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

1. Network Physics: A Vital Interlinked Anatomy and Physiology

Rombach, M. Puck, et al. Core-Periphery Structure in Networks. arXiv:1202.2684. While this network feature has been noted in social groupings, here systems scientists Rombach, and Mason Porter, Oxford University, James Fowler, UC San Diego, and Peter Mucha, University of North Carolina, give it a deeply technical foundation, as the Abstract alludes. See a later finesse by this group Detection of Core-Periphery Structure in Networks using Spectral Methods and Geodesic Paths in European Journal of Applied Mathematics (27/846, 2016). Along with multiplex, community and modular features these complements are a major explanation of neural net brain anatomy and function. For much more, search Danielle Bassett in Systems Neuroscience.

Intermediate-scale (or `meso-scale') structures in networks have received considerable attention, as the algorithmic detection of such structures makes it possible to discover network features that are not apparent either at the local scale of nodes and edges or at the global scale of summary statistics. Numerous types of meso-scale structures can occur in networks, but investigations of such features have focused predominantly on the identification and study of community structure. In this paper, we develop a new method to investigate the meso-scale feature known as core-periphery structure, which entails identifying densely-connected core nodes and sparsely-connected periphery nodes. In contrast to communities, the nodes in a core are also reasonably well-connected to those in the periphery. Our new method of computing core-periphery structure can identify multiple cores in a network and takes different possible cores into account. We illustrate the differences between our method and several existing methods for identifying which nodes belong to a core, and we use our technique to examine core-periphery structure in examples of friendship, collaboration, transportation, and voting networks. (Abstract)

Rosenberg, Eric. Fractal Dimensions of Networks. International: Springer, 2021. A veteran theorist and practitioner (bio below) in both academe and industry writes a book length treatment of nature’s self-similar arrays from universe to humanverse. Chapters include Network Box Counting Heuristics, Correlation Dimension and Infinite Networks.

The goal of the book is to provide a unified treatment of fractal dimensions of sets and networks. The book achieves this goal by first presenting the theory and algorithms for sets, along with their application to networks. The major fractal correlation, information, Hausdorff, multifractal, and spectrum dimensions are studied.

Eric Rosenberg received a Ph.D. in Operations Research from Stanford University and has taught courses in modelling and optimization at Princeton University, New Jersey Institute of Technology, Rutgers University and AT&T Labs.

Rossetti, Giulio and Remy Cazabet. Community Discovery in Dynamics: A Survey. ACM Computing Surveys. 51/1, 2020. Italian National Research Council and French National Research Centre information scientists provide a broad tutorial to this persistent modular aspect of temporal network studies. See also Identifying Communities in Dynamic Networks Using Information Dynamics by Zejun Sun, et al in Entropy (22/4, 2020).

Complex networks modeling real-world phenomena are characterized by striking properties: (i) they are organized according to community structure, and (ii) their structure evolves with time. Many researchers have worked on methods that can efficiently unveil substructures in complex networks, giving birth to the field of community discovery. Dynamic networks can be used to model the evolution of a system: nodes and edges are mutable, and their presence, or absence, deeply impacts the community structure that composes them. As a “user manual,” this work organizes state-of-the-art methodologies based on their rationale, and their specific instantiation. (Abstract)

Rozum, Jordan, et al.. Boolean Networks as Predictive Models of Emergent Biological Behaviors. arXiv:2319.12901. We cite this entry by SUNY Binghamton, University of Mount Union, Ohio, Penn State University and Indiana University researchers to convey how these deep mathematical lineaments are now serving many phases of biological and medical stu. The team is indeed led Reka Albert, an original cofounder with Albert Barabasi of network science. Google terms for a description and applications, often posted in the the Computational and Structural Biotechnology journal.

