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IV. Ecosmomics: Independent, UniVersal, Complex Network Systems and a Genetic Code-Script Source

1. Network Physics: A Vital Interlinked Anatomy and Physiology

Mariani, Manuel, et al. Nestedness in Complex Networks: Observation, Emergence, and Implications. Physics Reports. Volume 813, 2019. Ecological theorists based in China and Switzerland including Jordi Bascompte post a 140 page, 400 reference affirmation of nature’s evolutionary developmental genesis, as long sensed, by way of combining smaller entities (biomolecules, cells, species) within larger, reciprocally beneficial, whole systems. Akin to the major transitions scale and others, life’s long recurrent emergence from microbes to meerkats to a metropolis gains its 2020 sophisticated mathematical quantification.

The observed architecture of ecological and socio-economic networks differs significantly from that of random networks. From a network science standpoint, non-random structural patterns observed in real networks calls for an explanation of their emergence and systemic consequences. This article focuses on one of these patterns: nestedness. Given a network of interacting nodes, nestedness is a tendency for nodes to interact with subsets of the interaction partners of better-connected nodes. Nestedness has been found in diverse as ecological mutualistic organizations, world trade, inter-organizational relations, among many other areas. We survey results from variegated disciplines, including statistical physics, graph theory, ecology, and theoretical economics. (Abstract excerpt)

Perhaps one of the most intriguing features of real networks is the existence of common structural and dynamical patterns in a large number of systems from various domains of science, nature, and technology. The pervasiveness of structural patterns from various fields makes it possible to analyze them with a common set of tools. A popular example of such widespread patterns is the heavy-tailed degree distribution. Power-law degree distributions (often termed as ‘‘scale-free") have been reported in many different systems, ranging from social and information networks to protein–protein interaction networks. The ubiquity of heavy-tailed degree distributions has motivated studies aimed at unveiling plausible mechanisms that explain their emergence, understanding their implications for spreading, network robustness, synchronization phenomena, etc. (3)

Masucci, Adolfo, et al. Extracting Directed Information Flow Networks. Physical Review E. 83/026103, 2011. Researchers from Spain and Greece identify a universally applicable, seemingly independent, feature of complex systems in repetitive evidence across widely separate domains of genomic webs and the worldwide web. See also Masucci, et al “Wikipedia Information Flow Analysis Reveals the Scale-Free Architecture of the Semantic Space” in PLoS One (6/2, 2011).

We introduce a general method to infer the directional information flow between populations whose elements are described by n-dimensional vectors of symbolic attributes. The method is based on the Jensen-Shannon divergence and on the Shannon entropy and has a wide range of application. We show here the results of two applications: first we extract the network of genetic flow between meadows of the seagrass Poseidonia oceanica, where the meadow elements are specified by sets of microsatellite markers, and then we extract the semantic flow network from a set of Wikipedia pages, showing the semantic channels between different areas of knowledge. (026103)

Miranda, Manuel, et al. What Is in a Simplicial Complex? A Metaplex-Based Approach to Its Structure and Dynamics. Entropy. 25/12, 2023. As an example of how research studies continue to finesse their subject field, in a special Models, Topology and Inference of Multilayer and Higher-Order Networks issue edited by Ginestra Bianiconi, Institute of Cross-Disciplinary Physics and Complex Systems, IFISC (UIB- CSIC), Spain and Universitat Politècnica de Catalunya, Barcelona system theorists including Ernesto Estrada take these title features to a further insightful dynamic dimension. As these anatomy/physiology-like formations are increasingly found everywhere, they serve to add more evidence of a procreative organic genesis.

Geometric realization of simplicial complexes makes them a unique representation of complex systems. But local continuous spaces at the simplices level with global connectivity makes their analysis as dynamical systems on simplicial complexes a difficult.. Here, we generalize the concept of metaplexes to embrace that of geometric simplicial complexes, which includes the dynamical systems. A metaplex is formed by a continuous space interconnected of sinks and sources controlled by discrete (graph) operators. We study their generalities and apply it to a real-world simplicial complex representing the visual cortex of a macaque. (Excerpt)

Mizutaka, Shogo. Simple Model of Fractal Networks formed by Self-Organized Critical Dynamics. arXiv:1806:05397. An Ibaraki University, Japan mathematician proposes an affinity of universal self-similarity with nature’s propensity to seek and favor this most effective viable poise. See also Fractality and Degree Correlations in Scale-Free Networks in the European Physical Journal B (90/Art. 126, 2017).

