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

1. Network Physics: A Vital Interlinked Anatomy and Physiology

De Domenico, Malino, et al. Mathematical Formulation of Multilayer Networks. Physical Review X. 3/041022, 2013. An eight member team from Spain, Italy, and the UK, mostly the University of Zaragoza and Oxford University, advise that a shift of focus from single networks to the many layered scales they nest in can serve to reveal the presence of common, ubiquitous patterns. As a result, generic topologies can be identified, which will then be found in similar repetition everywhere. The journal considered this insightful work to merit home page praise, as in this note next.

Popular Summary: Describing a social network based on a particular type of human social interaction, say, Facebook, is conceptually simple: a set of nodes representing the people involved in such a network, linked by their Facebook connections. But, what kind of network structure would one have if all modes of social interactions between the same people are taken into account and if one mode of interaction can influence another? Here, the notion of a “multiplex” network becomes necessary. Indeed, the scientific interest in multiplex networks has recently seen a surge. However, a fundamental scientific language that can be used consistently and broadly across the many disciplines that are involved in complex systems research was still missing. This absence is a major obstacle to further progress in this topical area of current interest. In this paper, we develop such a language, employing the concept of tensors that is widely used to describe a multitude of degrees of freedom associated with a single entity.

Our tensorial formalism provides a unified framework that makes it possible to describe both traditional “monoplex” (i.e., single-type links) and multiplex networks. Each type of interaction between the nodes is described by a single-layer network. The different modes of interaction are then described by different layers of networks. But, a node from one layer can be linked to another node in any other layer, leading to “cross talks” between the layers. High-dimensional tensors naturally capture such multidimensional patterns of connectivity. Having first developed a rigorous tensorial definition of such multilayer structures, we have also used it to generalize the many important diagnostic concepts previously known only to traditional monoplex networks, including degree centrality, clustering coefficients, and modularity. We think that the conceptual simplicity and the fundamental rigor of our formalism will power the further development of our understanding of multiplex networks. (Editor)

De Domenico, Manlio and Jacob Biamonte. Spectral Entropies as Information-Theoretic Tools for Complex Network Comparison. arXiv:1609.01214.. Universitat Rovira I Virgili, Spain, and University of Malta theorists allude to affinities between nature’s ubiquitous network physiological anatomy and quantum phenomena by way of statistical physics. Search Biamonte for prior contributions.

Any physical system can be viewed from the perspective that information is implicitly represented in its state. However, the quantification of this information when it comes to complex networks has remained largely elusive. In this work, we use techniques inspired by quantum statistical mechanics to define an entropy measure for complex networks and to develop a set of information-theoretic tools, based on network spectral properties, such as Renyi q-entropy, generalized Kullback-Leibler and Jensen-Shannon divergences. Our results imply that spectral based statistical inference in complex networks results in demonstrably superior performance as well as a conceptual backbone, filling a gap towards a network information theory. (Abstract excerpts)

DeDeo, Simon and David Krakauer. Dynamics and Processing in Finite Self-Similar Networks. Journal of the Royal Society Interface. September 7, 2012. Cited more in Common Code, as complex systems science reaches a robust maturity, Santa Fe Institute resident theorists verify its ubiquitous aspects of component identity, structural topology, signal communication, recursive loops, and their nested iteration across life, genomes, cognition, and societies. An extensive bibliography provides further support. Nodes and links, hubs and connections, weight, communicate, branch, ramify, develop, merge and evolve everywhere.

Demongeot, Jacques, et al. Biological Networks Entropies: Examples in Neural Memory Networks, Genetic Regulation Networks and Social Epidemic Networks. Entropy. 20/1, 2018. Six theorists from France, Chile, and Tunisia contend that although nature’s ubiquitous geometries may vary in kind across these disparate domains, at this later date in their extensive study, each instance seems to exemplify the same generic form and process. In their regard, this similarity may be expressed in some degree by relative entropic levels.

Networks used in biological applications at different scales (molecule, cell and population) are of different types: neuronal, genetic, and social, but they share the same dynamical concepts, in their continuous differential versions as well as in their discrete Boolean versions (e.g., non-linear Hopfield system). We will give some general results available for both continuous and discrete biological networks, and then study some specific applications of three new notions of entropy: (i) attractor entropy, (ii) isochronal entropy and (iii) entropy centrality; in three domains: a neural network involved in the memory evocation, a genetic network responsible of the iron control and a social network accounting for the obesity spread in high school environment. (Abstract edits)

Diego, Xavier, et al. Key Features of Turing Systems are Determined Purely by Network Topology. Physical Review X. 8/021071, 2018. Into the 21st century, systems scholars with postings in Barcelona and Tubingen including James Sharpe advise that Alan Turing’s 1930s and 1940s theories and writings on pattern and morphogenesis formations by way of a computational source can now be appreciated to involve this heretofore unrecognized feature of generative topological linkages.

Into the 21st century, systems scholars with postings in Barcelona and Tubingen including James Sharpe advise that Alan Turing’s 1930s and 1940s theories and writings on pattern and morphogenesis formations by way of a computational source can now be appreciated to involve this heretofore unrecognized feature of generative topological linkages.

Dong, Gaogao, et al. Resilience of Networks with Community Structure Behaves as if Under an External Field. Proceedings of the National Academy of Sciences. 115/6911, 2018. A team of nine Chinese, Israeli, and American complexity theorists including Shlomo Havlin and Eugene Stanley expand understandings of nature’s ubiquitous social physiology by adding deeper rootings in and affinities with condensed matter physical phenomena.

Much work has focused on phase transitions in complex networks in which the system transitions from a resilient to a failed state. Furthermore, many of these networks have a community structure, whose effects on resilience have not yet been fully understood. Here, we show that the community structure can significantly affect the resilience of the system in that it removes the phase transition present in a single module, and the network remains resilient at this transition. Our findings provide insight into the resilience of many modular complex systems and clarify the important effects that community structure has on network resilience. (Abstract)

Dorogovtsev, Sergey. Lectures on Complex Networks. Oxford: Oxford University Press, 2010. In an Oxford Master Series in Statistical, Computational, and Theoretical Physics, the University of Aveiro, Portugal, and Ioffe Institute, Russia, scientist, after a decade of research studies, publications (search), and classroom presentations, pens this overview tutorial. Its contents run from classical graphs and small worlds to nets everywhere from cells to the Internet. From many cases can accrue generic self-organization, cross correlations, weightings, motifs, communities, traffic, systemic interactions, and so on. All told another sign that this window upon a dynamic nature, just a decade on, is reaching a robust maturity. Compare with Jordan, Estrada, Li and Peng, Costa, and others herein as the waxing discovery of a creative organic cosmos.

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)

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