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

1. Network Physics: A Vital Interlinked Anatomy and Physiology

Perotti, Juan, et al. Emergent Self-Organized Complex Network Topology out of Stability Constraints. Physics Review Letters. 103/108701, 2009. In an endeavor to understand the robust effectiveness of these ubiquitous webworks, scientists from Cordoba and Chicago, including Dante Chialvo, say they grow and flourish because new agents or nodes are admitted based on how they contribute to their overall viability. Which could be a good example of a natural principle of much advantage for social guidance. Rather than liberal or socialist vs. conservative libertarian, life’s vitality at every stage professes a mutual reciprocity of entity and group.

Although most networks in nature exhibit complex topologies, the origins of such complexity remain unclear. We propose a general evolutionary mechanism based on global stability. This mechanism is incorporated into a model of a growing network of interacting agents in which each new agent’s membership in the network is determined by the agent’s effect on the network’s global stability. It is shown that out of this stability constraint complex topological properties emerge in a self-organized manner, offering an explanation for their observed ubiquity in biological networks. (108701-1)

Complex networks of interacting agents are ubiquitous, in a wide range of scales, from the microscopic level of genetic, metabolic, and proteins networks to the macroscopic human level of the Internet. (108701-1)

Porter, Mason. Nonlinearity + Networks: A 2020 Vision. arXiv:1911.03805. The UCLA systems mathematician (search) broadly reviews and previews to date this expansive webwork field. Sections include Centrality, Clustering and Large-Scale Structures and Time-Dependence. And whenever might it dawn that all these lively phenomena and their studies are actually quantifying a natural anatomy and physiology?

I will briefly survey several fascinating topics, methods and ideas in networks and nonlinearity, which I anticipate to be important during the next several years. These include temporal networks (in which the entities and/or their interactions change in time), stochastic and deterministic dynamical processes on networks, adaptive networks (in which a dynamical process on a network is coupled to the network structure), and "higher-order" interactions (which involve three or more entities in a network). I draw examples from a variety of scenarios such as contagion dynamics, opinion models, waves, and coupled oscillators. (Abstract)

Porter, Mason, et al. Communities in Networks. Notices of the AMS. 56/9, 2009. In consideration, Oxford University mathematician Porter, along with Jukka-Pekka Onnela, a Helsinki University physicist lately at Harvard, and from the University of North Carolina, mathematician Peter Mucha, might themselves be imagined as agents interlinked in local and global neural-like webs that they study. By this view, Mindkind’s historic learning process may just be reaching critical robustness in such exemplary works, together with many other articles posted herewith (e.g., Barrat, et al above). As the quote cites, statistical physics and complex systems science are realizing they engage the same phenomena in different ways so a merger is underway, still largely unbeknownst. But viola, a revolutionary new kind of materiality is being revealed. Both an independent, implicate network geometry and dynamics that involves such node/link, modular, weighted clusters becomes evident, which then explicates into universally repetitive, nested occurrence from biosphere to blogosphere, from protein webs to international scientific collaborations. In a natural genesis, such a vista could appear as a parent to child genetic code.

Graphs can represent either man-made or natural constructs, such as the World Wide Web or neuronal synaptic networks in the brain. Agents in such networked systems are like particles in traditional statistical mechanics that we all know and (presumably) love, and the structure of interactions between agents reflects the microscopic rules that govern their behavior. (1082)

Radicchi, Filippo, et al. Classical Information Theory of Networks. arXiv:1908.03811. FR, Indiana University, with Dmitri Krioukov and Harrison Hartle, Northeastern University, and Ginestra Bianconi, Queen Mary University of London finesse a better synthesis of implicit network communicative content with nature’s ubiquitous multiplex geometries. The broad motive is a better way to recognize evident commonalities as they vitalize and inform both genomic and neuromic phases.

Heterogeneity is an important feature which characterizes real-world networks. The diverse concept provides a convenient way to analyze and enhance systemic features such as robustness, synchronization and navigability. However, a unifying information theory to explain the natural emergence of heterogeneity in complex networks does not yet exist. Here, we develop a theoretical framework by showing that among degree distributions that can generate random networks, the one emerging from the principle of maximum entropy exhibits a power law. The pertinent features of real-world air transportation networks are well described by the proposed framework. (Abstract excerpt)

The principle of maximum entropy states that the unique probability distribution, encoding all the information available about a system but not any other information, is the one with largest information entropy. Available information about the system corresponds to constraints under which entropy is maximized. The principle of maximum entropy has found applications in many different disciplines, including physics, computer science, geography, finance, molecular biology, neuroscience, learning, deep learning, etc. (1)

Rakshit, Sarbendu, et al. Transitions from Chimeras to Coherence: An Analytical Approach by Means of the Coherent Stability Function. arXiv:1908.01063. Indian Statistical Institute, Kolkata, Amirkabir University of Technology, Tehran and University of Maribor, Slovenia (Matjaz Perc) further quantify the dynamic cerebral presence of such dual, simultaneous, more or less orderly phases. Circa 2019, the paper is a good instance of the global collaborative breadth and depth of scientific endeavors.

The study of transitions from chimeras to coherent states remains a challenge. Here we derive the necessary conditions for this shift by a coherent stability function approach. In chimera states, there is typically at least one group of oscillators that evolves in a drifting, random manner, while other groups of oscillators follow a smoother, more coherent profile. We use leech neurons, which exhibit a coexistence of chaotic and periodic tonic spiking depending on initial conditions, coupled via non-local electrical synapses, to demonstrate our approach. We explore various dynamical states with the focus on the transitions between chimeras and coherence, fully confirming the validity of the coherent stability function. (Abstract)

Reggiani, Aura, et al, eds. Handbook on Entropy, Complexity and Spatial Dynamics. Northampton, MA: Edward Elgar, 2021. University of Bologna editors George Mason University, Washington have arranged four major Entropy, Space and Complexity, Complexity of Urban Evolution, Complexity and Resilence of Economic systems and Spatial Dynamics of Complex interactions sections chapters by Barkley Rosser, Michael Batty, Denise Pumain, Alan Wilson, Olivier Borin and many others. We especially note Ginestra Bianconi’s chapter Information Theory of Spatial Network Ensembles (arXiv:2206.05614).

This ground-breaking Handbook presents a state-of-the-art exploration of entropy, complexity and spatial dynamics from fundamental theoretical, empirical and methodological perspectives. It considers how foundational theories can contribute to new advances, including novel modeling and empirical insights at different sectoral, spatial and temporal scales. (E. Elgar)

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)

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