IV. Ecosmomics: An Independent, UniVersal, Source Code-Script of Generative Complex Network Systems

1. Network Physics: A Vital Interlinked Anatomy and Physiology

Berner, Rico, et al. Adaptive Dynamical Networks. arXiv:2304.05652. This April entry by Humboldt University and University of Munich theorists including Thilo Gross and Jurgen Kurths can serve to gather and note current contributions which altogether presage for a robust 2023 synthesis of nature’s anatomical vitality. In the same while, see also On the Transient and Equilibrium Features of Growing Fractal Complex Networks by Alexandre Benatti and Luciano da Costa at arXiv:2034.12780, Dense Network Motifs Enhance Dynamical Stability by Bnaya Gross, et al (2304.12044) and Emergent Stability in Complex Network Dynamics by Chandrakala Meena, et al in Nature Physics (April 2023) among a growing number.

Adaptive dynamical networks (ADNs) represent a broad class of systems that can change their connectivity over time depending on a dynamical state. Here we provide a detailed description of ADNs, note applications in research fields, highlight their arising dynamical phenomena, and give an overview of workable mathematical methods. (Excerpt)

Biamonte, Jacob, et al. Complex Networks: From Classical to Quantum. arXiv:1702.08459. Biamonte, University of Malta, Mauro Faccin, Catholic University of Louvain, and Manlio De Domenico, Universitat Rovirai Virgili, Spain (search each) post a working “unified analysis” of nonlinear dynamic theories. As an integral result, a further confluence with “quantum Information science” is scoped out, which leads to a natural cross-convergence of these disparate fields.

Recent progress in applying complex network theory to problems faced in quantum information and computation has resulted in a beneficial crossover between two fields. Complex network methods have successfully been used to characterize quantum walk and transport models, entangled communication networks, graph theoretic models of emergent space-time and in detecting community structure in quantum systems. Information physics is setting the stage for a theory of complex and networked systems with quantum information-inspired methods appearing in complex network science, including information-theoretic distance and correlation measures for network characterization. (Abstract excerpt)

Two types of quantum networks have been of primary focus in the series of pioneering results we review. The first consists of quantum systems whose connections are represented by entangled states. These quantum networks are used in secure quantum communication systems. The second area of focus consists of networks of quantum systems, such as atoms or superconducting quantum electronics, whose connections are physical. Such systems are used to develop quantum-enhanced algorithms or quantum information transport systems. (1)

Bianconi, Ginestra. Interdisciplinary and Physics Challenges of Network Theory. arXiv:1509.00345. As a grand synthesis across nature and nurture proceeds apace, a Queen Mary University of London mathematical physicist sketches out how a newly found “universally of complex networks” can be extended even to quantum domains. Such a perception then reveals their generic, scale-free presence from every cosmic to cerebral realm. See also her paper Network Geometry from Complexity to Quantum Geometry (1511.04539), Complex Quantum Network Manifolds in Dimension d > 2 are Scale-Free with Christoph Rahmede (search, 1506.02648).and Emergent Complex Network Geometry (1412.3405).

Bianconi, Ginestra. Multilayer Networks: Structure and Function. Oxford: Oxford University Press, 2018. A Queen Mary University of London mathematician provides a comprehensive tutorial on these novel insights into how ubiquitous and deep nature’s organic and cerebral connectivities actually are. After a technical survey, it covers Communities, Centrality Measures, Interdependence, Epidemic Diffusion, and much more. See also Multiplex Networks: Basic Formalism and Structural Properties by Cozzo, Emanuele, et al (SpringerBriefs, 2018).

Multilayer networks is a rising topic in Network Science which characterizes the structure and the function of complex systems formed by several interacting networks. Multilayer networks research has been propelled forward by the wide realm of applications in social, biological and infrastructure networks and the large availability of network data, as well as by the significance of recent results, which have produced important advances. This book presents a comprehensive account of this emerging field by way of a theoretical and practical introduction to multilayer network science.

