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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

Cinardi, Nicola, et al. Quantum Statistics in Network Geometry with Fractional Flavor. arXiv:1902.10035. Systems physicists NC and Andrea Rapisarda, University of Catania, and Ginestra Bianconi, Queen Mary University of London continue to finely season nature’s true anatomy and physiology as it ever arrays in similar kinds from quantum to neuronal realms.

Growing network models have been shown to display emergent quantum statistics when nodes are associated to a fitness value describing the intrinsic ability of a node to acquire new links. Recently it has been shown that quantum statistics emerge also in a growing simplicial complex model called Network Geometry with Flavor which allow for the description of many-body interaction between the nodes. In this case the faces of the simplicial complex are naturally described by the Bose-Einstein, Boltzmann and Fermi-Dirac distribution depending on their dimension. We show that in this case the statistical properties of the faces of the simplicial complex are described by the Bose-Einstein or the Fermi-Dirac distribution only. (Abstract flavor)

Cohen, Reuven and Shlomo Havlin. Complex Networks: Structure, Robustness and Function.. Cambridge: Cambridge University Press;, 2010. A Bar-Ilan University, Israel mathematician and a physicist provide a comprehensive survey of ever growing realizations of an innately interconnected nature, organisms, and societies.

Examining important results and analytical techniques, this graduate-level textbook is a step-by-step presentation of the structure and function of complex networks. Using a range of examples, from the stability of the internet to efficient methods of immunizing populations, and from epidemic spreading to how one might efficiently search for individuals, this textbook explains the theoretical methods that can be used, and the experimental and analytical results obtained in the study and research of complex networks. Giving detailed derivations of many results in complex networks theory, this is an ideal text to be used by graduate students entering the field.

Costa, Luciano da Fontoura, et al. Analyzing and Modeling Real-World Phenomena with Complex Networks. Advances in Physics. 60/3, 2011. Drawing upon a departmental focus on this field, eight University of Sao Paulo physicists provide a 108 page survey, with 565 references, of this real dynamic materiality across nature and society. After noting Basic Concepts, topical areas are Social, Communications, Economy, Finance, Computers, Internet, World Wide Web, Citations, Transportation Power Grids, Biomolecular, Medicine, Ecology, Neuroscience, Linguistics, Earthquakes, Physics, Chemistry, Mathematics, Climate, and Epidemics – that is everywhere. From these many exemplars can be distilled a common, independent, complex system topology. Circa 2012, how could it dawn upon international collaborative science that this ubiquitous discovery is actually revealing a procreative genesis universe? In such regard, other such citations lately weigh in, e.g., Li and Peng in Complex Human Societies, Dorogovtsev, the Nature Physics Insight review, all herein, boding a critical credence. We append extended quotes.

Drawing upon a departmental focus on this field, eight University of Sao Paulo physicists provide a 108 page survey, with 565 references, of this real dynamic materiality across nature and society. After noting Basic Concepts, topical areas are Social, Communications, Economy, Finance, Computers, Internet, World Wide Web, Citations, Transportation Power Grids, Biomolecular, Medicine, Ecology, Neuroscience, Linguistics, Earthquakes, Physics, Chemistry, Mathematics, Climate, and Epidemics – that is everywhere. From these many exemplars can be distilled a common, independent, complex system topology. Circa 2012, how could it dawn upon international collaborative science that this ubiquitous discovery is actually revealing a procreative genesis universe? In such regard, other such citations lately weigh in, e.g., Li and Peng in Complex Human Societies, Dorogovtsev, the Nature Physics Insight review, all herein, boding a critical credence. We append extended quotes.

Courtney, Owen and Ginestra Bianconi. Generalized Network Structures: The Configuration Model and the Canonical Ensemble of Simplicial Complexes. arXiv:1602.04110. Queen Mary University, London mathematicians employ this topological phrase for their perception of connective patterns commonly found across networks. After technicalities, generic, repetitive webs are defined which form and flow everywhere. See also such later postings as Centralities of Nodes and Influences of Layers in Large Multiplex Networks at 1703.05833, Weighted Growing Simplicial Complexes. 1703.01187, and Emergent Hyperbolic Network Geometry in Nature Scientific Reports (7/41974, 2017) which each have GB as a coauthor. Altogether these distinct, recurrent features would seem to imply and arise from a natural propensity.

