IV. Ecosmomics: Independent Complex Network Systems, Computational Programs, Genetic Ecode Scripts

5. Common Code: A Further Report of Reliable, Invariant Occasions

Perez-Mercader, Juan. Scaling Phenomena and the Emergence of Complexity in Astrobiology. Gerda Horneck and Christa Baumstark-Khan, eds. Astrobiology. Berlin: Springer, 2002. Deep in the scientific literature a new universe is being described which arises by emergent, nested sequential stages. Perez-Mercader contends that these phases from biomolecules to human persons to galactic networks are distinguished by a universality whereby the same, invariant form and process recurs over and over.

Finally, among the main patterns we can identify a systematic presence of systems within systems, within systems: planetary systems, within galaxies, within clusters of galaxies, or bases within DNA molecules, within chromosomes, within cell nuclei, within cells, etc. (339)

Picoli, S., et al. Scale-Invariant Structure of Size Fluctuations in Plants. Scientific Reports. 2/Article 328, 2012. Universidade Estadual de Maringá, Brazil, physicists untangle nature’s floral profusion by way of complex systems science to lately decipher this recurrent, recursive, “analogy of proper proportion” (Aquinas) scripture. See also Picoli and Mendes in Religion and Science.

A wide range of physical and biological systems exhibit complex behaviours characterised by a scale-invariant structure of the fluctuations in their output signals. In the context of plant populations, scaling relationships are typically allometric. In this study, we analysed spatial variation in the size of maize plants (Zea Mays L.) grown in agricultural plots at constant densities and found evidence of scaling in the size fluctuations of plants. The findings indicate that the scaling of the probability distribution of spatial size fluctuation exhibits non-Gaussian behaviour compatible with a Lévy stable process. The scaling relationships were observed for spatial scales spanning three orders of magnitude. These findings should provide additional information for the selection and development of empirically accurate models of pattern formation in plant populations.

Poggialini, Anna, et al. Networks with many structural scales: a Renormalization Group perspetive. arXiv:2406.19104. We cite this work by Università “Sapienza” Rome and Universidad de Granada (Miguel Munoz) system physicists as an example of the increasing avail of this foundational theory in many far removed cerebral, bioregion and public phases. As the second quotes advises, by the mid 2020s such a consistently apt utiliety can then be seen to imply a true universal invariance. See also, e.g., Laplacian renormalization group: heterogeneous coarse-graining by Guido Caldarelli, et al in the Journal of Statistical Mechanics: (August 2, 2024). Gabriel, Nicholas, et al. Connecting the geometry and dynamics of many-body complex systems by Nicholas Gabriel, et al. at (arXiv:2502.15913).

Scale invariance profoundly influences the dynamics and structure of complex systems from critical phenomena to network architecture. Here, we propose a precise definition of scale-invariant networks by leveraging the concept of a constant entropy-loss rate in a renormalization-group coarse-graining setting. This approach differentiates between scale-free and scale-invariant networks, revealing characteristics within each class. We then survey genuine networks to show that the human connectome exhibits true scale invariance. (Excerpt)

The network paradigm captures essential attributes of real-world complex systems, offering a natural framework for studying entangled interconnected systems across disciplines like neuroscience [1], ecology [2], and epidemiology [3], among others [4]. Understanding the evolution-ary dynamics of complex networks, as they adapt their connectivity patterns to achieve diverse goals, is crucial to understanding their long-term stability or other features influencing functional roles and performance [5, 6]. Notably, amidst the multitude of potential network structures, one organization ubiquitously arises in natural systems: the scale-free architecture. (1)

Potirakis, Stelios, et al. Dynamical Analogy between Economical Crisis and Earthquake Dynamics within the Nonextensive Statistical Mechanics Framework. Physica A. Online February, 2013. University of Athens physicists drawn upon these thermodynamic theories of Constantino Tsallis to discern across disparate realms the presence of deep similarities, which are extended to seizures, magnetic storms and solar flares. So are we closing on a great historic realization, as other ages and cultures long aver, of an infinitely recurrent natural creation which so springs as if by universally applicable, genetic-like code. See also in regard “The Earth as a Living Planet” at arXiv:1210.4804 (October 2012) by Y. Contoyiannis, with Potirakis, whence more analogies are noted between geological criticalities and human physiology.

