IV. Ecosmomics: An Independent, UniVersal, Source Code-Script of Generative Complex Network Systems

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

Garcia-Ruiz, Ronald and Adam Vernon. Emergence of Simple Patterns in Many-Body Systems from Macroscopic Objects to the Atomic Nucleus. arXiv:1911.04819. . R. Garcia Ruiz is posted at CERN Geneva and MIT, while A. Vernon is with KU Leuven, Belgium and the University of Manchester. Among an increasing number of reports, this entry with 175 references is a good example to date of a global scientific endeavor now able to quantify a substantial nature that everywhere gives rise to common forms and flows by its own propensities. With a root basis in nuclear shell clusters, a recurrent regularity spreads in kind across micro-physical and macro-biological realms. As the second quote cites, iconic mathematical shapes can found throughout, aka “magic numbers.” See also Underlying Structure of Collective Bands and Self-Organization in Quantum Systems by Takaharu Otsuka, et al at arXiv:1907.10759, and Magic Number Colloidal Clusters as Minimum Free Energy Structures by Junwei Wang, et al in Nature Communications (9/5259, 2018.)

Strongly correlated many-body systems often display the emergence of simple patterns and regular behavior of their global properties. Phenomena such as clusterization, collective motion and shell structures are commonly observed across different size, time, and energy scales in our universe. Although at the microscopic level their individual parts are described by complex interactions, the collective behavior of these systems can exhibit strikingly regular patterns. This contribution provides an overview of the experimental signatures that are used to identify the emergence of structures and collective phenomena in distinct physical systems, along with macroscopic examples. (Abstract)

Throughout nature, driving forces give rise to the arrangement of constituents in many-body systems at almost every size. On biological scales, this manifests in collective phenomena and pattern formation such as the phyllotaxis of plants, where growth patterns appear in the leaves or flowers around a plant stem. A striking example is observed in the seeds in a sunflower head, which follows the Fibonacci sequence. Complex many-body systems often form clusters to minimise their energy by interactions between neighbours and their mean field. This can form “magic” numbers, as in the atomic nucleus, where certain integer numbers of constituents of a given system result in greater stability of its collective whole. Another instance is the abundance distribution of isotopes in the universe following nucleosynthesis. (2, edits)

In nuclear physics, a magic number is a number of nucleons (either protons or neutrons, separately) such that they are arranged into complete shells within the atomic nucleus. The seven most widely recognized magic numbers as of 2019 are 2, 8, 20, 28, 50, 82, and 126. For protons, this corresponds to the elements helium, oxygen, calcium, nickel, tin, and lead. (Wikipedia)

Giometto, Andrea, et al. Scaling Body Size Fluctuations. Proceedings of the National Academy of Sciences. 110/4646, 2013. École Polytechnique Fédérale de Lausanne, Swiss Federal Institute of Aquatic Science and Technology, and Università di Padova, researchers describe a ubiquitous natural propensity to reiterate “universal forms” across spatial and temporal, evolutionary and environmental occasions, as the extended quotes attest.

The size of an organism matters for its metabolic, growth, mortality, and other vital rates. Scale-free community size spectra (i.e., size distributions regardless of species) are routinely observed in natural ecosystems and are the product of intra- and interspecies regulation of the relative abundance of organisms of different sizes. Intra- and interspecies distributions of body sizes are thus major determinants of ecosystems’ structure and function. We show experimentally that single-species mass distributions of unicellular eukaryotes covering different phyla exhibit both characteristic sizes and universal features over more than four orders of magnitude in mass. Remarkably, we find that the mean size of a species is sufficient to characterize its size distribution fully and that the latter has a universal form across all species. We show that an analytical physiological model accounts for the observed universality, which can be synthesized in a log-normal form for the intraspecies size distributions. We also propose how ecological and physiological processes should interact to produce scale-invariant community size spectra and discuss the implications of our results on allometric scaling laws involving body mass. (Abstract)

Why should a continuous, gap-free spectrum of organismic sizes emerge from the ecological and evolutionary processes that shape their ecosystems? The origins and the implications of the absence of preferential body sizes, which is routinely observed across a variety of ecosystems regardless of broad differences in climatic and environmental conditions, have been attracting much interest from field and theoretical ecologists. Scale invariance, epitomized by power-law probability distributions, requires regularities of the component parts (the species’ size distributions) making up the whole [the community size spectra (i.e., the probability distributions of size regardless of species)]. In particular, a necessary condition for scaling community size spectra is the lack of peaks that pinpoint frequent occurrences, and therefore excess abundance (and vice versa) within any given range of sizes. Such features are particularly interesting if robust to environmental fluctuations because their dynamic origin could lie in the self-organization of complex adaptive systems. (4646)

Gisiger, T. Scale Invariance in Biology: Coincidence or Footprint of a Universal Mechanism? Biological Reviews. 76/2, 2001. After an introduction to dynamical systems in their physical embodiment, their power law self-similarity properties are shown to pervade biological and neurological realms so as to affirm a ‘universality’ throughout nature.

