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

1. Network Physics: A Vital Interlinked Anatomy and Physiology

Kostic, Daniel, et al. Unifying the Essential Concepts of Biological Networks. Philosophical Transactions of the Royal Society B. February, 2020. DR, University of Bordeaux, Claus Hilgetaf, University Medical Center Hamburg, and Marc Tittgemeyer, MPI Metabolism Research introduce a special issue with this integrative title. Its content is composed of both life science and philosophical considerations since both views need join together. For example, see General Theory of Topological Explanations and Explanatory Asymmetry by D. Kostic, Hierarchy and Levels by William Bechtel, Exploring Modularity by Maria Serban, and Network Architectures Supporting Learnability by Perry Zurn and Danielle Bassett, From Inert Matter to Global Society by David Chavalarias and Evolving Complexity by Richard Sole and Sergi Valverde (search for these last three).

Over the last decades, network-based approaches have become highly popular in diverse fields of biology, including neuroscience, ecology, molecular biology and genetics. While these approaches continue to grow very rapidly, some of their conceptual and methodological aspects still require a programmatic foundation. This challenge particularly concerns the question of whether a generalized account of explanatory, organizational and descriptive levels of networks can be applied universally across biological sciences. To this end, this highly interdisciplinary theme issue focuses on the definition, motivation and application of key concepts in biological network science, such as explanatory power of distinctively network explanations, network levels and network hierarchies. (Abstract)

Our organism constantly integrates information about the internal state with external environmental cues to adapt behavioural and autonomic responses to ensure physiological homeostasis. The Translational Neurocircuitry Group investigates how the human brain represents, integrates and prioritizes these internal and external signals to initiate adequate behavioural and physiological responses with a special focus on circuit-level models, metabolic mechanisms and human cognition. (Marc Tittgemeyer)

Kovacs, Istvan, et al. Community Landscapes: An Integrative Approach to Determine Overlapping Network Module Hierarchy, Identify Key Nodes and Predict Network Dynamics. PLoS One. 5/9, 2010. Cited more in Common Code, in this 100 page entry with bioinformatic programs and references, Semmelweis University, Budapest, living system scientists, including Peter Csermely, parse modular networks to uncover a ubiquitous topological feature. Indeed, nature seems intent on forming communal groupings of an appropriate size and populace at each and every strata and instance. Might one even broach an “ubuntu Universe.”

Krioukov, Dmitri, et al. Network Cosmology. Nature Scientific Reports. 2/793, 2012. . On occasion, a paper comes along of such unique, meritous content that it bodes for a significant breakthrough and synthesis. A team of five University of California, San Diego, systems scientists with Marian Boguna, a University of Barcelona physicist, proceed via sophisticated quantifications to discern the same nonlinear dynamics that infuse from proteins to cities within celestial topological networks. Its technical acumen and depth requires several excerpts. For example, Figure 2, “Mapping between the de Sitter universe and complex networks” illustrates many isomorphic affinities. As per Figure 4, “Degree distribution and clustering in complex networks and space time,” Internet, social network, brain anatomy, and hyperbolic spatial lineaments all graph on the same line, indicating common node and link geometries. As the quotes allude, a grand unification of universe, life, cognition, and humankind could be in the offing, a nascent witness of a biological genesis uniVerse.

Kumpula, Jussi, et al. Emergence of Communities in Weighted Networks. Physics Review Letters. 99/228701, 2007. As scale-free networks grow in intricacy, they reveal an inherent propensity to form modular and communal topologies. This “quite general paradigm” is then evident across a nested nature from metabolic to neural to societal systems, each amenable to this common physical explanation. And one might add, what is implied by such findings is an organic developing cosmos.