The field of study of complex systems considers that the dynamics of complex systems are founded on universal principles that may be used to describe a great variety of scientific and technological approaches of different types of natural, artificial, and social systems. Several authors have suggested that earthquake dynamics and the dynamics of economic (financial) systems can be analyzed within similar mathematical frameworks. We apply concepts of the nonextensive statistical physics, on time-series data of observable manifestations of the underlying complex processes ending up to these different extreme events, in order to support the suggestion that a dynamical analogy exists between a financial crisis (in the form of share or index price collapse) and a single earthquake. (Abstract)

Proekt, Alex, et al. Scale Invariance in the Dynamics of Spontaneous Behavior. Proceedings of the National Academy of Sciences. 109/10564, 2012. Physician Proekt, physicists Jayanth Banavar and Amos Martin, and neurobiologist Donald Pfaff, find animal activities to exhibit the same nested recurrence of self-organized phenomena as everywhere else in nature and society, as this site documents, from galaxies to genomes, brains, language, and our noosphere.

Typically one expects that the intervals between consecutive occurrences of a particular behavior will have a characteristic time scale around which most observations are centered. Surprisingly, the timing of many diverse behaviors from human communication to animal foraging form complex self-similar temporal patterns reproduced on multiple time scales. We present a general framework for understanding how such scale invariance may arise in nonequilibrium systems, including those that regulate mammalian behaviors. Our analyses reveal that the specifics of the distribution of resources or competition among several tasks are not essential for the expression of scale-free dynamics. Rather, we show that scale invariance observed in the dynamics of behavior can arise from the dynamics intrinsic to the brain. (Abstract)

pyo, Andrew, et al. Proximity to Criticality Predicts Surface Properties of Biomolecular Condensates. PNAS. 120/23, 2023. This mid 2023 entry by Princeton and Johns Hopkins University biologists including Ned Wingreen is a good example of the wide and deep convergent synthesis that is presently underway. The paper notably views the title biological functions as primarily due to deep self-organizing energies as they serve ti generate life’s oriented developmental evolution. A further vital finding is a constant propensity to seek and reside at a optimum critical point.

In Common Code we also cite concurrent physical instances such as Self-Organized Patterning on Azo Molecular Glass Film via Optical Near-Field Effect and Self-Organization of Ferroelectric Domains Reinforced via Ultrasonic Vibration both in the Nature journal Communications Materials (May 2023). To continue with nature’s dynamic universality, see Statistical thermodynamics of self-organization in the adaptive immune system by Jozsef Prechl, (2306.04665), From Autopoiesis to Self-Organization: Toward an Enactive Model of Biological Regulation by Tom Froese, et al (bioRxiv. June 9, 2023), Programmable Self-organization of heterogeneous microrobot collectives by Steven Ceron in PNAS (120/24, 2023) and Critical Scaling of Whole-Brain Resting-State Dynamics by Adrian Ponce-Alvarez, et al in Communications Biology (June 2023).