In the spirit of complex systems, we should try not to look at these examples as physical processes or reactions between chemical reactants, but instead as systems made of many particles, or 'agents,’ which interact with each other via certain rules. (163) These findings might therefore illustrate how an ecosystem self-organizes into a critical state as the web of interactions between species and individuals develops. (185) Scale invariance is very common in nature, but it is only since the early 1970s that the mathematical tools necessary to define it more clearly were introduced. (204)

Grimm, Volker, et al. Pattern-Oriented Modeling of Agent-Based Complex Systems. Science. 310/987, 2005. This international collaboration with ten authors describes a novel method of understanding ecological systems, and how it may be applied throughout scientific fields. Autonomous, adaptive agents are everywhere: immune cells, plants, citizens, investors, and so on. Their collective behavior can be quantified by “individual-based” (IBM) or “pattern-oriented” (POM) modeling by “bottom-up” simulations, seen as another name for complex adaptive systems (CAS). These approaches have been implemented by studies of ultra complex and stratified ecosystems. As a reflection, one more recognition of a quite different natural materiality via its universal creative complementarity.

Agent-based complex systems are dynamics networks of many interacting agents; examples include ecosystems, financial markets, and cities. (987) In particular, experiments contrasting hypotheses for the behavior of interacting agents will lead to an accumulation of theory for how the dynamics of systems from molecules to ecosystems and economies emerge from bottom-level processes. This approach may change our whole notion of scientific theory, which until now has been based on the theories of physics. (991)

Harte, John. Toward a Synthesis of the Newtonian and Darwinian Worldviews. Physics Today. October, 2002. In this 2001 Leo Szilard Award Lecture, a theoretical ecologist attempts to join the universality of physical systems and the interdependent detail of ecosystems by way of complexity principles.

A self-similar pattern, as the phrase is used in the study of fractals, is one that looks the same on all spatial scales….My students and I have been employing a variety of analytical methods, including renormalization-group techniques developed for the study of scaling in self-similar phenomena in physics, to understand better the origins, implications, and interconnections of the power-law and self-similar relationships one finds in ecology. (33) I suggest that particularity and contingency, which characterize the ecological sciences, and generality and simplicity, which characterize the physical sciences, are miscible, and indeed necessary, ingredients in the quest to understand humankind’s home in the universe. (34)

Haugland, Sindre, et al. Self-Organized Alternating Chimera States in Oscillatory Media. Nature Scientific Reports. 5/9883, 2015. Technische Universität München, Nonequilibrium Chemical Physics, researchers including Katharina Kirscher, contribute to studies upon nature’s substantial propensity to switch between orderly or chaotic conditions. A biological example is the unihemispheric sleep pattern of avian animals which varies from synchronization to incoherence. We thus find another instance whence cosmos and life seems to persist in a dynamic poise of complementary modes. See also Spatially Organized Dynamical States in Chemical Oscillator Networks by Mahesh Wickramasinghe and Istvan Kiss in PLoS One (8/11, 2013) for another Taoist tango.

Oscillatory media can exhibit the coexistence of synchronized and desynchronized regions, so-called chimera states, for uniform parameters and symmetrical coupling. In a phase-balanced chimera state, where the totals of synchronized and desynchronized regions, respectively, are of the same size, the symmetry of the system predicts that interchanging both phases still gives a solution to the underlying equations. We observe this kind of interchange as a self-emerging phenomenon in an oscillatory medium with nonlinear global coupling. An interplay between local and global couplings renders the formation of these alternating chimeras possible. (Abstract)

Herrada, E. Alejandro, et al. Universal Scaling in the Branching of the Tree of Life. PLoS ONE. 3/7, 2008. Novel applications of scale-free network theory are utilized to reveal consistent, non-random patterns across life’s evolutionary florescence. Google this Public Library of Science online journal along with the author’s name to access the article.

The finding of non-random universal patterns of phylogenetic differentiation suggests that similar evolutionary forces drive diversification across the broad range of scales, from macro-evolutionary to micro-evolutionary processes, shaping the diversity of life on the planet. (1) In summary, the remarkably similar allometric exponents reported here to characterize universally the scaling properties of intra- and inter-specific phylogenies across kingdoms, reproductive systems and environments, strongly suggests the conservation of branching rules, and hence of the evolutionary processes that drive biological diversification, across the entire history of life. (3-4)

Jagers op Akkerhuis, Gerard. Analysing Hierarchy in the Organization of Biological and Physical Systems. Biological Reviews. 83/1, 2008. A Wageningen University research ecologist proposes, after several earlier versions and much literature review, a formal scheme by which to rank nature’s successive spatial emergence of ‘developmental stages’ from superstrings to encephalized organisms. This is accomplished by two attributes or groupings – operators and interactions, or elemental organization and relational dynamics. Along with William Lidicker’s paper (Dynamic Ecosystems) in the same issue, what is noteworthy is that after some 50 years of study, and centuries of intimation, a confirmation is dawning that cosmic and earthly creation is indeed stratified in kind, and distinguished by a repetitive scale of being and becoming.

