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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

Pajevic, Sinisa and Dietmar Plenz. The Organization of Strong Links in Complex Networks. Nature Physics. Online March, 2012. As a good example of the nascent advance to detect such deep similarities, National Institute of Health systems theorists find the same dynamics and topologies to hold for genomic, neuronal, social webs, linguistic, vehicle transport, and scientific collaborations. In so doing, a notable common quality is suggested. The nodal components of each domain - neurons, truck drivers, word usage – engage in a “local learning” from which arises an “integrative weight organization.” Once again, this grand natural reciprocity of entity and whole, self and group, accrues everywhere, to the benefit of both phases.

Many complex systems reveal a small-world topology, which allows simultaneously local and global efficiency in the interaction between system constituents. Here, we report the results of a comprehensive study that investigates the relation between the clustering properties in such small-world systems and the strength of interactions between its constituents, quantified by the link weight. For brain, gene, social and language networks, we find a local integrative weight organization in which strong links preferentially occur between nodes with overlapping neighbourhoods.. Our findings identify a general organization for complex systems that strikes a balance between efficient local and global communication in their strong interactions, while allowing for robust, exploratory development of weak interactions. (Abstract, 429) The predominance of integrative weight organization in natural, complex networks seems to reflect a general local weighting principle that results in networks which maintain robust functionality and efficient communication while adapting their weights to changing environments. (435)

Papadopoulos, Lia, et al. Network Analysis of Particles and Grains. arXiv:1708.08080. We cite this entry as another example of nature’s innate propensity to form an anatomy and physiology of multi-connective webs everywhere. It is also notable because coauthors Karen Daniels, Mason Porter and Danielle Bassett achieve this through creative studies and applications of neural network architectures and performance.

The arrangements of particles and forces in granular materials and particulate matter have a complex organization on multiple spatial scales that range from local structures to mesoscale and system-wide ones. The theoretical study of particle-level, force-chain, domain, and bulk properties requires the development and application of appropriate mathematical, statistical, physical, and computational frameworks. Recently, tools from network science have emerged as powerful approaches for probing and characterizing heterogeneous architectures in complex systems, and a diverse set of methods have yielded fascinating insights into granular materials. In this paper, we review work on network-based approaches to studying granular materials and explore the potential of such frameworks to provide a useful description of these materials and to enhance understanding of the underlying physics. (Abstract)

Perc, Matjaz. Diffusion Dynamics and Information Spreading in Multilayer Networks: An Overview. European Physical Journal Special Topics. 228/2351, 2019. The University of Maribor, Slovenia theorist (search) emphasizes how nature’s multiplex networks not only engender neural, physiological, and social structures but also, by their title features, serve life’s vital communicative conveyance. It is then said that a better working knowledge of network phenomena can help avoid problems with power grids, traffic flow, and so on.

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)

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