In this paper, a simple dynamical model in which fractal networks are formed by self-organized critical (SOC) dynamics is proposed; the proposed model consists of growth and collapse processes. It has been shown that SOC dynamics are realized by the combined processes in the model. Thus, the distributions of the cluster size and collapse size follow a power-law function in the stationary state. Moreover, through SOC dynamics, the networks become fractal in nature. The criticality of SOC dynamics is the same as the universality class of mean-field theory. The model explains the possibility that the fractal nature in complex networks emerges by SOC dynamics in a manner similar to the case with fractal objects embedded in a Euclidean space. (Abstract)

Mokhlissi, Raihana, et al. The Structural Properties and Spanning Trees Entropy of the Generalized Fractal Scale-Free Lattice. Journal of Complex Networks. Online August, 2019. RM, Dounia Lotfi, and Mohamed El Marraki, Mohammed V University, Rabat, Morocco and Joyati Debnath, Winona State University, USA mathematicians post a sophisticated description of nature’s innate geometries. While invisible, their linkages are truly present as they unite and vivify all the overt objects and entities.

Enumerating all the spanning trees of a complex network is theoretical defiance for mathematicians, electrical engineers and computer scientists. In this article, we propose a generalization of the Fractal Scale-Free Lattice and study its structural properties. As its degree distribution follows a power law, we prove that the proposed generalization does not affect the scale-free property. In addition, we use equivalent transformations to count the number of spanning trees in the generalized Fractal Scale-Free Lattice. Finally, in order to evaluate the robustness of the generalized lattice, we compute and compare its entropy with other complex networks. (Abstract)

Dr. Joyati Debnath is a Full Professor of Mathematics and Statistics at Winona State University. She received an M. S. in Pure Mathematics and Ph. D. in Applied Mathematics from Iowa State University. She received numerous Honors and Awards including the Best Teaching Award from Iowa State University, and the Outstanding Woman of Education Award. Dr. Debnath has research interest in the areas of Topological Graph Theory, Integral Transform Theory, Partial Differential Equations and Boundary Value Problem, Associations of Variables, Discrete Mathematics, and Software Engineering Metrics. (WSU page)

Molkenthin, Nora and Marc Timme. Scaling Laws in Spatial Network Formation. Physical Review Letters. 117/168301, 2016. While many papers nowadays report a specific instance of complex systems (galaxies, brains, language), herein MPI Network Dynamics and Self-Organization physicists distill an independent, universally recurrent constancy which can be seen to take on self-similar forms and flows everywhere.

Geometric constraints impact the formation of a broad range of spatial networks, from amino acid chains folding to proteins structures to rearranging particle aggregates. How the network of interactions dynamically self-organizes in such systems is far from fully understood. Here, we analyze a class of spatial network formation processes by introducing a mapping from geometric to graph-theoretic constraints. Combining stochastic and mean field analyses yields an algebraic scaling law for the extent (graph diameter) of the resulting networks with system size, in contrast to logarithmic scaling known for networks without constraints. (Abstract)

Taken together, we uncovered an algebraic scaling law for network formation processes under geometric constraints. We have analyzed a spatial network formation model by mapping geometric constraints in space to purely graph-theoretical constraints on the topological changes of a network. Direct numerical simulations as well as analytic mean field calculations strongly indicate a scaling law with the graph diameter growing algebraically with system size, representing spatially self-similar (`fractal') networks. This algebraic law scaling is largely independent of the details of the model setup and clearly induced by geometric constraints. More generally, our results may suggest that geometric constraints generically induce algebraic (rather than logarithmic) scaling laws of networks in space. (4-5)

Moreno, Yamir and Matjaz Perc, eds. Focus on Multileyer Networks. New Journal of Physics. Circa 2018,, 2019. University of Zaragoza, Spain and University of Maribor, Slovenia physicists open a special collection with this title, as the quote notes. We note, for example, Inter-Layer Competition in Adaptive Multiplex Network by Elena Pitsik (20/075004) and Communicability Geometry of Multiplexes by Ernesto Estrada (21/015004, 2019).

