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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

Porter, Mason. Nonlinearity + Networks: A 2020 Vision. arXiv:1911.03805. The UCLA systems mathematician (search) broadly reviews and previews to date this expansive webwork field. Sections include Centrality, Clustering and Large-Scale Structures and Time-Dependence. And whenever might it dawn that all these lively phenomena and their studies are actually quantifying a natural anatomy and physiology?

I will briefly survey several fascinating topics, methods and ideas in networks and nonlinearity, which I anticipate to be important during the next several years. These include temporal networks (in which the entities and/or their interactions change in time), stochastic and deterministic dynamical processes on networks, adaptive networks (in which a dynamical process on a network is coupled to the network structure), and "higher-order" interactions (which involve three or more entities in a network). I draw examples from a variety of scenarios such as contagion dynamics, opinion models, waves, and coupled oscillators. (Abstract)

Porter, Mason, et al. Communities in Networks. Notices of the AMS. 56/9, 2009. In consideration, Oxford University mathematician Porter, along with Jukka-Pekka Onnela, a Helsinki University physicist lately at Harvard, and from the University of North Carolina, mathematician Peter Mucha, might themselves be imagined as agents interlinked in local and global neural-like webs that they study. By this view, Mindkind’s historic learning process may just be reaching critical robustness in such exemplary works, together with many other articles posted herewith (e.g., Barrat, et al above). As the quote cites, statistical physics and complex systems science are realizing they engage the same phenomena in different ways so a merger is underway, still largely unbeknownst. But viola, a revolutionary new kind of materiality is being revealed. Both an independent, implicate network geometry and dynamics that involves such node/link, modular, weighted clusters becomes evident, which then explicates into universally repetitive, nested occurrence from biosphere to blogosphere, from protein webs to international scientific collaborations. In a natural genesis, such a vista could appear as a parent to child genetic code.

Graphs can represent either man-made or natural constructs, such as the World Wide Web or neuronal synaptic networks in the brain. Agents in such networked systems are like particles in traditional statistical mechanics that we all know and (presumably) love, and the structure of interactions between agents reflects the microscopic rules that govern their behavior. (1082)

Radicchi, Filippo, et al. Classical Information Theory of Networks. arXiv:1908.03811. FR, Indiana University, with Dmitri Krioukov and Harrison Hartle, Northeastern University, and Ginestra Bianconi, Queen Mary University of London finesse a better synthesis of implicit network communicative content with nature’s ubiquitous multiplex geometries. The broad motive is a better way to recognize evident commonalities as they vitalize and inform both genomic and neuromic phases.

Heterogeneity is an important feature which characterizes real-world networks. The diverse concept provides a convenient way to analyze and enhance systemic features such as robustness, synchronization and navigability. However, a unifying information theory to explain the natural emergence of heterogeneity in complex networks does not yet exist. Here, we develop a theoretical framework by showing that among degree distributions that can generate random networks, the one emerging from the principle of maximum entropy exhibits a power law. The pertinent features of real-world air transportation networks are well described by the proposed framework. (Abstract excerpt)

The principle of maximum entropy states that the unique probability distribution, encoding all the information available about a system but not any other information, is the one with largest information entropy. Available information about the system corresponds to constraints under which entropy is maximized. The principle of maximum entropy has found applications in many different disciplines, including physics, computer science, geography, finance, molecular biology, neuroscience, learning, deep learning, etc. (1)

Rakshit, Sarbendu, et al. Transitions from Chimeras to Coherence: An Analytical Approach by Means of the Coherent Stability Function. arXiv:1908.01063. Indian Statistical Institute, Kolkata, Amirkabir University of Technology, Tehran and University of Maribor, Slovenia (Matjaz Perc) further quantify the dynamic cerebral presence of such dual, simultaneous, more or less orderly phases. Circa 2019, the paper is a good instance of the global collaborative breadth and depth of scientific endeavors.

