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

Johnson, Stephen. Emergence. New York: Scribner, 2001. A computer scientist and writer explains how a spontaneously creative nature employs the same pattern and dynamics of multiple interacting agents at every stage from social insects to neural nets, cities, and computer software.

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)

Kauffman, Stuart. Investigations. New York: Oxford University Press, 2000. More conceptual insights into a view of Earth life that creates itself by means of intentional, autonomous agents which continually expand the niche of animate complexity. Kauffman’s frontier thinking offers glimpses of a “fourth law of thermodynamics,” a “general biology” for emergent life, autocatalytic biospheres, and a “coconstructing cosmos.”

Kauffman, Stuart. The Origins of Order: Self-Organization and Selection on Evolution. New York: Oxford University Press, 1993. A breakthrough work that reports on biologist and physician Kauffman’s decades of research studies on a deep theoretical basis for the innate self-organization of complex living systems which is in creative effect prior to the winnowing action of natural selection. (Also see Kauffman’s At Home in the Universe in Part III,An Organic Universe.)

Kelso, Scott and David Engstrom. The Complementary Nature. Cambridge: MIT Press, 2006. This important work is mainly noted in Current Vistas and by an extensive review in Recent Writings.

Khelifi, Mounir, et al. A Relative Multifractal Analysis. Chaos, Solitons and Fractals. Vol. 140, 2020. University of Monastir, Tunisia mathematicians provide a further finesse of nature’s infinite self-similar formulations. We also cite amongst a wide array of international 2020 papers such as Multifractal Analysis of Embryonic Eye Structures in Mice (Sijilmassi, Ouafa, et al, Universidad Complutense de Madrid, 138), The Origin of Collective Phenomena in Firm Sizes (Ji, Guseon, et al, Graduate School of Future Strategy, KAIST, S. Korea, 136), Using Network Science to Unveil Badminton Performance Patterns (Gomez, Miguel-Angel, et al, Universidad Politécnica de Madrid, 135), A Symbiosis between Cellular Automata and Genetic Algorithms (Cerruti, Umberto, et al, University of Torino, 134), and The Fractal Description Model of Rock Fracture Networks (LiLi, Sui, et al, North China Institute of Science, 129). Our aim is to document in this consummate year how every manifest social, biologic and physical phase is deeply guided by common mathematic sources.

The University of Monastir is a Tunisian multidisciplinary university with its own financial and administrative autonomy located on the Gulf of Hammamet, south of Tunis. It was founded in 2004 following the reform of the university higher education system and is organized in 5 Faculties, 2 graduate schools and 9 institutes.

Kiel, L. Douglas. Knowledge Management, Organizational Intelligence and Learning, and Complexity. UNESCO-EOLSS Joint Committee. Knowledge for Sustainable Development. Volume 1. Paris: UNESCO Publishing; Oxford: EOLSS Publishers, 2002. A good primer on complexity sciences. As these become more familiar, they are motivating organizations to become dynamic, adaptive, ecologically sensitive and constantly learning.

These discoveries focus on both order and disorder in the universe and on the increasing complexity and similarities across universal process, and have led to a new paradigm in the sciences – the self-organizing paradigm that focuses on how form and structure are produced in a dynamic and creative universe. (854) There is a growing recognition that the same processes that lead to a self-organizing universe have also led to the tremendous complexity of human cultures and human affairs. (855)

Knona, Mikail, et a. Global modules robustly emerge from local interactions and smooth gradients. Nature. February 19, 2025. MIT neuroscientists including Ila Fiete provide another, novel explanation for nature’s apparent spontaneous, oriented propensity to organize itself into ascendant entity/ensemble vitalities.

Modular structure and function are ubiquitous in biology from the organization of animal brains and bodies to the scale of ecosystems. However, the way modularity emerges from non-modular precursors remain unclear. Here we introduce the principle of peak selection, a process by which purely local interactions and smooth gradients can drive the self-organization of discrete global modules. The process combines the positional and Turing pattern-formation mechanisms into a model for morphogenesis. (Excerpt)

Krakauer, David, ed. Worlds Hidden in Plain Sight: The Evolving Idea of Complexity at the Santa Fe Institute 1984 – 2019. Santa Fe, NM: Santa Fe Institute Press, 2019. The SFI evolutionary biologist and current president gathers 35 years of contributions from events, seminars, projects, talks, and more which can well track the revolutionary discovery of a natural anatomy, physiology, cerebral, and cultural essence. A 1984 - 1999 section notes Mavericks such as John Holland, Murray Gell-Mann, and Simon Levin. 2000 - 2014 turns to Unifers like Harold Morowitz, Jessica Flack and Brian Arthur. 2015 and Beyond then completes 37 chapters with entries by Luis Bettencourt, Geoffrey West, Mirta Galesic, Simon DeDeo, Samuel Bowles, and Jennifer Dunne.

The book opens with a yearly topical list from initial glimpses of a nonlinear physics across astral and material systems all the way to active societies and economies. 2019 titles are Humans in Ecological Networks and Eco-Evolutionary Synthesis. A prime SFI founder George Cowan saw the promise of an iconic, common motif which similarly recurred everywhere. Three and a half decades later, as we try to document, a self-organizing complex adaptive network system of node element and link relation within a whole, viable entity seems to well fulfill this goal. I visited SFI in 1987 to hear a talk by Morowitz, when one sensed that a new animate frontier was opening. We cite a prescient 1992 affirmation by Murray Gell-Mann, another founder, along with a 2015 verification by David Krakauer.