Ginestra Bianconi is Reader (Associate Professor) in Applied Mathematics and Director of the MSc in Network Science at the School of Mathematical Sciences, Queen Mary University of London. A physicist by training, since 2001 she has made network theory and its applications her central subject of investigation publishing more than one hundred papers. Currently her research focuses on multilayer networks, network geometry and percolation theory.

Bianconi, Ginestra. Welcome to JPhys Complexity. Journal of Physics: Complexity. 1/010201, 2020. The Queen Mary University of London systems mathematician and author (search) introduces this inaugural Institute of Physics IOP journal. Actually its occasion is a bit overdue within the 21st century shift in physical studies from inorganic parts and energies to nature’s constant, intricate topologies and lively dynamics as they rise from statistical phenomena to genomic, physiology, neural and national phases. As the quote cites, once again this advance is about moving from separate pieces to their equally real inter-linkages in a genesis uniVerse.

Typical papers in the first two issues are Simplicial Complexes, Road Network Development, Classical Information Theory of Networks and Observables in Complex Quantum Networks. In addition, Guido Caldarelli offers A Perspective on Complexity and Networks Science, with an emphasis on financial phases.

Complex systems are ubiquitous in both natural and man-made contexts; with examples including the brain, the climate, the economy, and society. All of these systems are formed by many elements, and their complex interactions can give rise to unexpected emergent properties. Borrowing the famous title of PW Anderson’s 1972 paper we can say that for complex systems ‘more is different’ because they display collective phenomena that cannot be understood by studying their constituents in isolation. For instance, brain function cannot be understood by studying a single neuron in isolation and human culture cannot be explained if interactions and influences between individuals are not taken into account. (1)

Boccaletti, Stefano, et al. Complex Dynamics in Networks, Multilayered Structures and Systems. Chaos. 26/6, 2016. An introduction to a focus section about dynamic network topologies which are actually composed of nested multitudes, often in self-similar communities, modules, rich hubs, and so on across every cosmic, physiological, cerebral, social media and ecosystem realm. For a sample pithy see A Biplex Approach to PageRank Centrality by Francisco Pedroche, et al, Optimal Distributions for Multiplex Logistic Networks by Luis Sola Conde, and Extracting Information from Multiplex Networks by Jacopo Iacovacci and Ginestra Bianconi.

In the last years, network scientists have directed their interest to the multi-layer character of real-world systems, and explicitly considered the structural and dynamical organization of graphs made of diverse layers between its constituents. Most complex systems include multiple subsystems and layers of connectivity and, in many cases, the interdependent components of systems interact through many different channels. Such a new perspective is indeed found to be the adequate representation for a wealth of features exhibited by networked systems in the real world. The contributions presented in this Focus Issue cover, from different points of view, the many achievements and still open questions in the field of multi-layer networks, such as: new frameworks and structures to represent and analyze heterogeneous complex systems, different aspects related to synchronization and centrality of complex networks, interplay between layers, and applications to logistic, biological, social, and technological fields. (Boccaletti Abstract)

Multilayer networks are formed by nodes connected by links describing interactions with different connotations. When the same set of nodes can be connected by different types of links, the resulting multilayer network is also called a multiplex network. Most social networks are multiplex, since the same set of people might be connected by different types of social ties or might communicate through different means of communication. As networks are ultimately a way to encode information about a complex set of interactions, one of the most pressing and challenging problems in network science is to extract relevant information from them. Here, we show evidence that the Multiplex PageRank algorithm and the recently introduced indicator function Θ˜S are able to extract from multiplex networks an information than cannot be inferred by analyzing the single layers taken in isolation or the aggregated network in which links of different type are not distinguished. (Iacovacci Abstract)

Boccaletti, Stefano, et al. The Structure and Dynamics of Multilayer Networks. Physics Reports. Online July, 2014. The 150 page paper is also at arXiv:1407.0742. A tutorial by researchers from Complex Systems Institutes in Italy, Israel, UK, Spain, China, Singapore, and Portugal for these latest theories and discoveries by a “Worldwide Knowledge Society” as they array across nonlinear nature. As now commonly possible, a first part elucidates independent, universal network topologies and processes such as ensembles, resilience, percolation, synchronization, interactions, and so on. By this relational view extant living and social systems can be seen as pervaded with evolving neural network-like geometries and vital activities. Their evidence and effect is then noted for social, technical, economic, biomedicine, climatic, and psychological realms. By these understandings, palliative social and environmental improvements can be informed and accomplished.