Simplicial complexes are generalized network structures able to encode interactions occurring between more than two nodes. Simplicial complexes describe a large variety of complex interacting systems ranging from brain networks, to social and collaboration networks. Here we characterize the structure of simplicial complexes using their generalized degrees that capture fundamental properties of one, two, three or more linked nodes. We evaluate the entropy of these ensembles, finding the asymptotic expression for the number of simplicial complexes in the configuration model. We provide the algorithms for the construction of simplicial complexes belonging to the configuration model and the canonical ensemble of simplicial complexes. (Abstract)

A large variety of interacting complex systems are characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links, triangles, tetrahedra) that have a natural geometric interpretation. Here, by extending our knowledge of growing complex networks to growing simplicial complexes we investigate the nature of the emergent geometry of complex networks and explore whether this geometry is hyperbolic. Specifically we show that an hyperbolic network geometry emerges spontaneously from models of growing simplicial complexes that are purely combinatorial. The statistical and geometrical properties of the growing simplicial complexes strongly depend on their dimensionality and display the major universal properties of real complex networks (scale-free, small-world and communities) at the same time. (GB/Rahmede)

Csermely, Peter. Fast and Slow Thinking – of Networks. arXiv:1511.01238. As 2014 and 2015 additions to our Introduction convey, intensive research since the early 1990s to the mid 2010s has reached a phase of consolidation and universality. This posting by the Semmelweis University, Budapest, systems biochemist (search) is a synopsis of a book chapter Plasticity-Rigidity Cycles at arXiv:1511.01239, we both review together. In this contribution, the robust field of scale-free networks is shown to apply to these evolutionary and personal cognitive modes. The main reference is the popular 2011 book Thinking, Fast and Slow by Daniel Kahneman about the dual systems model, as reported in A Complementary Brain and Thought Process. A subtitle “The complementary ‘elite’ and ‘wisdom of crowds’ of amino acid, neuronal and social networks” cites a first rapid response core network that draws on past experiences. If inadequate for novel, unfamiliar inputs, a weakly linked cerebral periphery is activated, often with conflicting views.

The longer posting expands this model to “A general adaptation mechanism” applicable from protein folding and birdsong learning to financial markets and environments. As a result, a dynamic structural universality across natural and social realms can now be affirmed. And a further surmise presents itself. The first page of the summary depicts these archetypal complements as a yin-yang symbol. Yet while dual process attributes match left and right brain hemisphere qualities, this association is rarely made. If to think about it, what might be averred in late 2015 is the worldwide discovery, with similar bicameral modes, of an integral, iterative natural genome code.

Complex systems may have billion components making consensus formation slow and difficult. Recently several overlapping stories emerged from various disciplines, including protein structures, neuroscience and social networks, showing that fast responses to known stimuli involve a network core of few, strongly connected nodes. In unexpected situations the core may fail to provide a coherent response, thus the stimulus propagates to the periphery of the network. Here the final response is determined by a large number of weakly connected nodes mobilizing the collective memory and opinion, i.e. the slow democracy exercising the 'wisdom of crowds'. This mechanism resembles to Kahneman's "Thinking, Fast and Slow" discriminating fast, pattern-based and slow, contemplative decision making. The generality of the response also shows that democracy is neither only a moral stance nor only a decision making technique, but a very efficient general learning strategy developed by complex systems during evolution. The duality of fast core and slow majority may increase our understanding of metabolic, signaling, ecosystem, swarming or market processes, as well as may help to construct novel methods to explore unusual network responses, deep-learning neural network structures and core-periphery targeting drug design strategies. (Abstract: Fast and Slow Thinking)

Successful adaptation helped the emergence of complexity. Alternating plastic- and rigid-like states were recurrently considered to play a role in adaptive processes. However, this extensive knowledge remained fragmented. In this paper I describe plasticity-rigidity cycles as a general adaptation mechanism operating in molecular assemblies, assisted protein folding, cellular differentiation, learning, memory formation, creative thinking, as well as the organization of social groups and ecosystems. (Abstract: Plasticity-Rigidity Cycles)

