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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

Dorogovtsev, Sergey and Jose Mendes. The Nature of Complex Networks. Oxford: Oxford University Press, 2022. University of Aveiro, Portugal systems physicists proceed with a thorough introduction to network phenomena by way of a novel synthesis with statistical mechanics. As a result these disparate fields are current seen to be lately finding similar themes and common ground.

Eom, Young-Ho, et al. Network-based Model of the Growth of Termite Nests. Physical Review E. 92/062810, 2015. Complexity theorists with postings in Italy, France, Finland, and the USA, including Santo Fortunato and Guy Theraulaz at once detail how network phenomena can help quantify how, for example, social insect build and maintain niche constructions. It is then recognized that this facility implies nature’s avail of a universally recurrent geometry everywhere.

We present a model for the growth of the transportation network inside nests of the social insect subfamily Termitinae (Isoptera, termitidae). The model based on the empirical analysis of the real nest networks combined with pruning and a memory effect successfully predicts emergent nest properties. Our results provide an example of how complex network organization and efficient network properties can be generated from simple building rules based on local interactions and contribute to our understanding of the mechanisms that come into play for the formation of termite networks and of biological transportation networks in general. (Abstract excerpts)

Faccin, Mauro, et al. Community Detection in Quantum Networks. arXiv:1310.6638. Theorists from Torino, Barcelona, and Oxford including Jacob Biamonte, continue the reinvention and integration of these depths by way of macro complex systems theories. From many aspects, over the past years, by picking up on information qualities, such subatomic activities are found to contain the same nonlinear forms and dynamics as everywhere else, the nested cosmos becomes one whole again. Mauro Faccin and others are planning a Quantum Frontiers in Network Science symposia at the large NetSci conference in June 2014 at UC Berkeley (Google). See also Degree Distribution in Quantum Walks on Complex Networks by Faccin, et al, at arXiv:1305.6078.

Fayez-Aziz, Muhammad, et al. The Early History and Emergence of Molecular Functions and Modular Scale-Free Network Behavior. Nature Scientific Reports. 6/25058, 2016. With coauthors Kelsey and Gustavo Caetano-Anolles, University of Illinois, Evolutionary Bioinformatics Laboratory researchers contend that these common interactive topologies are similarly in place for life’s original occasion. These propensities occur along with biochemical, nucleotide and protocell rudiments, which they proceed to organize and activate. And the authors see fit to introduce the article with Jorge Borges, as the second quote conveys.

The formation of protein structural domains requires that biochemical functions, defined by conserved amino acid sequence motifs, be embedded into a structural scaffold. Here we trace domain history onto a bipartite network of elementary functional loop sequences and domain structures defined at the fold superfamily level of SCOP classification. The resulting ‘elementary functionome’ network and its loop motif and structural domain graph projections create evolutionary ‘waterfalls’ describing the emergence of primordial functions. They also uncover a dynamics of modular motif embedding in domain structures that is ongoing, which transfers ‘preferential’ cooption properties of ancient loops to emerging domains. Remarkably, we find that the emergence of molecular functions induces hierarchical modularity and power law behavior in network evolution as the network of motifs and structures expand metabolic pathways and translation. (Abstract)

“… I saw the Aleph from every vantage point, I saw in the Aleph the earth and in the earth again the Aleph, I saw my face and viscera, I saw your face and in vertigo I wept, for my eyes had seen that secret and conjectural object whose name is usurped by men …”— Jorge Luis Borges, The Aleph and Other Stories.

Filan, Daniel, et al. Neural Networks are Surprisingly Modular. arXiv:2003.04881. UC Berkeley and Boston University computer engineers find a way to emphasize and increase the practical presence of these local, clustered concentrations of specific cognitive functions in net topologies, just as biological systems draw upon nested modularities for their development and sustenance. Once again, the tacit assumption is a ready transferability of this independent, iconic source as manifest in connectomic and genomic phenomena.

The learned weights of a neural network are often considered devoid of scrutable internal structure. In order to discern structure in these weights, we introduce a measurable notion of modularity for multi-layer perceptrons (MLPs), and investigate their modular structure as trained on datasets of small images. A "module" as we conceive, is a set of neurons with strong internal connectivity but weak external connectivity. We find that MLPs that undergo training and weight pruning are significantly more modular than random networks. (Abstract excerpt)

Fortunato, Santo and Darko Hric. Community Detection in Networks. Physics Reports. 659/1, 2016. This “user’s guide” tutorial by Indiana University, and Aalto University, Finland, systems theorists contributes to Albert Barabasi’s “network revolution” (2012). The effort resides in the genre of distilling independent, generic properties of their universally recurrent node and link dynamic topologies from cosmic to social media. A salient tendency is to form subscales of modular communities within newly perceived multiplexities. Whether body or brain, an organized viability is achieved by nested whole units due to a reciprocity of elemental dots and integral connections.

Fortunato, Santo and Mark Newman. 20 Years of Network Community Detection. arXiv:2208.0111. Senior University of Indiana and University of Michigan systems theorists (search each) provide insider insights to findings and clarifications on the way to appreciating how nature’s ubiquitous interconnectivity proceeds to join into dynamic communal units.

A fundamental technical challenge in the analysis of network data is the automated discovery of communities - groups of nodes that are strongly connected or that share similar features or roles. In this commentary we review progress in the field over the last 20 years.