In the past years, network theory has successfully characterized the interaction among the constituents of a variety of complex systems, ranging from biological to technological, and social systems. However, up until recently, attention was almost exclusively given to networks in which all components were treated on equivalent footing, while neglecting all the extra information about the temporal- or context-related properties of the interactions under study. Only in the last years, taking advantage of the enhanced resolution in real data sets, network scientists have directed their interest to the multiplex character of real-world systems, and explicitly considered the time-varying and multilayer nature of networks. We offer here a comprehensive review on both structural and dynamical organization of graphs made of diverse relationships (layers) between its constituents, and cover several relevant issues, from a full redefinition of the basic structural measures, to understanding how the multilayer nature of the network affects processes and dynamic. (Abstract)

If we just turn our eyes to the immense majority of phenomena that occur around us, we realize immediately that they are nothing but the result of the emergent dynamical organization of systems that, on their turn, involve a multitude of basic constituents (or entities) interacting with each other via somehow complicated patterns. One of the major effort of modern physics is then providing proper and suitable representations of these systems, where constituents are considered as nodes (or units) of a network, and interactions are modeled by links of that same network. Indeed, having such a representation in one hand and the arsenal of mathematical tools for extracting information in the other (as inherited by several gifted centuries of thoughts, concepts and activities in applied mathematics and statistical mechanics) is the only suitable way through which we can even dare to understand the observed phenomena, identify the rules and mechanisms that are lying behind them, and possibly control and manipulate them conveniently. (4)

The last fifteen years have seen the birth of a movement in science, nowadays very well known under the name of complex networks theory. It involved the interdisciplinary effort of some of our best scientists in the aim of exploiting the current availability of big data in order to extract the ultimate and optimal representation of the underlying complex systems and mechanisms. The main goals were i) the extraction of unifying principles that could encompass and describe (under some generic and universal rules) the structural accommodation that is being detected ubiquitously, and ii) the modeling of the resulting emergent dynamics to explain what we actually see and experience from the observation of such systems. (4)

Complexity science is the study of systems with many interdependent components, which, in turn, may interact through many different channels. Such systems – and the self-organization and emergent phenomena they manifest – lie at the heart of many challenges of global importance for the future of the Worldwide Knowledge Society. The development of this science is providing radical new ways of understanding many different mechanisms and processes from physical, social, engineering, information and biological sciences. (6-7)

Boguna, Marian, et al. Network Geometry. arXiv:2001.03241. Six senior complexity scientists including Dmitri Krioukov and Shlomo Havlin offer a January 2020 posting which couldl be a bidecadal capsule of how much studies of nature’s innate node/link multiplex anatomy and physiology has been found in vivifying evidence from physical depths and galactic clusters and to evolutionary bodies, brains, groupings and onto economies and cultures. This entry describes how “fractal self-similarities, diffusion dynamics, and functional modularity” have been found from a chemical-space renormalization to cellular communities across life’s biota, as shown in intricate displays. Into the 2010s, an increasing implication is the presence of an independent, mathematic source in exemplary manifestation at each and every scale and instance. See also Geometric Origins of Self-Similarity in the Evolution of Real Networks by this group at 1912.00704 and Scale-free Networks Revealed from Finite-size Scaling at 1805.09512.

Networks are natural geometric objects. Yet the discrete metric structure of shortest path lengths in a network is not the only reservoir of geometric distances. Other forms of network-related topologies are continuous latent spaces underlying many networks, and the effective geometry induced by dynamical processes. A growing amount of evidence shows that the three approaches are well related. Network geometry is thus quite efficient in discovering hidden symmetries, such as scale-invariance, and other fundamental physical and mathematical properties, along with a variety of applications from the understanding how the brain works to routings in the Internet. Here, we review theoretical and practical developments in network geometry in the last two decades, and offer perspectives on future research for this novel complexity frontier. (Abstract)

Buchanan, Mark and Guido Caldarelli. A Networked World. Physics World. February, 2010. A lead article for a special report on how some two decades of complexity science have lately achieved both a theoretical depth and a worldwide utility. From immune systems and nonlinear genomes to H1N1 flu epidemics and banknote transfers, the same, distinctive principles are found everywhere as interactive agents constantly communicate. Other articles are Dirk Brockmann’s “Following the Money,” “Simplicity and Complexity” by Jim Crutchfield and Karoline Wiesner, and “The Flu Fighters” by Vittoria Colizza and Alessandro Vespignani.

