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

1. Network Physics: A Vital Interlinked Anatomy and Physiology

Harush, Uzi and Baruch Barzel. Dynamic Patterns of Information Flow in Complex Networks. Nature Communications. 8/2181, 2017. We cite this entry by Bar-Ilan University, Israel mathematicians because after some 20 years of node/link multiplex network studies, the detection of common recurrences everywhere must imply “universal laws” in effect. The paper was cited by Paul Davies in The Demon in the Machine as proof that the generative “informative patterns” he and colleagues propose are indeed “coherent things with an independent existence.” (101)

Although networks are extensively used to visualize information flow in biological, social and technological systems, translating topology into dynamic flow continues to challenge us, as similar networks exhibit different flow patterns, driven by other interaction mechanisms. To uncover a network’s actual flow patterns, we use a perturbative formalism, tracking the contribution of all nodes/paths to the flow of information, exposing the rules that link structure and dynamic flow for a broad range of nonlinear systems. We find that the diversity of patterns can be mapped into a single universal function, characterizing the interplay between the system’s topology and its dynamics. (Abstract excerpt)

Our results show that despite the diversity of potential interaction mechanisms, the patterns of information flow are governed by universal laws that can be directly linked to the system’s microscopic dynamics. (2) From neuronal signals to gene regulation, complex networks unction by enabling the flow of information between nodes. Understanding the rules that govern this flow is a crucial step toward establishing a theory of network dynamics. (10) In a broader perspective, our predicted universality indicates that the macroscopic flow patterns of complex systems are controlled by only a few relevant parameters of the system’s microscopic dynamics. (10)

Havlin, Shlomo, et al. Challenges in Network Science: Applications to Infrastructures, Climate, Social Systems and Economics. European Physical Journal Special Topics. 214/1, 2012. In this FuturICT issue, a dozen systems thinkers from Israel, Germany, Switzerland and Hungary, including Eshel Ben-Jacob and Jurgen Kurths, provide a tutorial about nature’s universally evident animate topologies and dynamical interactions and how they might be intentionally availed to better effect these vital areas.

Network theory has become one of the most visible theoretical frameworks that can be applied to the description, analysis, understanding, design and repair of multi-level complex systems. Complex networks occur everywhere, in man-made and human social systems, in organic and inorganic matter, from nano to macro scales, and in natural and anthropogenic structures. (Abstract)

Network theory has revolutionized our understanding of complex systems in diverse areas and offers a deeper understanding on how e.g., people, computers, or proteins are connected among their kind. Many systems can be efficiently modeled using a network structure where the system entities are the network nodes and the relations between the entities are the network links. The universal appeal of the field led researchers from different disciplines to embrace network theory as a common paradigm of true inter-discipliner nature. (276)

Holme, Petter. Modern Temporal Network Theory. European Physical Journal B. 88/9, 2016. An introduction to a special collection in this regard such as From Calls to Communities: A Model for Time-varying Social Networks, and Temporal Fidelity in Dynamic Social Networks. For a 5 year update see Networks of Climate Change by PH and Jaun Rocha (2105.12537)

The power of any kind of network approach lies in the ability to simplify a complex system so that one can better understand its function as a whole. Sometimes it is beneficial, however, to include more information than in a simple graph of only nodes and links. Adding information about times of interactions can make predictions and mechanistic understanding more accurate. The drawback, however, is that there are not so many methods available, partly because temporal networks is a relatively young field, partly because it is more difficult to develop such methods compared to for static networks. In this colloquium, we review the methods to analyze and model temporal networks and processes taking place on them, focusing mainly on the last three years. This includes the spreading of infectious disease, opinions, rumors, in social networks; information packets in computer networks; various types of signaling in biology, and more.

Hristova, Desislava, et al. A Multilayer Approach to Multiplexity and Link Prediction in Online Geo-Social Networks. EPJ Data Science. Online July, 2016. Since circa 2010 complexity theorists have increasingly realized that nature’s pervasive webworks are distinguished by many nested, scintillating iterative scales. This advanced extension of their study has been given a multiplexity moniker. Here Cambridge University computer scientists show how Twitter and Foursquare media exhibit these intricate, animate features.