Jiang, Luo-luo and Matjaz Perc. Spreading of Cooperative Behavior Across Interdependent Groups. Nature Scientific Reports. 3/2483, 2013. Indicative of the present 21st century global reach of an electronic noosphere, Wenzhou University, China, and University of Maribor, Slovenia theorists apply network mathematics to anthropological studies of hunter-gather groups, such as the Hadza of Tanzania, to identify their success as due to an “intermediate interdependence” via a reciprocity of member and troop. Thus one more such phrase occurs to identify this universal natural principle from microbes to civilizations.

Recent empirical research has shown that links between groups reinforce individuals within groups to adopt cooperative behaviour. Moreover, links between networks may induce cascading failures, competitive percolation, or contribute to efficient transportation. Here we show that there in fact exists an intermediate fraction of links between groups that is optimal for the evolution of cooperation in the prisoner's dilemma game. We consider individual groups with regular, random, and scale-free topology, and study their different combinations to reveal that an intermediate interdependence optimally facilitates the spreading of cooperative behaviour between groups. Excessive between-group links simply unify the two groups and make them act as one, while too rare between-group links preclude a useful information flow between the two groups. Interestingly, we find that between-group links are more likely to connect two cooperators than in-group links, thus supporting the conclusion that they are of paramount importance. (Abstract)

Jordan, Ferenc, et al. A Hierarchy of Networks Spanning from Individual Organisms to Ecological Landscapes. Estrada, Ernesto, et al, eds. Network Science: Complexity in Nature and Technology. London, Springer, 2010. Jordan, with Federica Ciocchetta, Centre for Computational and Systems Biology, University of Trento, and Gabriella Baranyi, Institute of Environmental Studies, Eotvos University, in this volume about this natural phenomena from common principles, and instantiation from protein to financial webs, provide a cogent paper over this ubiquity. As the quotes convey, a nested net repetition or iteration is the evident case, as informed by convergent statistical physics and systems ecology approaches.

Living systems are hierarchically organised. A number of components are linked by the multiplicity of interactions at each level (from organisms to species to ecosystems). This kind of compositional and hierarchical complexity is a computational and conceptual challenge. We need new approaches to determine the key components of large interaction networks and we need to better understand how they influence the system dynamics horizontally (at the same level) and vertically (between organisational levels). We provide examples for various interaction networks (animal social group, food web, landscape) and discuss how to dynamically link them. (Abstract, 165)

Biological systems are composed of a large number of various components, like millions of molecules in a cell, thousands of cells in an organism, hundreds of individuals in a population and dozens of species in an ecological system. Yet, biosystems are complex not primarily because of the number of components but rather because of composition: the multiplicity of interactions among similar components and the hierarchical, nested nature of different kinds of components at several organizational levels. These components are composed of subsystems as well as compose larger systems, and all layers have been coevolved in evolution. (165)

Kaschube, Matthias, et al. Universality in the Evolution of Orientation Columns in the Visual Cortex. Science. 330/1113, 2010. German and American neurogeneticists first report a specific instance of how dynamic nonlinearites are found to guide the formation and acuity of optical shapes, and go on, re the second quote, to advise that their common prevalence across living systems would attest to a generative spontaneity on a par with genetic and behavioral influences. For our nascent 2010 revolution, here is tangible evidence of an innately creative complexity that is manifest in a similar fashion everywhere. This implicate independence can then be realized to take on a genomic identity, so as to grace, propel, and ascend through, a natural genesis.

The brain’s visual cortex processes information concerning form, pattern, and motion within functional maps that reflect the layout of neuronal circuits. We analyzed functional maps of orientation preference in the ferret, tree shrew, and galago—three species separated since the basal radiation of placental mammals more than 65 million years ago—and found a common organizing principle. A symmetry-based class of models for the self-organization of cortical networks predicts all essential features of the layout of these neuronal circuits, but only if suppressive long-range interactions dominate development. We show mathematically that orientation-selective long-range connectivity can mediate the required interactions. Our results suggest that self-organization has canalized the evolution of the neuronal circuitry underlying orientation preference maps into a single common design. (Abstract, 1113)

We conclude that wherever such complex biological systems unfold, especially in the mammalian brain where they are likely to abound, the principles of dynamical network self-organization may design and constrain system behavior as powerfully as an organisms genetic endowment or early life experiences. (1116)

Kashtan, Padav and Uri Alon. Spontaneous Evolution of Modularity and Network Motifs. Proceedings of the National Academy of Sciences. 102/13773, 2005. Another example of how new understandings of evolution by way of complexity theory can identify a universally emergent structure and dynamics.

Biological networks have an inherent simplicity: they are modular with a design that can be separated into units that perform almost independently. Furthermore, they show reuse of recurring patterns termed network motifs. (13773)

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