Network theory has undergone a remarkable development over the last decade and has contributed significantly to our understanding of complex systems, ranging from genetic transcriptions to the Internet and human societies. (228701-1) Understanding how the microscopic mechanisms translate into mesoscopic communities and macroscopic social systems is a key problem in its own right and one that is accessible within the scope of statistical physics. (228701-1)

Lalli, Margherita and Diego Gariaschelli. Geometry-free renormalization of directed networks: scale-invariance and reciprocity. arXiv:2403.00235. IMT School for Advanced Studies, Lucca, Italy physicists are able to demonstrate an effective integrity of this physical attribute with multiplex phenomena across diverse, practical instances. See also Renormalization of Complex Networks with Partition Functions by Jung, Sungwon, et al at arXiv:2403.07402

Recent research has tried to extend the concept of renormalization to more general networks with arbitrary topology. Here we show that the Scale-Invariant Model can be extended to directed networks without an embedding geometry or Laplacian structure. Moreover, it can account for the tendency of links to occur in mutual pairs more or less often than predicted by chance. By way of renormalization rules, we propose a multiscale international trade network with nontrivial reciprocity and an annealed model where positive reciprocity emerges spontaneously. (Excerpt)

Landry, Nicholas, et al. The simpliciality of higher-order networks. arXiv:2308.13918. University of Vermont and Grinnell College system theorists heighten our understandings as nature's vital connectivities ever expand and deepen. See also Topology and dynamics of higher-order multiplex networks by Sanjukta Krishnagopal and Ginestra Bianconi at arXiv:2308.14189.
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Higher-order networks are widely used to describe complex systems in which interactions can involve more than two entities at once. In this paper, we focus on inclusion within higher-order networks, referring to situations where specific entities participate in an interaction, and subsets of those entities also interact with each other. Traditional modeling approaches to higher-order networks tend to either not consider inclusion at all (e.g., hypergraph models) or explicitly assume perfect and complete inclusion (e.g., simplicial complex models). To allow for a more nuanced assessment of inclusion in higher-order networks, we introduce the concept of "simpliciality" and several corresponding measures. Contrary to current modeling practice, we show that empirically observed systems rarely lie at either end of the simpliciality spectrum. (Abstract)

A wide range of complex systems are shaped by interactions involving several entities at once: social networks are driven by group behavior [1], emails often have multiple recipients [2–4], molecular pathways in cells involve multi-protein interactions [5], and scientific articles in-
volve groups of co-authors [6]. Higher-order networks are a natural extension to networks explicitly designed to model such multiway relationships [7]

Laurent, Hebert-Dufresne, et al. Complex Networks as an Emerging Property of Hierarchical Preferential Attachment. Physical Review E. 92/6, 2015. Cited also in Universality Affirmations, University of Laval, Quebec and University of Barcelona physicists open this survey on the state of complexity science by tracing its advent to a 1962 paper The Architecture of Complexity by the pioneer theorist Herbert Simon in the Proceedings of the American Philosophical Society (106/467). Some half century later, as this 2015 section documents, the Grail goal of one, same, infinitely iterated, self-organizing system has been proven from quantum to human to cosmic realms, so as to imply a common, independent, universally manifest, source.

Laurienti, Paul, et al. Universal Fractal Scaling of Self-Organized Networks. Physica A. 390/20, 2011. Cited more in Common Code, after some two decades of complex systems studies from every angle, in disparate fields and terms, on every continent, a maturity is lately being reached so it is possible, for example, for this team of Wake Forest University biomedical researchers to propose a natural “universality” of “node and interaction” dynamic network phenomena. To wit, the same fractal pattern and process faithfully recurs across broad Biological, Information, Social, and Technological domains. These extended quotes might portend, circa 2011, a new animate nature suffused with intrinsic creativities that repeat and reiterate across every regnant realm. At what point, and by what insight, might this realization become a revolution, and its spontaneity be appreciated as genetic in kind?