Interacting biological systems at all organizational levels display emergent behavior. Modeling these systems is challenging by the number and variety of components and interactions such as molecules in gene regulatory networks to species in ecological networks. Boolean networks have emerged as a powerful tool in this regard. After an introduction, we describe the process of building, analyzing, and validating a Boolean model. We then make predictions about the system's response to perturbations and about how to influence its behavior. We emphasize the interplay between structural and dynamical properties of Boolean networks and illustrate them in three case studies from disparate levels of biological organization. (excerpt)

Samoylenko, Ivan, et al. Why are there Six Degrees of Separation in a Social Network?. arXiv:2211.09643.. For the first time, some 14 systems theorists with postings in Russia, Taiwan, Italy, Austria, Slovenia, the USA, Israel and India including Matjaz Perc and Stefano Boccaletti achieve an explanation as to why this popular degree of personal association is built into nature’s network topologies.

A wealth of evidence shows that real world networks are endowed with a small-world format whence the maximal distance between any two nodes scales logarithmically rather than linearly with their size. In addition, most social networks are organized so that no individual is more than six links apart from any other, an empirical feature known as six degrees of separation. Why social networks have this ultra-small world organization, whereby the graph's diameter is independent of the network size over several orders of magnitude, is still unknown. Here we show that this inherent property results from the equilibrium state of any network where individuals weigh between their aspiration to improve their centrality and the costs incurred in forming connections. Thus simple evolutionary rules associated with human cooperation and altruism can also account for a most intriguing attributes of social networks. (Abstract)

Samsel, Mateusz, et al. Towards fractal origins of the community structure in complex networks. arXiv:2309.11126.. In this year Warsaw University of Technology theorists advance further ways to perceive an inherent self-similarity across multiplex phenomena.

In this paper, we pose a hypothesis that the structure of communities in complex networks may result from their latent fractal properties. Quantitative arguments supporting this hypothesis are that many non-fractal real complex networks that have a well-defined community structure reveal fractal properties and the scale-free community size distributions observed in many real networks directly relates to scale-invariant box mass distributions. A fractal core can be identified as a macroscopic component when the edges between modules identified by the community detection algorithm. (Excerpt)

Serafino, Matteo, et al. Scale-Free Networks Revealed from Finite-Size Scaling. arXiv:1905.09512. Organic physicists based in Italy, the USA and UK including Amos Maritan and Guido Caldarelli describe a method to analyze common features of natural linkages such as protein interactions, technological computer hyperlinks, and informational citation and lexical networks. As a result, spontaneous self-organization to a critical-like state then becomes evident, which seems to hold across all manner of net topologies.

Siebert, Bram, et al. The Role of Modularity in Self-Organization Dynamics in Biological Networks. arXiv:2003.12311. University of Limerick and University of Bristol theorists including Malbor Asliani post another 2020 example of how much the presence of these complexity features are commonly accepted as a working explanation. But a contradiction remains between this self-assembling natural reality with universal node/link, modular, system viabilities at every and an older “Ptolemaic” paradigm (Brian Greene 2020) seems to be unaware of these revolutionary findings.

Interconnected ensembles of biological entities are some of the most complex systems that modern science has encountered so far. Many biological networks are now known to be constructed in a hierarchical way with two main properties: short average paths that join two distant nodes (neuronal, species, or protein patches) and a high proportion of nodes in modular aggregations. Here we show that network modularity is vital for the formation of self-organising patterns of functional activity. We show that spatial patterns at the modular scale can develop in this case, which may explain how spontaneous order in biological networks follows their modular structures. We test our results on real-world networks to confirm the important role of modularity for macro-scale patterns. (Abstract excerpt)

Siew, Cynthia, et al. Cognitive Network Science: A Review of Research on Cognition through the Lens of Network Representations, Processes, and Dynamics. Complexity. Art. 2108423, 2019. Within a special issue on this subject, University of Warwick. Basel, Wisconsin, and Pennsylvania including Nicole Beckage contribute to this 2010s revolution (see Barabasi 2012) by an observance of how a common, representative form and utility, as if a natural anatomy and physiology, is now well in place. By so doing (second quote) it can then join the prior pieces altogether. As a topical example, their occasion even in literary syntactic and informational content is confirmed. Again by turns, we note that an independent, universal network reality would be deeply textual in kind. See also From Topic Networks to Distributed Cognitive Maps by Akexander Mehler, et al in this issue.

