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

1. Network Physics: A Vital Interlinked Anatomy and Physiology

Newman, Mark. The Physics of Networks. Physics Today. November, 2008. The Paul Dirac Collegiate Professor of Physics at the University of Michigan provides a tutorial on the ubiquitous mathematics of interconnected groups, characterized by arrays of nodes and edges or links. See also the extensive volume: The Structure and Dynamics of Networks edited by Newman, et al (Princeton UP, 2006).

The observation of a power-law distribution thus indicates that the placement of edges in the network is, in a sense, far from being random. (34)

Nicolaides, Christos, et al. Self-Organization of Network Dynamics into Local Quantized States. arXiv:1509.05243. We cite this posting by MIT and Technical University of Madrid scientists as a 2015 representation of a generic nonlinear complex system via a reciprocity of unitary agents and informed relations. As the paper alludes, its independent, universal presence can be identified across natural and social realms, which can then provide a guide for future designs.

Self-organization and pattern formation in network-organized systems emerges from the collective activation and interaction of many interconnected units. A striking feature of these non-equilibrium structures is that they are often localized and robust: only a small subset of the nodes, or cell assembly, is activated. Understanding the role of cell assemblies as basic functional units in neural networks and socio-technical systems emerges as a fundamental challenge in network theory. A key open question is how these elementary building blocks emerge, and how they operate, linking structure and function in complex networks. Here we show that a network analogue of the Swift-Hohenberg continuum model---a minimal-ingredients model of nodal activation and interaction within a complex network---is able to produce a complex suite of localized patterns. Hence, the spontaneous formation of robust operational cell assemblies in complex networks can be explained as the result of self-organization, even in the absence of synaptic reinforcements. Our results show that these self-organized, local structures can provide robust functional units to understand natural and socio-technical network-organized processes. (Abstract)

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)

Pal, Kumar Palash, et al. Pal, Kumar Palash, et al. Global synchronizatin in generalized multilayer higher-order networks. arXiv:2406.03771. Indian Statistical Institute, Kolkata and University of Maribor, Slovenia system physicists including Matjaz Perc and Dibakar Ghosh continue to trace multiplex features and benefits of nature’s essential organismic anatomy and physiology as it becomes evident and suffuses from physical to societal interactive vitalities.

Networks incorporating higher-order interactions introduce novel dynamics into various processes such as synchronization. Here, we investigate these coordinations in multilayer networks beyond pairwise connections, both within and across layers. We demonstrate the existence of a stable global synchronous state resembling a master stability function. Our findings are supported by simulations using Hindmarsh-Rose neuronal and Rössler oscillators which illustrate how synchronization is facilitated by multiplex forms, over scenarios involving interactions within single layers. (Excerpt)

The study of complex networks has emerged as a prominent area of research. This interest growing arises from their capacity to model interconnected dynamical systems across many fields, such as physics, biology, ecology, social sciences, and engineering [1–3]. These networks are comprised of nodes, representing entities or elements, and links, representing connections or pairwise interactions between them. Many real-world systems can be conceptualized as multilayer networks include transportation networks [6], neuronal networks in the brain [7, 8], and various types of social networks [9]. A multilayer network consists of individual networks, each with its set of nodes and links (referred to as intralayer links), interconnected through interlayer links. The representation of multilayer networks hinges on a fundamental assumption: the complex connections among individuals within and across layers are comprehensively elucidated through pairwise links.

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)

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