In the later past century and early 2000's, the availability of data about real-world systems made it possible to study the topology of large networks. This work has revealed the structure, dynamics and functions of complex networks, as well as new models for synthetic networks. During the last 5 years, also backed up by new results, scientists have realized that many systems and processes cannot be described with single-layer nets since they have a multilayer geometry made up of many layers. The study of these multiplex networks has pointed out that their structure, dynamics, and evolution exhibit non-trivial relationships and interdependencies that give rise to new phenomena. (Scope)

Motter, Adilson and Yang Yang. The Unfolding and Control Network Cascades. Physics Today. January, 2017. A Northwestern University astrophysicist and a biochemical engineer initially record how these active interconnective topologies have now been found to occur throughout nature and society. As a result, generic, universally applicable structures and dynamics, e.g. neural net behavior, can be distilled. Because they are so pervasive and important the paper proposes novel ways for their salutary management. See concurrently Understanding the Controllability of Complex networks from the Microcosmic to the Macrocosmic by Peng Sun and Xiaoke Ma in the New Journal of Physics (19/013022, 2017), and Networks in Motion by Motter and Reka Albert in Physics Today (April 2012).

A characteristic property of networks is their ability to propagate influences, such as infectious diseases, behavioral changes, and failures. An especially important class of such contagious dynamics is that of cascading processes. These processes include, for example, cascading failures in infrastructure systems, extinctions cascades in ecological networks, and information cascades in social systems. In this review, we discuss recent progress and challenges associated with the modeling, prediction, detection, and control of cascades in networks.

Mulder, Daan and Ginestra Bianconi. Network Geometry and Complexity. arXiv:1711.06290. Queen Mary University of London mathematicians continue their project (search GB) to express a common, independent network form and function in a way that can be given a nonlinear, nonequilibrium physical basis. See also Non-Euclidean Geometry in Nature by Sergei Nechaev at 1705.08013.

Recently higher order networks describing the interactions between two or more nodes are attracting large attention. Most notably higher order networks include simplicial complexes formed not only by nodes and links but also by triangles, tetrahedra, etc. glued along their faces. Simplicial complexes and in general higher order networks are able to characterize data as different as functional brain networks or collaboration networks beyond the framework of pairwise interactions. Interestingly higher order networks have a natural geometric interpretation and therefore constitute the natural way to explore the discrete network geometry of complex networks. Here we investigate the rich interplay between emergent network geometry of higher order networks and their complexity in the framework of a non-equilibrium model called Network Geometry with Flavor. (Abstract excerpt)

Munoz, Victor and Eduardo Flandez. Complex Network Study of Solar Magnetograms. Entropy. 24/6, 2022. We cite this work by University of Chile astrophysics as a new instance of how such generic multiplex theories can find good application even across these stellar realms. (We also note how the 400 category journal MDPI (search) open access site can serve as an open forum for quality work which might have difficulty with an older periodical.)

In this paper, we study solar magnetic activity by means of a complex network approach based on the space and time evolution of sunspots. Their image recognition is provided by algorithmic studies during the complete 23rd solar cycle. Both directed and undirected networks were built, with degree distributions, clustering coefficient, average shortest path, centrality measures. Thus, we show that complex network analysis can yield useful information on temporal solar activities and universal features at any solar cycle stage. (Excerpt)

Newman, Mark. Networks: An Introduction. New York: Oxford University Press, 2018. In this second edition, the University of Michigan systems theorist provides a further essential guide to nature’s ubiquitous propensity for relational nodes and links in dynamic communities from life’s origin, genomics and proteomics, to local and global environments.

The study of networks, including computer, social , and biological networks, has attracted enormous interest in the last few years. The study of networks is broadly interdisciplinary and central developments have occurred in many fields, including mathematics, physics, computer and information sciences, biology, and the social sciences. Topics covered include the measurement of networks; methods for analyzing network data, including methods developed in physics, statistics, and sociology; fundamentals of graph theory; computer algorithms; mathematical models of networks, including random graph models and generative models; and theories of dynamical processes taking place on networks.

Newman, Mark. The Physics of Networks. Physics Today. November, 2008. The Paul Dirac Collegiate Professor of Physics at the University of Michigan provides a tutorial on the ubiquitous mathematics of interconnected groups, characterized by arrays of nodes and edges or links. See also the extensive volume: The Structure and Dynamics of Networks edited by Newman, et al (Princeton UP, 2006).

The observation of a power-law distribution thus indicates that the placement of edges in the network is, in a sense, far from being random. (34)

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