To reflect, in addition to all the parts and pieces of science’s reductive phase, such organizational dynamics ought to be seen as equally real, which can then distinguish and reveal a wholly new kind of nature. Two attributes are of especial note. From galaxies to Gaia, a grand nested repetition occurs as self-similar patterns and processes iterate over and over. And this epochal discovery, not possible much earlier, can imply that such universal phenomena springs from and exemplify original, independent physical and mathematical principles, as if a cosmic genetic code.

Caetano-Anolles, Gustavo, et al. Emergence of Hierarchical Modularity in Evolving Networks Uncovered by Phylogenomic Analysis. Evolutionary Bioinformatics. 15/1, 2019. University of Illinois, Heidelberg Institute for Theoretical Studies, Gebze Technical University, Turkey, Seoul National University, and European Molecular Biology Laboratory, Germany system biologists (search lead author) advance their phylogenomomic project by showing how this theoretical approach can provide novel explanations of life’s anatomic physiology.

Networks describe how parts associate with each other to form integrated systems which often have modular and hierarchical structure. In biology, network growth involves two processes, one that unifies and the other that diversifies. Here, we propose a biphasic (bow-tie) theory of module emergence. In the first phase, emerging, self-organized interactions join nodal parts into modular linkages. In the second phase, modular variants become components for a new generative cycle of higher level organization. Remarkably, phylogenomic analyses uncover this emergence in the rewiring of metabolomic and transcriptome-informed metabolic networks, the nanosecond dynamics of proteins, and evolving metabolism, elementary functionomes, and protein domain networks. (Abstract)

Caldarelli, Guido. Scale-Free Networks. Oxford: Oxford University Press, 2007. In some ten years since their discovery, this class of ‘real world,’ self-organized, interconnected systems distinguished by preferred nodes and links whose structure and dynamics repeat at any level have been studied both with regard to an independent universality, and to their manifest presence throughout in nature and society. As a result, a work such as this by the University of Rome complexity scientist can now describe their common properties, and as the quote notes, how an iterative invariance is evident from molecules to a metropolis.

The structure of this book…starts with some basic notions of graph theory. After that we spend some time in explaining (mainly by use of fractals) why scale-free behavior is so interesting. After the theory we present an overview of the application of the above concepts. The areas selected are those of natural sciences (protein interactions, metabolic and gene regulatory networks, food webs, taxonomies, and river networks), information technology (Inter and WWW), and socio-economic sciences (collaboration, cognitive networks, and financial systems). (4)

Caldarelli, Guido, et al. Progress in the Physics of Complex Networks. European Physical Journal Special Topics. 212/1, 2012. Italian and British scientists introduce a topical issue on this growing interdisciplinary synthesis of statistical physics and nonlinear systems. A typical technical paper is “Von Neumann’s Growth Model: Statistical Mechanics and Biological Applications” by Andrea De Martino, Enzo Marinari, and Andrea Romualdi. At what point, by what means, might it then dawn and be availed that beyond all the theories, a profoundly phenomenal genesis uniVerse is being discovered?

The presence of self-similar phenomena in Statistical Physics has a long tradition. From the classical studies of critical phenomena and renormalization group, we moved in the seventies and eighties of the last century to the analysis of scale-invariance in the geometrical features of self-similar phenomena. A further evolution of this approach resulted in the analysis of scale-invariance in the time dynamics of these systems with concepts such as Self-Organized Criticality and studies of the so-called “sandpile models”, an example of which is present in this issue. Most of the activity is now focussed on the search for scale-invariance in the topology, that is, in the way things are connected to each other. (1)

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