Self-organization through the phase separation of biomolecular condensates is ubiquitous in living cells. What general principles relate these macroscopic properties to the underlying microscopic features of biomolecules? By using universal ratios of thermodynamic quantities in the vicinity of a critical point, condensate physical properties can be inferred from a small number of thermodynamic parameters. We confirm that the range of validity of the critical region is large enough to cover the physiologically relevant range in living cells. (Pyo Significance excerpt)

Overall, these results suggest that the framework of critical phenomena can be utilized as a principled approach to understand the effect of microscopic features on the macroscopic properties of many biomolecular condensates. (Pyo 2)

The universality of behavior near a critical point provides an inherently principled way to relate microscopic features to macroscopic properties. Within a model for biomolecular phase separation, this affinity infers that polymer sequences influence surface tension by shifting the distance to the critical point. Notably, these interdependent scaling laws are not limited to a particular model system but are generally applicable within the 3D Ising universality class. (Pyo 5, 6)

Radicchi, Filippo and Ginestra Bianconi. Epidemic Plateau in Critical SIR Dynamics with Non-trivial Initial Conditions. arXiv:2007.15034. We cite this entry by Indiana University and Alan Turing Institute, London network theorists as an example amongst a flood of similar papers about how the active COVID-19 pandemic seems to exhibit and be moved by intrinsic mathematical patterns and dynamics. See also An Infection Process near Criticality by P. Krapivsky at 2009.08940. And we wonder if this international effort, aided global coordination, could come to a common synthesis, it would result a concerted focus going forward to mitigate and prevent any more –demics.

Containment measures implemented by some countries to suppress the spread of COVID-19 have resulted in a slowdown of the epidemic characterized by a time series of daily infections plateauing over extended periods of time. We prove that such a dynamical pattern is compatible with critical Susceptible-Infected-Removed (SIR) dynamics. In traditional analyses of the SIR model, the critical dynamical regime is started from a single infected node. We describe that such non-trivial starting conditions affect the outbreak size as an increasing function of the initial number of infected individuals, while the expected duration of the outbreak is a non-monotonic function of the initial number of infected individuals. (Abstract excerpt)

Radicchi, Filippo, et al. Complex Networks Renormalisation. Physics Review Letters. 101/148701, 2008. In our midst today, if we might inquire, is an imminent discovery via the sum of myriad contributions such as this finding of an invariant resonance whose nested nets from universe to human repeat the same archetypal pattern and process. Renormalization group theory, from 1982 physics Nobel laurate Kenneth Wilson, is yet another window upon nature’s innate universality, but is said to need better terminologies that could aid such a translation.

Generally speaking, an object is self-similar if any part of it, however small, maintains the general properties of the whole object. Self-similarity is a characteristic feature of fractals and it expresses the invariance of a geometrical set under a length-scale transformation. Many complex systems such as the World-Wide-Web (WWW), the Internet, social and biological systems, have a natural representation in terms of graphs, which often display heterogeneous distributions of the number of links per node (the degree k). These distributions can be described by a power law decay, i.e. are scalefree: they remain invariant under a rescaling of the degree variable, suggesting that suitable transformations of the networks’ structure may leave their statistical properties invariant. (148701)

Ramstead, Maxwell, et al. Answering Shrodinger’s Question: A Free-Energy Formulation. Physics of Life Reviews. Online September, 2017. Canadian, Australian, and British neurosciences including lead author Karl Friston post a new response to the 1944 What is Life? book by the Nobel laureate Erwin Schrodinger which has inspired the scientific quest for an integral definition grounded in physical principles. While ranging over a wide area, there is a growing confidence in the later 2010s that this essential rooting and explanation is within reach. In this journal, papers come with peer reviews, we note Michael Levin, John O. Campbell, Leot Leydesdorff, and others (14 men). But the whole project might benefit, it seems, from a toning down and clarity of technical terms.