Fronczak, Agata, et al.. Scaling Theory of Fractal Complex Networks: Bridging Local Self-Similarity and Global Scale-Invariance. arXiv:2306.13751. Warsaw University of Technology physicists advance a latest quantification of nature’s structural consistency as an infinite repetition in exemplary kind from universe to humanverse. See also Fractal Dimensions of Networks by Eric Rosenberg for another treatment. We then make note that by midyear this perennial above/below, macro/micro ecosmic has well gained a scientific veracity as a phenomenal revelation. See also A General Model of Hierarchical Fractal Scale-Free Networks y Kousuke Yakubo and Yuka Fujiki in PLoS One (March 21. 2022) for another record of nature's infinite regularity.

We show that fractality in complex networks arises from the geometric self-similarity of their built-in hierarchical community-like mathematical structure. This box-based approach drawn from both phase transition scales and renormalization group theory leads to fractal deep analogies. We successfully verify our findings in real networks situated in various fields (information - the World Wide Web, biological - the human brain, and social - scientific collaborations). (Excerpt)

Frottier, Theo, et al. Harmonic Structures of Beethoven Quarters: A Complex Network Approach. arXiv:2201.08796. Into these 2020s, system physicists TF and Bertrand Georgeot, University of Toulouse and Olivier Giraud, University of Paris provide novel insights into how even musical compositions are distinguished by a common interconnective topology. As we may perceive, a universal anatomy and physiology, a music of the universe and humanverse, is just now being revealed. See also How Network-based Approaches can Complement Studies in Dementia by Cemile Kocoglu, et al in Trends in Genetics. (38/9, 2022) for another example.

We propose a complex network approach to the harmonic structure which underlies western tonal music. From a database of Beethoven's string quartets, we construct a directed network whose nodes are musical chords and edges connect chords. We show that the network is scale-free and has specific properties when ranking algorithms are applied. We explore its community structure and musical interpretation, and propose statistical measures from network theory to distinguish stylistically between periods of composition. (Excerpt)

The present work shows that the complex network approach can be fruitfully applied to the harmonic structure of musical works. Based on the example of Beethoven string quartets, we specified the properties of this new type of networks, and in particular we discussed the relationship between the spectrum of the Google matrix, the community structures, and musical specificities of the scores. (6)

Garcia-Perez, Guillermo, et al. Multiscale Unfolding of Real Networks by Geometric Renormalization. Nature Physics. 14/6, 2018. University of Barcelona systems theorists Garcia-Perez, Marian Boguna, and Angeles Serrano find this physical and mathematical theory helps tease out inherent regularities across multiplex webworks. This deep conception, while naturally apt, does strain attempts to explain it. A Critical History of Renormalization by Kerson Huang at arXiv:1310.5533, written as a tribute to Nobel laureate Kenneth Wilson (1936-2013), is a good entry. See also Mutual Information, Neural Networks and the Renormalization Group by Koch-Janusz and Ringel (2018 search). We also quote from Wikipedia.

Symmetries in physical theories denote invariance under some transformation, such as self-similarity under a change of scale. The renormalization group provides a powerful framework to study these symmetries, leading to a better understanding of the universal properties of phase transitions. However, the small-world property of complex networks complicates application of the renormalization group. Here, we provide a framework for the investigation of complex networks at different resolutions. We find that real scale-free networks show geometric scaling under this renormalization group transformation. This in turn offers a basis for exploring critical phenomena and universality in complex networks. (Abstract)

In theoretical physics, the renormalization group refers to a mathematical apparatus that allows systematic investigation of the changes of a physical system as viewed at different scales. In particle physics, it reflects the changes in the underlying force laws (codified in a quantum field theory) as the energy scale at which physical processes occur varies, energy/momentum and resolution distance scales being effectively conjugate under the uncertainty principle. A change in scale is called a scale transformation. The renormalization group is intimately related to scale invariance and conformal invariance, symmetries in which a system appears the same at all scales (self-similarity). (Wikipedia)

Gershenson, Carlos and Mikhail Prokopenko. Complex Networks. Artificial Life. Online July, 2011. An Introduction for a forthcoming issue of eight articles on the title subject drawn from the 2010 ALife XI conference in Odense, Denmark. Click on Early Access at the journal’s MIT Press site to view abstracts. Indeed in the past decade a sudden, revolutionary realization has occurred that every physical, organismic, neural, ecological, linguistic and societal domain is distinguished by the same vital nested, invariant, systemic networks. In this regard, the authors cite number of recent books in further support of this natural propensity: Reuven Cohen and Shlomo Havlin Complex Networks: Structure, Robustness and Function (Cambridge, 2010); Mark Newman Networks: An Introduction (Oxford, 2011); one could add Mark Buchanan, et al, eds. Networks in Cell Biology (Cambridge, 2010).

Gosak, Marko, et al. Network Science of Biological Systems at Different Scales. Physics of Life Reviews. Online November, 2017. Akin to Khaluf 2017 who cite a common scale invariance, seven University of Maribor, Slovenia researchers from physics, mathematics, physiology and medical departments including Matjaz Perc report a similar maturation of network studies whence multiplex entity nodes and relational links are found across life’s bacterial, cellular and multicellular phases. Along with all the discrete components (mitochondria, eukaryotes, organisms), equally present interconnections serve an integral communicative physiologies. Once again, the same universal, independent geometries and dynamics animate everywhere.

Network science is today established as a backbone for description of structure and function of various physical, chemical, biological, technological, and social systems. Here we review recent advances in the study of complex biological systems that were inspired and enabled by methods of network science. First, we present research highlights ranging from determination of the molecular interaction network within a cell to studies of architectural and functional properties of brain networks and biological transportation networks. Second, we focus on synergies between network science and data analysis, which enable us to determine functional connectivity patterns in multicellular systems. Third, we concentrate on the emerging field of multilayer networks and review the first endeavors and novel perspectives offered by this framework in exploring biological complexity. (Abstract excerpts)

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