Csermely, Peter. The Wisdom of Networks: A General Adaptation and Learning Mechanism of Complex Systems. BioEssays. Online November, 2017. The Semmelweis University, Budapest, medical chemist also advises that a salient feature of networks is their broad array into a faster, constrained detail, core area, (seeds or words), and a slower periphery (search term) capable of viewing a contextual field. While the rigid core keeps doing the same thing, the freer outliers are open to beneficial variations. Akin to Miguel Munoz and others, the paper cites many phases such as proteins, metabolic signaling, neural nets, ecosystems, and social media whence this independent, common trait is exemplified in kind. See also Structure and Dynamics of Core/Periphery Networks by P. Csermely, et al in Journal of Complex Networks (1/93, 2013).

I hypothesize that re-occurring prior experience of complex systems mobilizes a fast response, whose attractor is encoded by their strongly connected network core. In contrast, responses to novel stimuli are often slow and require the weakly connected network periphery. Upon repeated stimulus, peripheral network nodes remodel the network core that encodes the attractor of the new response. This “core-periphery learning” theory reviews and generalizes the heretofore fragmented knowledge on attractor formation by neural networks, periphery-driven innovation, and a number of recent reports on the adaptation of protein, neuronal, and social networks. Moreover, the power of network periphery-related “wisdom of crowds” inventing creative, novel responses indicates that deliberative democracy is a slow yet efficient learning strategy developed as the success of a billion-year evolution. (Abstract)

Csoma, Attila, et al. Routes Obey Hierarchy in Complex Networks. Nature Scientific Reports. 7/7243, 2017. As complex system studies proceed to fill in a multiplex multiverse, a ten person team from Budapest University of Technology and Economics, Eotvos Lorand University, Budapest, Indiana University, University Medical Center Utrecht, Lausanne University Hospital, and Lausanne Ecole Polytechnique discern a common presence across cerebral, transport, Internet, and word association games. See Arora, et al herein for a similar 2017 take.

The last two decades of network science have discovered stunning similarities in the topological characteristics of real life networks (many biological, social, transportation and organizational networks) on a strong empirical basis. However our knowledge about the operational paths used in these networks is very limited, which prohibits the proper understanding of the principles of their functioning. Today, the most widely adopted hypothesis about the structure of the operational paths is the shortest path assumption. Here we present a striking result that the paths in various networks are significantly stretched compared to their shortest counterparts. Stretch distributions are also found to be extremely similar. This phenomenon is empirically confirmed on four networks from diverse areas of life. We also identify the high-level path selection rules nature seems to use when picking its paths. (Abstract)

D’Agostino, Gregorio and Antonio Scala. Networks of Networks: The Last Frontier of Complexity. International: Springer, 2014. As website entries convey, around 2014 a further appreciation of nature’s ubiquitous node and link topology arose that this topology actually comes as intricate nested layers, a multiplex. Italian systems physicists gather one of the first volumes about this advance. Typical chapters are Multiplex Networks by Kyu-Min Lee (search) et al, Networks of Interdependent Networks by Dror Kenett, et al, and Network Physiology by Plamen Evanov and Ronny Bartsch. See also Interconnected Networks, edited by Antonios Garas (Springer, 2014) for more.

The present work is meant as a reference to provide an organic and comprehensive view of the most relevant results in the exciting new field of Networks of Networks. Seminal papers have recently been published posing the basis to study what happens when different networks interact, thus providing evidence for the emergence of new, unexpected behaviors and vulnerabilities. From those seminal works, the awareness on the importance understanding Networks of Networks has spread to the entire community of Complexity Science. The contents have been aggregated under four headings; General Theory, Phenomenology, Applications and Risk Assessment. We are currently making the first steps to reduce the distance between the language and the way of thinking of the two communities of experts in real infrastructures and the complexity scientists.

De Arruda, Henrique, et al. Connecting Network Science and Information Theory. arXiv:1704.03091. University of Sao Paulo physicists and computer scientists including Diego Amancio and Filipi Silva aid current unifications across diverse fields and methods by noting similarities between these related approaches of figuring and parsing living, cognitive systems. See also Representation of Texts as Complex Networks by this group at arXiv:1606:09636.

