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IV. Ecosmomics: An Independent Source Script of Generative, Self-Similar, Complex Network Systems

1. Network Physics: A Vital Anatomy and Physiology

Bagrow, James and Dirk Brockmann. Natural Emergence of Clusters and Bursts in Network Evolution. Physical Review X. 3/021016, 2013. We cite this entry by Northwestern University mathematicians as a quantification of what seems to be a universal source of self-organizing, complex adaptive systems that exists on their independent own, as they manifest everywhere from cosmos to culture.

Barabasi, Albert-Laszlo. Linked: The New Science of Networks. Cambridge, MA: Perseus Books, 2002. In the past few years, sparked by this University of Notre Dame physicist and colleagues, a significant finding has been made that complex networks are not random geometries but exhibit a nested, scale-free topology of how their nodes (agents) and links (local relations) are interconnected and weighted. A well-written story of nested, dynamic natural networks of great consistency everywhere from genes to galaxies and especially the World Wide Web. (This review was written a decade ago. Since this early work by its main founder, as this section attests natural networks abound and connect everywhere in an intricate cosmos.)

A string of recent breathtaking discoveries has forced us to acknowledge that amazingly simple and far-reaching natural laws govern the structure and evolution of all the complex networks that surround us. (6) Taken together, the similar large-scale topology of the metabolic and the protein interaction networks indicate the existence of a high degree of harmony in the cell’s architecture: Whichever organizational level we examine, a scale-free topology greets us. (189)

Barabasi, Albert-Laszlo. Love is All You Need. https://www.barabasilab.com/post/love-is-all-you-need. The co-conceiver (search) of scale-free networks in the late 1990s and their prolific advocate and articulator as they were found everywhere in nature and society writes a rebuttal to a Scale Free Networks are Rare posting at arXiv:1801.03400. The six page statement is also a succinct survey of the revolutionary endeavor and how pervasive this universal mode of multiplex nodes and linkages actually has proven to be.

Barabasi, Albert-Laszlo. Network Science: From Structure to Control. www.physics.umass.edu/seminars. A departmental colloquium at the University of Massachusetts, Amherst on October 30, 2015 by the main founder of this scale-free natural topology from proteins to people. Presently at Northeastern University, he has several international postings and many collaborations. Google “Barabasi Lab” for activities, publications, and Nature Physics papers such as The Network Takeover (Jan. 2012) and Universality in Network Dynamics (Oct. 2013). A salutary discovery may lately be realized from these worldwide theoretical and practical studies over the past 15 years. A generic geometry and dynamics is established with archetypal node elements and link connections within a whole modular system, which is found to repeat in kind from cosmos to culture. As one views the now familiar images of complementary nodes and links, however could this 21st century paradigm revise national politics which are locked in a battle of node and link parties?

Systems as diverse as the world wide web, Internet or the cell are described by highly interconnected networks with amazingly complex topology. Recent studies indicate that these networks are the result of self-organizing processes governed by simple but generic laws, resulting in architectural features that makes them much more similar to each other than one would have expected by chance. I will discuss the order characterizing our interconnected world and its implications to network robustness, and control. Indeed, while control theory offers mathematical tools to steer engineered and natural systems towards a desired state, we lack a framework to control complex self-organized systems. I will discuss a recently developed analytical framework to study the controllability of an arbitrary complex directed network, identifying the set of driver nodes whose time-dependent control can guide the system’s dynamics. (Abstract)

Barabasi, Albert-Laszlo. The Network Takeover. Nature Physics. 8/1, 2012. In a special stock-taking Complexity section, the Northeastern University, Center for Complex Network Research, physicist and founder from the late 1990s, with many colleagues, of the theory of scale-free networks across nature and society advances this scenario as the true essence of nonlinear phenomena.

Born at the twilight of the twentieth century, network theory aims to understand the origins and characteristics of networks that hold together the components in various complex systems. By simultaneously looking at the World Wide Web and genetic networks, Internet and social systems, it led to the discovery that despite the many differences in the nature of the nodes and the interactions between them, the networks behind most complex systems are governed by a series of fundamental laws that determine and limit their behaviour. (15)

Reductionism deconstructed complex systems, bringing us a theory of individual nodes and links. Network theory is painstakingly reassembling them, helping us to see the whole again. One thing is increasingly clear: no theory of the cell, of social media or of the Internet can ignore the profound network effects that their interconnectedness cause. Therefore, if we are ever to have a theory of complexity, it will sit on the shoulders of network theory. (15)

Barrat, Alain, et al. Complex Networks: From Biology to Information Technology. Journal of Physics A: Mathematical and Theoretical. 41/22, 2008. An introduction to the proceedings of a July 2007 STATPHYS23 meeting on the subject which then divides into two main categories – their common Structure and Dynamics, and ubiquitous Biological, Social, and Technological applications. See Porter, et al below for more on this genesis nature.

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.

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)

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