Iniquez, Gerardo, et al. Universal Dynamics of Ranking. arXiv:2104.13439. GI, Central European University, Vienna, Carlos Pineda and Carlos Gershenson, National Autonomous University Mexico, and Albert-Laszlo Barabasi, Northeastern University theorists extend their complexity studies to discern how constant changes in subject rank listings, as an example of our penchant to arrange everything into a relative order, can exhibit common, temporal patterns and features. A universality is then depicted across many social instances. An allusion to statistical, many-body physical phenomena in effect could also be made.

Virtually anything can be and is ranked; people and animals, universities and countries, words and genes. Rankings reduce the components of highly complex systems into ordered lists, aiming to capture the fitness or ability of each element to perform relevant functions. Far less is known, however, about ranking dynamics, when the elements change their rank in time. Here we explore the dynamics of 30 ranking lists in natural, social, economic, and infrastructural systems, comprising millions of elements, whose temporal scales span from minutes to centuries. We find that the flux governing the arrival of new elements into a ranking list reveals systems with identifiable patterns of stability: in high-flux systems only the top of the list is stable, while in low-flux systems the top and bottom are equally stable.

Jalan, Sarika, et al. Unveiling the Multi-Fractal Structure of Complex Networks. arXiv:1610.06662. Indian Institute of Technology Indore, and CNR Institute of Complex Systems, Florence, Italy researchers including Stefano Boccaletti point out the invariant self-similar character of the universal connections that link all the discrete elements and entities. Into autumn 2016 this grand display of me and We reciprocal communities increasingly seems to imply a natural genetic code in infinite effect from uniVerse to us.

The fractal nature of graphs has traditionally been investigated by using the nodes of networks as the basic units. Here, instead, we propose to concentrate on the graph edges, and introduce a practical and computationally not demanding method for revealing changes in the fractal behavior of networks, and particularly for allowing distinction between mono-fractal, quasi mono-fractal, and multi-fractal structures. We show that degree homogeneity plays a crucial role in determining the fractal nature of the underlying network, and report on six different protein-protein interaction networks along with their corresponding random networks. Our analysis allows to identify varying levels of complexity in the species. (Abstract)

Kenett, Dror, et al. Networks of Networks. Chaos, Solitons, & Fractals. 80/1, 2015. With coauthors Matjaz Perc and Stefano Boccaletti, an introduction to an issue in preparation on this latest expansion of network science. As the second quotes notes, akin to other current work such as Scott Tremaine’s study of planetary systems, an endeavor is made to situate, and interpret such ubiquitous organic phenomena by way of statistical physics theory.

Recent research and reviews attest to the fact that networks of networks are the next frontier in network science. Not only are interactions limited and thus inadequately described by well-mixed models, it is also a fact that the networks that should be an integral part of such models are often interconnected, thus making the processes that are unfolding on them interdependent. From the World economy and transportation systems to social media, it is clear that processes taking place in one network might significantly affect what is happening in many other networks. Within an interdependent system, each type of interaction has a certain relevance and meaning, so that treating all the links identically inevitably leads to information loss. Networks of networks, interdependent networks, or multilayer networks are therefore a much better and realistic description of such systems, and this Special Issue is devoted to their structure, dynamics and evolution, as well as to the study of emergent properties in multi-layered systems in general. Topics of interest include but are not limited to the spread of epidemics and information, percolation, diffusion, synchronization, collective behavior, and evolutionary games on networks of networks. (Abstract)

Ever since the discovery of network reciprocity by Nowak and May (1992), who showed that in social dilemmas cooperators can survive by forming compact clusters in structured populations, the evolution of cooperation on lattice, networks and graphs has been a vibrant topic across social and natural sciences. The emergence of cooperation and the phase transitions leading to other favorable evolutionary outcomes depend sensitively on the structure of the interaction network and type of competing strategies. Studies making use of statistical physics and network science have led to significant advances in our understanding of the evolution of cooperation. (3-4)

Kepes, Francois, ed. Biological Networks. Singapore: World Scientific, 2008. Over the past decade within the field of complexity studies, the ubiquitous presence of scale-free, web-like, systems of weighted nodes and links has been well quantified and found across natural and societal kingdoms. This volume of international players such as Ricard Sole and Neo Martinez surveys their common, recurrent properties.