Lee, Kyu-Min, et al. Towards Real-World Complexity: An Introduction to Multiplex Networks. European Physical Journal B. 88/2, 2015. In this edition for Condensed Matter and Complex Systems, Korea University physicists offer a succinct tutorial for these novel findings of a lively nature from cosmos to cerebral to culture as graced by nested networks in iterative hierarchies. With statistical and nonlinear physics as Keywords, the paper joins a mid 2010s revolution from mechanical particles only to pervasive animate, neural interconnections, whose latest epitome of human persons and societies is able to achieve its own vital self-realization.

Many real-world complex systems are best modeled by multiplex networks of interacting network layers. The multiplex network study is one of the newest and hottest themes in the statistical physics of complex networks. Pioneering studies have proven that the multiplexity has broad impact on the system’s structure and function. In this Colloquium paper, we present an organized review of the growing body of current literature on multiplex networks by categorizing existing studies broadly according to the type of layer coupling in the problem. Major recent advances in the field are surveyed and some outstanding open challenges and future perspectives will be proposed. (Abstract)

Lee, Sang Hoon. Network Nested as Generalized Core-Periphery Structures. arXiv:1602.00093. We cite this entry by a Korea Institute for Advanced Study physicist as an example of how such a generic recurrent scale, which seeks and reaches complementary fast dense and slower expanse phases, are gaining notice as natural archetypes from universe to human. See also later entries on this eprint site by the author and colleagues for practical applications such as 3D chromosome and power-grid geometries.

The concept of nestedness, in particular for ecological and economical networks, has been introduced as a structural characteristic of real interacting systems. We suggest that the nestedness is in fact another way to express a mesoscale network property called the core-periphery structure. With real ecological mutualistic networks and synthetic model networks, we define the network-level measures for nestedness and core-periphery-ness in the case of weighted and bipartite networks. Therefore, there must exist structurally interwoven properties in more fundamental levels of network formation, behind this seemingly obvious relation between nestedness and core-periphery structures. (Abstract)

Lee, UnCheol and George Mashour. Role of Network Science in the Study of Anesthetic State Transitions. Anesthesiology. 129/1029, 2018. University of Michigan Medical School neuroscientists, who are involved with consciousness studies at UMMS (search each author), illustrate how the common multiplex networks found everywhere also provide functional structures as brains pass into and out of relatively unconscious states. It is then affirmed that as these conditions exhibit a self-organized criticality with scale-free power laws, this phenomena appears to manifestly arise from universal, lawful principles. Within this approach, the array of nodes, links, hubs, and dynamic topologies are cited as a major determinant of global information processing.

University of Michigan Medical School neuroscientists, who are involved with consciousness studies at UMMS (search each author), illustrate how the common multiplex networks found everywhere also provide functional structures as brains pass into and out of relatively unconscious states. It is then affirmed that as these conditions exhibit a self-organized criticality with scale-free power laws, this phenomena appears to manifestly arise from universal, lawful principles. Within this approach, the array of nodes, links, hubs, and dynamic topologies are cited as a major determinant of global information processing.

Leli, Vito, et al. Deep Learning Super-Diffusion in Multiplex Networks. arXiv:1811.04104. As the Abstract details, VL, Saeed Osat and Timur Tlyachev, Skolkovo Institute of Science and Technology, Moscow and Jacob Biamonte, Deep Quantum AI, Moscow conceive a working method based on natural phenomena so to better analyze and design intricate nets of many kinds.

Complex network theory has shown success in understanding the emergent and collective behavior of complex systems. Many real-world complex systems were recently discovered to be more accurately modeled as multiplex networks in which each interaction type is mapped to its own network layer such as transportation networks, coupled social networks, metabolic and regulatory networks, etc. A salient physical phenomena emerging from multiplexity is super-diffusion via an accelerated diffusion by the multi-layer structure as compared to any single layer. Here we show that modern machine (deep) learning, such as fully connected and convolutional neural networks, can classify and predict the presence of super-diffusion in multiplex networks. (Abstract excerpts)

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