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

1. Network Physics: A Vital Interlinked Anatomy and Physiology

Barthelemy, Marc. Spatial Networks. Physics Reports. 499/1, 2011. An 86 page review by an Institut de Physique Théorique, Paris, physicist which serves to articulate this representative characteristic of a natural genesis. It is fully accessible at arXiv.1010.0302.

Complex systems are very often organized under the form of networks where nodes and edges are embedded in space. Transportation and mobility networks, Internet, mobile phone networks, power grids, social and contact networks, and neural networks, are all examples where space is relevant and where topology alone does not contain all the information. Characterizing and understanding the structure and the evolution of spatial networks is thus crucial for many different fields, ranging from urbanism to epidemiology. An important consequence of space on networks is that there is a cost associated with the length of edges which in turn has dramatic effects on the topological structure of these networks. We will thoroughly explain the current state of our understanding of how the spatial constraints affect the structure and properties of these networks. We will review the most recent empirical observations and the most important models of spatial networks. We will also discuss various processes which take place on these spatial networks, such as phase transitions, random walks, synchronization, navigation, resilience, and disease spread. (Abstract, 1)

Battiston, Federico, et al. Network beyond Pairwise Interactions: Structure and Dynamics. Physics Reports. June, 2020. As network science enters the 2020s, an eight person team from across Europe and the USA including Vito Latora and Alice Patania posts a 109 page, 734 reference tutorial on the “higher-order representation of networks.” These further insights and appreciations involve features such as simplical homology, complexes, motifs, spreading dynamics, evolutionary games and more. With this expansive theory in place, an array of social, biologic, neural and ecological applications are reviewed. See also Growing Scale-Free Simplexes by K. Kovalinko, et al at arXiv:2006.12899. In regard, we record still another 21st century revolutionary discovery of a genesis nature as it reaches mature verification. See also a Nature Physics summary paper The Physics of Higher-Order Interactions in Complex Systems in Nature Physics (October 2021) and a response Disentangling High-order Mechanisms and Behaviors in Complex Systems by F. Rosas, et al (May 2022).

The complexity of many biological, social and technological systems stems from the richness of the interactions among their units. Over the past decades, complex systems have been described as networks whose interacting pairs of nodes are connected by links. Yet, in human communication, chemical reactions and ecological systems, interactions can occur in groups of three or more nodes. Here, we present an overview of the emerging field of networks beyond pairwise interactions. We discuss the methods to represent higher-order interactions and present different frameworks used to describe them. We review ways to characterize the structure of these systems such as random and growing simplicial complexes, bipartite graphs and hypergraphs. We conclude with a summary of empirical applications, providing an outlook on current modeling and conceptual frontiers. (Abstract excerpt)

Battiston, Federico, et al. The New Challenges of Multiplex Networks. arXiv:1606.09221. As “complex relational systems” become realized everywhere, Queen Mary University of London mathematicians consider better treatments of their actual nested, intertwined character.

What do societies, the Internet, and the human brain have in common? They are all examples of complex relational systems, whose emerging behaviours are largely determined by the non-trivial networks of interactions among their constituents, namely individuals, computers, or neurons. Only recently we have realised that multiplexity, i.e. the coexistence of several types of interactions among the constituents of a complex system, is responsible for substantial qualitative and quantitative differences in the type and variety of behaviours that a complex system can exhibit. Here we provide an overview of some of the measures proposed so far to characterise the structure of multiplex networks, and a selection of models aiming at reproducing those structural properties and at quantifying their statistical significance. (Abstract excerpts)

Battiston, Frederic, et al. Determinants of Public Cooperation in Multiplex Networks. arXiv:1704.04542. As the short quote says, Battiston and Vito Latora, Queen Mary University of London, with Matjaz Perc, University of Marbor, Slovenia, broach a unified nature across widest domains of physical substrates, evolutionary dynamics, and onto human cooperative behaviors as they manifest nature’s network topologies. See also a later paper by this group and colleagues Multiplex Core-Periphery Organization of the Human Connectome at 1801.01913.

Synergies between evolutionary game theory and statistical physics have significantly improved our understanding of public cooperation in structured populations. Multiplex networks, in particular, provide the theoretical framework within network science that allows us to mathematically describe the rich structure of interactions characterizing human societies. (Abstract)

Benson, Austin, et al. Higher-Order Organization of Complex Networks. Science. 353/163, 2016. Stanford and Purdue computer scientists contribute to this field of study as it reveals many natural, organic, cerebral, and societal dimensions. A commentary in the same issue, Network Analysis in the Age of Big Data, makes note of these advances. For an example of specific usage see Integrative Methods for Analyzing Big Date in Precision Medicine in Proteomics (16/741, 2016), and Topology-Function Conservation in Protein-Protein Interaction Networks in Bioinformatics (31/1632, 2015).

Networks are a fundamental tool for understanding and modeling complex systems in physics, biology, neuroscience, engineering, and social science. Many networks are known to exhibit rich, lower-order connectivity patterns that can be captured at the level of individual nodes and edges. However, higher-order organization of complex networks—at the level of small network subgraphs—remains largely unknown. Here, we develop a generalized framework for clustering networks on the basis of higher-order connectivity patterns. This framework provides mathematical guarantees on the optimality of obtained clusters and scales to networks with billions of edges. The framework reveals higher-order organization in a number of networks, including information propagation units in neuronal networks and hub structure in transportation networks. Results show that networks exhibit rich higher-order organizational structures that are exposed by clustering based on higher-order connectivity patterns.

Bergermann, Kai and Francesco Tudisco. Core-periphery detection in multilayer networks.. arXiv:2412.04179. Technische University of Chemnitz, Germany and University of Edinburgh mathematicians illuminate this formidable frame of net topologies and then add a finesse which improve their acuity.

Multilayer networks provide a way to model complex systems with various interactions between entities across multiple layers. Core-periphery detection involves partitioning a network into core nodes which are highly connected and peripheral nodes, which are connected to the core but sparsely among themselves. In this paper, we propose a new view of core-periphery relations that spans the core and periphery structures of both nodes and layers in weighted and directed multilayer networks. Our version gains novel insights in three empirical multilayer networks: the citation network of complexity scientists, the European airlines network, and the world trade network.

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, Stefam, et al. The Structure and Dynamics of Networks with Higher Order Interactions. Physics Reports. Vol. 1018, 2023. Seven senior European complexity researchers take their studies of nature’s pervasive organic anatomies to a further integrative level. Thus a multiplex multiversality of discrete nodal entities and communicative associations is coming to vivify and distinguish a true ecosmic procreation.

All beauty, richness and harmony in the emergent dynamics of a complex system depends much on the certain way its nodal components interact. The last twenty-five years have seen the advent and advance of Network Science, wherein an array of distributed systems in physics, biology, social sciences and engineering are found to be distinguished by this relative anatomy and physiology. But many networks involve pairwise behaviors, whereas real-world functions have multiplex actions as groups of nodes. In this report, we review the extensive literature on the structure and dynamics of hypergraphs and simplicial complexes as they gain relevance via better data sets and analysis techniques. (Excerpt)

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