energetic stage. As a reflection, when I began these studies long ago (e.g., 1987 at the Santa Fe Institute to hear Harold Morowitz) the SO universality of the second quote was a remote hope. Today, in these critical condition 2020s, due to John Beggs and many others, it is vital that our worldwise natural philosopher sapience once again is able at last to perceive and realize what an epochal, numinous discovery has been achieved.

Self-organized criticality emerges in dynamical complex systems driven out of equilibrium and characterizes a wide range of classical phenomena in physics, geology, and biology. We report on a quantum coherence–controlled self-organized critical transition observed in the light localization behavior of a coherence-driven nanophotonic configuration. Our system is composed of a gain-enhanced plasmonic heterostructure controlled by a coherent drive, in which photons close to the stopped-light regime interact in the presence of the active nonlinearities. In this system we observe quantum coherence–controlled self-organized criticality in the emergence of light localization arising from the synchronization of the photons. (Excerpt)

The self-organization of many nonequilibrium complex systems toward an “ordered” state is a profound concept in basic science, ranging from biochemistry to physics.. Examples include the group movement of flocks of birds (, motions of human crowds, neutrino oscillations in the early universe, and the formation of shapes (morphogenesis) in biological organisms. An intriguing trait of this nonequilibrium, driven-dissipative systems is that their self-organization can lead them to a phase transition and to critical behavior — a phenomenon known as self-organized criticality. (1)

Voit, Maximilian and Hildegard Meyer-Ortmans. Emerging Criticality at Bifurcation Points in Heteroclinic Dynamics. Physical Review Research. 2/043097, 2020. Jacobs University, Bremen physicists enter one more finely perceived instance of nature’s deep propensity to seek, arrive and poise at this optimum condition, which lately seems to be in evidence at each and every occasion.

Heteroclinic dynamics is a suitable framework to describe transient dynamics that is characteristic for ecological as well as neural systems, in particular for cognitive processes. We consider different heteroclinic networks and zoom into the dynamics that emerges right at different bifurcation points. We identify features of criticality such as a proliferation of the dynamical repertoire and slowing down of the dynamics at the very bifurcations and in their immediate vicinity. It qualifies these bifurcation points as candidates for working points in systems which store and transfer information. (Abstract)

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