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

1. Network Physics: A Vital Interlinked Anatomy and Physiology

Motter, Adilson and Yang Yang. The Unfolding and Control Network Cascades. Physics Today. January, 2017. A Northwestern University astrophysicist and a biochemical engineer initially record how these active interconnective topologies have now been found to occur throughout nature and society. As a result, generic, universally applicable structures and dynamics, e.g. neural net behavior, can be distilled. Because they are so pervasive and important the paper proposes novel ways for their salutary management. See concurrently Understanding the Controllability of Complex networks from the Microcosmic to the Macrocosmic by Peng Sun and Xiaoke Ma in the New Journal of Physics (19/013022, 2017), and Networks in Motion by Motter and Reka Albert in Physics Today (April 2012).

A characteristic property of networks is their ability to propagate influences, such as infectious diseases, behavioral changes, and failures. An especially important class of such contagious dynamics is that of cascading processes. These processes include, for example, cascading failures in infrastructure systems, extinctions cascades in ecological networks, and information cascades in social systems. In this review, we discuss recent progress and challenges associated with the modeling, prediction, detection, and control of cascades in networks.

Mulder, Daan and Ginestra Bianconi. Network Geometry and Complexity. arXiv:1711.06290. Queen Mary University of London mathematicians continue their project (search GB) to express a common, independent network form and function in a way that can be given a nonlinear, nonequilibrium physical basis. See also Non-Euclidean Geometry in Nature by Sergei Nechaev at 1705.08013.

Recently higher order networks describing the interactions between two or more nodes are attracting large attention. Most notably higher order networks include simplicial complexes formed not only by nodes and links but also by triangles, tetrahedra, etc. glued along their faces. Simplicial complexes and in general higher order networks are able to characterize data as different as functional brain networks or collaboration networks beyond the framework of pairwise interactions. Interestingly higher order networks have a natural geometric interpretation and therefore constitute the natural way to explore the discrete network geometry of complex networks. Here we investigate the rich interplay between emergent network geometry of higher order networks and their complexity in the framework of a non-equilibrium model called Network Geometry with Flavor. (Abstract excerpt)

Munoz, Victor and Eduardo Flandez. Complex Network Study of Solar Magnetograms. Entropy. 24/6, 2022. We cite this work by University of Chile astrophysics as a new instance of how such generic multiplex theories can find good application even across these stellar realms. (We also note how the 400 category journal MDPI (search) open access site can serve as an open forum for quality work which might have difficulty with an older periodical.)

In this paper, we study solar magnetic activity by means of a complex network approach based on the space and time evolution of sunspots. Their image recognition is provided by algorithmic studies during the complete 23rd solar cycle. Both directed and undirected networks were built, with degree distributions, clustering coefficient, average shortest path, centrality measures. Thus, we show that complex network analysis can yield useful information on temporal solar activities and universal features at any solar cycle stage. (Excerpt)

Newman, Mark. Networks: An Introduction. New York: Oxford University Press, 2018. In this second edition, the University of Michigan systems theorist provides a further essential guide to nature’s ubiquitous propensity for relational nodes and links in dynamic communities from life’s origin, genomics and proteomics, to local and global environments.

The study of networks, including computer, social , and biological networks, has attracted enormous interest in the last few years. The study of networks is broadly interdisciplinary and central developments have occurred in many fields, including mathematics, physics, computer and information sciences, biology, and the social sciences. Topics covered include the measurement of networks; methods for analyzing network data, including methods developed in physics, statistics, and sociology; fundamentals of graph theory; computer algorithms; mathematical models of networks, including random graph models and generative models; and theories of dynamical processes taking place on networks.

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)

Nokkala, Johannes, et al. Complex Quantum Networks: a Topical Review. arXiv:2311.16265. University of Turku, Finland and Queen Mary University of London mathematicians including Ginestra Bianconi provide a tutorial about this on-going, facile cross-integration between “classical” nonlinear sciences and this fundamental realm as nature at last becomes one unified whole (as David Bohm foresaw). See also Gravity from entropy by GB at arXiv:2408.14391 for another pyro-theoretic contribution.

Network science is proving to be an ideal mathematical and computational framework to capture the complexity of interacting systems. Here we review of the consequential field of complex quantum networks to provide design principles for quantum algorithms. This novel phase can reveal how quantum physics can predict novel properties for phase transitions and quantum communication networks. We then draw attention to how between these several research lines can lead to new opportunities and discoveries at the interface between quantum physics and network science. (Excerpt)

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)

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