The free-energy principle (FEP) is a formal model of neuronal processes that is widely recognised in neuroscience as a unifying theory of the brain and biobehaviour. More recently, however, it has been extended beyond the brain to explain the dynamics of living systems, and their unique capacity to avoid decay. The aim of this review is to synthesise these advances with a meta-theoretical ontology of biological systems called variational neuroethology, which integrates the FEP with Tinbergen's four research questions to explain biological systems across spatial and temporal scales. We exemplify this framework by applying it to Homo sapiens, before translating variational neuroethology into a systematic research heuristic that supplies the biological, cognitive, and social sciences with a computationally tractable guide to discovery. (Abstract)

In other words, an organism does not just encode a model of the world, it is a model of the world – a physical transcription of causal regularities in its eco-niche that has been sculpted by reciprocal interactions between self-organization and selection over time. On the basis of these distinctions, we turn next to defining a fully generalizable ontology for biological systems based on a multiscale free energy formulation, which we call “variational neuroethology.” (5)

Ribeiro, Tiago, et al. Scale-Free Dynamics in Animal Groups and Brain Networks. Frontiers in Systems Neuroscience. January, 2021. Into the 2020s, TR and Dietmar Plenz, NIH Critical Dynamics Group and Dante Chialvo, Universidad Nacional de San Martin, Argentina are able to perceive and delineate strong similarities between these disparate phases. An especial quality is the spontaneous presence of a self-organized criticalities in both active instances. Here then is an excellent instance of our Earthuman acumen just now attaining such a convergent synthesi of universal recurrence in kind.

The collective emergence of order in myriad interactive entities occurs over a vast range of physical and biological systems. Their key feature is an adaptive behavior beyond individual components. This article focuses on recent insights for two seemingly disparate phenomena: flocking in animal groups and neuronal ensembles in the brain. We report upon the spontaneous organization in bird flocks and whole human brain activity utilizing correlation functions and critical dynamics. Scale-free correlation functions capture the collective organization of neuronal avalanches in nonhuman primates and between neurons during visual processing in rodents. We conclude that at or near a phase-transition, neuronal information can propagate in the brain with similar efficiency to the collective adaptive response observed in some animal groups. (Abstract excerpt)

Roehner, Bertrand. Driving Forces in Physical, Biological and Socio-Economic Phenomena. Cambridge: Cambridge University Press, 2007. A University of Paris physicist applies network principles to group bonding and pathologies. Somewhat narrow and technical, it is noted because it opens with the observation that both the widely separated early elemental universe and later Neolithic societies can be seen to form by the same aggregative dynamics.

Root-Bernstein, Robert. A Modular Hierarchy-based Theory of the Chemical Origins of Life Based on Molecular Complementarity. Accounts of Chemical Research. 45/12, 2012. The Michigan State University polymath physiologist stays on message with another exposition about nature’s constant propensity to create and evolve by way of reciprocal mating pairs. With a philosophy PhD with Thomas Kuhn and a postdoc with Jonas Salk, he has made contributions to AIDS and autoimmunity research, along with blending science and the arts. See also his The Ribosome as a Missing Link in the Evolution of Life in the Journal of Theoretical Biology (Online December 2014), and Molecular Complementarity Between Simple, Universal Molecules and Ions with Vic Norris, et al in Biology Direct (9/28, 2014).

Molecular complementarity plays critical roles in the evolution of chemical systems and resolves a significant number of outstanding problems in the emergence of complex systems. All physical and mathematical models of organization within complex systems rely upon nonrandom linkage between components. Molecular complementarity provides a naturally occurring nonrandom linker. More importantly, the formation of hierarchically organized stable modules vastly improves the probability of achieving self-organization, and molecular complementarity provides a mechanism by which hierarchically organized stable modules can form. In sum, I propose that molecular complementarity is ubiquitous in living systems because it provides the physicochemical basis for modular, hierarchical ordering and replication necessary for the evolution of the chemical systems upon which life is based. I conjecture that complementarity more generally is an essential agent that mediates evolution at every level of organization. (Abstract)

Understanding the principles of evolution by modular complementarity suggests mechanism by which natural selection prunes away huge numbers of possibilities to direct evolution toward the increasingly integrated system. This pruning process transforms evolution from a probabilistic near-impossibility into an almost certain consequence of our Earthly chemistry. Complementarity principles may be “scale-free,” applicable to every level of organization from molecular to societal. (2170)

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