A framework integrating information theory and network science is proposed, giving rise to a potentially new area. By incorporating and integrating concepts such as complexity, coding, topological projections and network dynamics, the proposed network-based framework paves the way not only to extending traditional information science, but also to modeling, characterizing and analyzing a broad class of real-world problems, from language communication to DNA coding. Basically, an original network is supposed to be transmitted, with or without compaction, through a sequence of symbols or time-series obtained by sampling its topology by some network dynamics, such as random walks. We show that the degree of compression is ultimately related to the ability to predict the frequency of symbols based on the topology of the original network and the adopted dynamics. (Abstract)

The areas of information theory and complex networks have been developed in a mostly independent way. However, as argued in the present work, these two areas present several shared and complementary elements which, when integrated, can be used to model, characterize and analyze a broad range of important real-world problems ranging from spoken/written language to DNA sequences. (5)

De Domenico, Malino, et al. Mathematical Formulation of Multilayer Networks. Physical Review X. 3/041022, 2013. An eight member team from Spain, Italy, and the UK, mostly the University of Zaragoza and Oxford University, advise that a shift of focus from single networks to the many layered scales they nest in can serve to reveal the presence of common, ubiquitous patterns. As a result, generic topologies can be identified, which will then be found in similar repetition everywhere. The journal considered this insightful work to merit home page praise, as in this note next.

Popular Summary: Describing a social network based on a particular type of human social interaction, say, Facebook, is conceptually simple: a set of nodes representing the people involved in such a network, linked by their Facebook connections. But, what kind of network structure would one have if all modes of social interactions between the same people are taken into account and if one mode of interaction can influence another? Here, the notion of a “multiplex” network becomes necessary. Indeed, the scientific interest in multiplex networks has recently seen a surge. However, a fundamental scientific language that can be used consistently and broadly across the many disciplines that are involved in complex systems research was still missing. This absence is a major obstacle to further progress in this topical area of current interest. In this paper, we develop such a language, employing the concept of tensors that is widely used to describe a multitude of degrees of freedom associated with a single entity.

Our tensorial formalism provides a unified framework that makes it possible to describe both traditional “monoplex” (i.e., single-type links) and multiplex networks. Each type of interaction between the nodes is described by a single-layer network. The different modes of interaction are then described by different layers of networks. But, a node from one layer can be linked to another node in any other layer, leading to “cross talks” between the layers. High-dimensional tensors naturally capture such multidimensional patterns of connectivity. Having first developed a rigorous tensorial definition of such multilayer structures, we have also used it to generalize the many important diagnostic concepts previously known only to traditional monoplex networks, including degree centrality, clustering coefficients, and modularity. We think that the conceptual simplicity and the fundamental rigor of our formalism will power the further development of our understanding of multiplex networks. (Editor)

De Domenico, Manlio and Jacob Biamonte. Spectral Entropies as Information-Theoretic Tools for Complex Network Comparison. arXiv:1609.01214.. Universitat Rovira I Virgili, Spain, and University of Malta theorists allude to affinities between nature’s ubiquitous network physiological anatomy and quantum phenomena by way of statistical physics. Search Biamonte for prior contributions.

Any physical system can be viewed from the perspective that information is implicitly represented in its state. However, the quantification of this information when it comes to complex networks has remained largely elusive. In this work, we use techniques inspired by quantum statistical mechanics to define an entropy measure for complex networks and to develop a set of information-theoretic tools, based on network spectral properties, such as Renyi q-entropy, generalized Kullback-Leibler and Jensen-Shannon divergences. Our results imply that spectral based statistical inference in complex networks results in demonstrably superior performance as well as a conceptual backbone, filling a gap towards a network information theory. (Abstract excerpts)

DeDeo, Simon and David Krakauer. Dynamics and Processing in Finite Self-Similar Networks. Journal of the Royal Society Interface. September 7, 2012. Cited more in Common Code, as complex systems science reaches a robust maturity, Santa Fe Institute resident theorists verify its ubiquitous aspects of component identity, structural topology, signal communication, recursive loops, and their nested iteration across life, genomes, cognition, and societies. An extensive bibliography provides further support. Nodes and links, hubs and connections, weight, communicate, branch, ramify, develop, merge and evolve everywhere.

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