Network science provides a set of quantitative methods to investigate complex systems, including human cognition. Although cognitive theories in different domains are strongly based on a network perspective, the application of network methodologies to quantitatively study cognition has so far been limited. This review shows how such approaches have been applied to the study of human cognition and can uniquely provide novel insight on important questions related to the complexity of cognitive systems. Drawing on the literature in cognitive network science, with a focus on semantic and lexical networks, we argue three points. (i) Network science provides aquantitative approach to represent cognitive systems. (ii) This method enables cognitive scientists to achieve a deeper understanding of how the neural network processes interact to produce behavioral phenomena. (iii) Network science provides a quantitative framework to model the dynamics of cognitive systems as structural changes on different timescales and resolutions. (Abstract)

Networks are composed of two elements: nodes that represent the conceptual entities of interest (e.g., persons, websites, or words) and edges that represent the relationships among those units (e.g., friendship, hyperlinks, or semantic similarity). While additional aspects can be considered as is done in bipartite and multiplex networks, identifying these two basic elements in the system of study is sufficient to formalize the system as a network and to employ the powerful tools provided by network science. Network science approaches often capitalize on the fact that relationships between nodes (i.e., edges) can be as important as the nodes themselves. A challenge in studying cognitive systems as networks is to represent these systems in a meaningful way in terms of nodes and edges. (2)

Song, Chaoming, et al. Self-Similarity of Complex Networks. Nature. 433/392, 2005. The power-law scaling which distinguishes small world networks is found to exhibit a self-repeating fractal geometry. This is achieved by a renormalization procedure that ‘coarse-grains’ the system into a nest of nodes and modules. This novel work is introduced by Steven Strogatz in the same issue (365) with the title Romanesque Networks since this property is ideally displayed by broccoli of this name.

Here we show that real complex networks, such as the world-wide web, social, protein-protein interaction networks and cellular networks are invariant or self-similar under a length-scale transformation. (392) These fundamental properties help to explain the scale-free nature of complex networks and suggest a common self-organization dynamics. (392)

Sorek, Matan, et al. Stochasticity, Bistability and the Wisdom of Crowds: A Model for Associative Learning in Genetic Regulatory Networks. PLoS Computational Biology. 9/8, 2013. With Nathalie Balaban and Yonatan Loewenstein, Hebrew University of Jerusalem neuroscientists identify deep similarities between a brain’s neural networks and genomic interactive systems. Once again nature uses the same universal and independent communicative dynamics in these separate realms. Might we imagine in turn that our thought processes are somehow “genetic” in kind?

It is generally believed that associative memory in the brain depends on multistable synaptic dynamics, which enable the synapses to maintain their value for extended periods of time. However, multistable dynamics are not restricted to synapses. In particular, the dynamics of some genetic regulatory networks are multistable, raising the possibility that even single cells, in the absence of a nervous system, are capable of learning associations. Here we study a standard genetic regulatory network model with bistable elements and stochastic dynamics. We demonstrate that such a genetic regulatory network model is capable of learning multiple, general, overlapping associations. The capacity of the network, defined as the number of associations that can be simultaneously stored and retrieved, is proportional to the square root of the number of bistable elements in the genetic regulatory network. Moreover, we compute the capacity of a clonal population of cells, such as in a colony of bacteria or a tissue, to store associations. We show that even if the cells do not interact, the capacity of the population to store associations substantially exceeds that of a single cell and is proportional to the number of bistable elements. Thus, we show that even single cells are endowed with the computational power to learn associations, a power that is substantially enhanced when these cells form a population. (Abstract)

Sporns, Olaf and Richard Betzel. Modular Brain Networks. Annual Review of Psychology. 67/613, 2016. Indiana University neuroscientists emphasize a propensity of generic network phenomena is to form modules, aka communities, as nature’s way of gaining and maintaining a robust performance.

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