Ultimately, we can argue that it is the self-similarity of the structure of fundamental physical law that dictates the continuing usefulness of mathematics. At the modest level of earlier science, this sort of self-similarity is strikingly apparent. Electricity, gravitation, and magnetism all have the same force, and Newton suggested that there might be some short-range force. Now that scientists are paying attention to scaling phenomena, we see in the study of complex systems astonishing power laws extending over many orders of magnitude. The renormalization group turns out to apply not only to condensed matter but to numerous other subjects. The biological and social sciences are just as much involved in these discoveries of scaling behavior as the physical sciences. We are always dealing with nature consonant and conformable to herself. So the approximate self-similarity of the laws of nature runs the gamut from underlying laws of physics to the phenomenological laws of the most complex realms. (Murray Gell-Mann, 1992, 38-39)

For the last few decades we have been steadily surveying the landscape of complex phenomena, and it is gratify that along the way we find that complex systems nominally unrelated bear strong family resemblances. These similarities include how the structure of evolutionary adaption looks a lot like the mathematics of learning, that the distribution of energy within a body made of tissues and fluids follows rules similar to those governing the flow of energy in a society, that networks within cells adhere to the geometric principles we find on the internet, and that the rise and fall of ancient civilizations follow a sequence similar to the present growth of urban centers. (David Krakauer, 2015, 230)

Krishnagopal, Sanjukta, et al. Synchronization Patterns: From Network Motifs to Hierarchical Networks. arXiv:1607.08798. In this prepost of a paper to appear in Philosophical Transactions A, Technical University of Berlin physicists including Eckehard Scholl try to define these common characteristics of a universally nonlinear nature. Of special note is a choice of brain neural networks as a prime exemplar, as if a cerebral microcosm for all complex, self-organizing systems. In regard, as their presence becomes evident from quantum to cultural realms, an analogous macrocosm may once again well accord with human qualities

We investigate complex synchronization patterns such as cluster synchronization and partial amplitude death in networks of coupled Stuart-Landau oscillators with fractal connectivities. The study of fractal or self-similar topology is motivated by the network of neurons in the brain. This fractal property is well represented in hierarchical networks, for which we present three different models. In addition, we introduce an analytical eigensolution method and provide a comprehensive picture of the interplay of network topology and the corresponding network dynamics, thus allowing us to predict the dynamics of arbitrarily large hierarchical networks simply by analyzing small network motifs. We also show that oscillation death can be induced in these networks, even if the coupling is symmetric, contrary to previous understanding of oscillation death. Our results show that there is a direct correlation between topology and dynamics: Hierarchical networks exhibit the corresponding hierarchical dynamics. This helps bridging the gap between mesoscale motifs and macroscopic networks. (Abstract)

The work presented here is of particular interest for neuroscience where recently a lot of emphasis has been put on the relation between structural connectivity and functional connectivity in the brain. Evidence from empirical studies suggests that the presence of a direct anatomical connection between two brain areas is associated with stronger functional interactions between these two areas. Our results support these empirical results through theoretical investigation. In addition, they can give valuable insight because they provide a completely analytical framework while employing a complex hierarchical structure that mimics the hierarchical nature of neurons in the brain. The fractal or self-similar hierarchical organization of neural networks is studied in [83–86]. The advantage of this theoretical study is that it allows for investigating the interplay of dynamics and topology on every scale, from the smallest to the largest structural level as well as the investigation of dynamics of each individual node. (16)

Kulkarni, Suman, et al. Information Content of Note Transitions in the Music of J. S. Bach.. arXiv:2301.00783. University of Pennsylvania and CCNY interdisciplinary theorists including Danielle Bassett open with an appreciation of our human social love of tuneful melodic compositions, as they now become amenable to 21st mathematical sciences of network forms, linguistics, and so on. It is noted that these findings hold to the same scale and metre as everywhere else in nature. See also Fractal Patterns in Music by John McDonough and Andrzej Herczyhski at arXiv:2221.12497, and The Song of the Cell by Siddhartha Mukherjee (Scribner, 2022).

Music has a complex structure that expresses emotion and conveys information, which people process through an imperfect cognitive gestalt version of reality. To address and analyze this wide issue, we study J. S. Bach's music by way of network science and information theory. Bach's work is highly structured over wide range of fugues and choral pieces that we view as a network of note transitions to quantify the information in each piece and how they can be grouped together. Our findings shed new light network properties of Bach's music and gain insight into features that make networks of information effective for communication. (Excerpt)

Lee, Deokjae, et al. Universal Mechanism for Hybrid Percolation Transitions. Nature Scientific Reports. 7/5723, 2017. A Korean - Hungarian collaboration of Seoul National University and Central European University systems physicists cites another example whence physical materiality can be seen to innately possess generic, commonly repetitive, formative features.

Hybrid percolation transitions (HPTs) induced by cascading processes have been observed in diverse complex systems such as k-core percolation, breakdown on interdependent networks and cooperative epidemic spreading models. Here we present the microscopic universal mechanism underlying those HPTs. We show that the discontinuity in the order parameter results from two steps: a durable critical branching (CB) and an explosive, supercritical (SC) process, the latter resulting from large loops inevitably present in finite size samples. This crossover mechanism and scaling behavior are universal for different HPT systems. Our result implies that the crossover time O(N1/3) is a golden time, during which one needs to take actions to control and prevent the formation of a macroscopic cascade, e.g., a pandemic outbreak. (Abstract)

Percolation is a prototypical model of disorder, which is often used to illustrate the emergence and the resilience of a giant cluster as links between individuals are added and deleted one by one, respectively. A giant cluster at a transition point in the mean field limit is to good approximation a critical branching (CB) tree with unit mean number of offspring. The giant cluster of recovered nodes at a transition point of a simple epidemiological model, the so-called susceptible/infective/removed (SIR) model, is one of such percolating clusters grown in the CB processes. Percolation transition is known as a robust continuous transition. (1)

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