Khanra, P., et al. Endowing Networks with Desired Symmetries and Modular Behavior. arXiv:2302.10548. Ten system scientists in the USA, India, Spain, and Italy including Stefano Boccaletti post a latest example of on-going theoretical distillations of an actual independent, universal, genetic domain with these additional life-friendly, anatomy/physiological attributes.

Symmetries in a network regulate its organization into functional clustered states. Given a generic ensemble of nodes and a desirable cluster (or group of clusters), we exploit the direct connection between the elements of the eigenvector centrality and the graph symmetries to generate a network equipped with the desired cluster(s), with such a synthetical structure being furthermore perfectly reflected in the modular organization of the network's functioning. Our results solve a relevant problem of reverse engineering, and are of generic application in all cases where a desired parallel functioning needs to be blueprinted.

Synchronization of networked units is a behavior observed far and wide in natural and man made systems: from brain dynamics and neuronal firing, to epidemics, or power grids, or financial networks [1–10]. It may either correspond to the setting of a state in which all units follow the same trajectory [11–13], or to the emergence of structured states where the ensemble splits into different subsets each one evolving in unison. This latter case is known as cluster synchronization (CS) [14–30], and is the subject of many studies in both single-layer [20, 21] and multilayer networks [31, 32]. Swarms of animals, or synchrony (within sub units) in power grids, or brain dynamics are indeed relevant examples of CS (1)

Kitsak, Maksim. Latent Geometry for Complementary Driven Networks. arXiv:2003.06665. A Northeastern University, Network Science Institute physicist elucidates another innate proclivity that networlds everywhere commonly appear to possess. As the abstract notes, reciprocal forms and/or actions seem to be drawn together so as to conceive a beneficial, more effective whole.

Networks of interdisciplinary teams, biological interactions as well as food webs are examples of networks that are shaped by complementarity principles: connections in these networks are preferentially established between nodes with complementary properties. We propose a geometric framework for this property by first noting that traditional methods which embed networks into latent metric spaces are not applicable. We then consider a cross-geometric representation which (i) follows naturally from the complementarity rule, (ii) is consistent with the metric property of the latent space, (iii) reproduces structural properties of real complementarity-driven networks and (iv) allows for prediction of missing links with accuracy surpassing similarity-based methods. (Abstract excerpt)

Kivela, Mikko, et al. Multilayer Networks. Journal of Complex Networks. 2/3, 2014. In this new Oxford journal, systems mathematicians from the UK, Spain, France and Ireland, including Mason Porter, post a 59 page introductory survey with 376 references that has become, along with Stefano Boccaletti’s work (search), a prime document for this latest expansion of nature’s intrinsic vitalities.

In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications. Such systems include multiple subsystems and layers of connectivity, and it is important to take such "multilayer" features into account to try to improve our understanding of complex systems. The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science. In this paper, we discuss the history of multilayer networks (and related concepts) and review the exploding body of work on such networks. To unify the disparate terminology in the large body of recent work, we discuss a general framework for multilayer networks, construct a dictionary of terminology to relate the numerous existing concepts to each other, and provide a thorough discussion that compares, contrasts, and translates between related notions such as multilayer networks, multiplex networks, interdependent networks, networks of networks, and many others. (Abstract)

Kleineberg, Kij-Kolja, et al. Hidden Geometric Correlations in Real Multiplex Networks. Nature Physics. 12/11, 2016. University of Barcelona and Cyprus University of Technology researchers including Martin Boguna tease out nature’s intricate orderliness by way of deeply persistent topological interconnections. In this regard, such phenomena serves as an independent source which becomes exemplified in kind across every cosmos to creature scale and instance.

Real networks often form interacting parts of larger and more complex systems. Examples can be found in different domains, ranging from the Internet to structural and functional brain networks. Here, we show that these multiplex systems are not random combinations of single network layers. Instead, they are organized in specific ways dictated by hidden geometric correlations between the layers. We find that these correlations are significant in different real multiplexes, and form a key framework for answering many important questions. Specifically, we show that these geometric correlations facilitate the definition and detection of multidimensional communities, which are sets of nodes that are simultaneously similar in multiple layers. They also enable accurate trans-layer link prediction, meaning that connections in one layer can be predicted by observing the hidden geometric space of another layer. And they allow efficient targeted navigation in the multilayer system using only local knowledge, outperforming navigation in the single layers only if the geometric correlations are sufficiently strong. (Abstract)

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