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

1. Network Physics: A Vital Interlinked Anatomy and Physiology

Artime, Oriol, et al. Multilayer Network Science: from Cells to Societies. arXiv:2401.04589. Ten physicists posted across Italy and Spain including Arsham Ghavasieh and Manlio De Domenico (search names) provide a latest theoretical review and preview as this 21st century, 2010s to date, revolution all about nature’s apparent anatomy and physiology becomes vividly evident across every animate phase from prokaryotes to peoples. See also Robustness and resilience of complex networks by this team in Nature Reviews Physics (January 2024).

Network structures are mathematical way to represent life’s complex systems from cells to societies. In the past decade, multilayer network science was found to be an effective analytical framework for a wide spectrum from biopolymer interactome and metabolomes to neuronal connectomes to urban and transportation regimes. Here we review salient theoretical aspects of functional dynamics and their applications to real-world interdependent phenomena. We discuss corresponding challenges in the field for the future. (Abstract)

Aste, Tomaso, et al. Complex, Inter-Networked Economic and Social Systems. European Physical Journal Special Topics. 225/10, 2016. n introduction to this subject issue as the ubiquitous presence of generic network phenomena becomes found in every cultural aspect. Papers vary from generic features in Discretized Kinetic Theory on Scale-Free Networks, and On the Convergence of the Fitness-Complexity Algorithm to practical examples in A Generation-Attraction Model for Renewable Energy Flows in Italy, and Interests Diffusion on a Semantic Multiplex.

Baccini, Frederica, et al.. Similarity Matrix Average for Aggregating Multiplex Networks. Journal of Physics: Complexity. 4/025017, 2023. University of Pisa, Siena and Torinl bioinformatic scientists conceive a tested approach to join and unify an array of social interactivities into a unified strata.

We introduce a novel method of average similarity matrices so as to integrate the layers of a multiplex network into a single monoplex form. Multiplex networks are used when relations of different nature (layers) arise between a set of elements from a given population (nodes). A way to analyze them is to aggregate the different layers in a single monoplex as a valid representation. Here we propose a theoretical approach and practical usage based on a similarity matrix average. This method is then applied to the Cambridge Journal of Economics contain co-citations, issue editors and article authors.

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)

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