The study of transitions from chimeras to coherent states remains a challenge. Here we derive the necessary conditions for this shift by a coherent stability function approach. In chimera states, there is typically at least one group of oscillators that evolves in a drifting, random manner, while other groups of oscillators follow a smoother, more coherent profile. We use leech neurons, which exhibit a coexistence of chaotic and periodic tonic spiking depending on initial conditions, coupled via non-local electrical synapses, to demonstrate our approach. We explore various dynamical states with the focus on the transitions between chimeras and coherence, fully confirming the validity of the coherent stability function. (Abstract)

Rombach, M. Puck, et al. Core-Periphery Structure in Networks. arXiv:1202.2684. While this network feature has been noted in social groupings, here systems scientists Rombach, and Mason Porter, Oxford University, James Fowler, UC San Diego, and Peter Mucha, University of North Carolina, give it a deeply technical foundation, as the Abstract alludes. See a later finesse by this group Detection of Core-Periphery Structure in Networks using Spectral Methods and Geodesic Paths in European Journal of Applied Mathematics (27/846, 2016). Along with multiplex, community and modular features these complements are a major explanation of neural net brain anatomy and function. For much more, search Danielle Bassett in Systems Neuroscience.

Intermediate-scale (or `meso-scale') structures in networks have received considerable attention, as the algorithmic detection of such structures makes it possible to discover network features that are not apparent either at the local scale of nodes and edges or at the global scale of summary statistics. Numerous types of meso-scale structures can occur in networks, but investigations of such features have focused predominantly on the identification and study of community structure. In this paper, we develop a new method to investigate the meso-scale feature known as core-periphery structure, which entails identifying densely-connected core nodes and sparsely-connected periphery nodes. In contrast to communities, the nodes in a core are also reasonably well-connected to those in the periphery. Our new method of computing core-periphery structure can identify multiple cores in a network and takes different possible cores into account. We illustrate the differences between our method and several existing methods for identifying which nodes belong to a core, and we use our technique to examine core-periphery structure in examples of friendship, collaboration, transportation, and voting networks. (Abstract)

Rossetti, Giulio and Remy Cazabet. Community Discovery in Dynamics: A Survey. ACM Computing Surveys. 51/1, 2020. Italian National Research Council and French National Research Centre information scientists provide a broad tutorial to this persistent modular aspect of temporal network studies. See also Identifying Communities in Dynamic Networks Using Information Dynamics by Zejun Sun, et al in Entropy (22/4, 2020).

Complex networks modeling real-world phenomena are characterized by striking properties: (i) they are organized according to community structure, and (ii) their structure evolves with time. Many researchers have worked on methods that can efficiently unveil substructures in complex networks, giving birth to the field of community discovery. Dynamic networks can be used to model the evolution of a system: nodes and edges are mutable, and their presence, or absence, deeply impacts the community structure that composes them. As a “user manual,” this work organizes state-of-the-art methodologies based on their rationale, and their specific instantiation. (Abstract)

Serafino, Matteo, et al. Scale-Free Networks Revealed from Finite-Size Scaling. arXiv:1905.09512. Organic physicists based in Italy, the USA and UK including Amos Maritan and Guido Caldarelli describe a method to analyze common features of natural linkages such as protein interactions, technological computer hyperlinks, and informational citation and lexical networks. As a result, spontaneous self-organization to a critical-like state then becomes evident, which seems to hold across all manner of net topologies.

Siebert, Bram, et al. The Role of Modularity in Self-Organization Dynamics in Biological Networks. arXiv:2003.12311. University of Limerick and University of Bristol theorists including Malbor Asliani post another 2020 example of how much the presence of these complexity features are commonly accepted as a working explanation. But a contradiction remains between this self-assembling natural reality with universal node/link, modular, system viabilities at every and an older “Ptolemaic” paradigm (Brian Greene 2020) seems to be unaware of these revolutionary findings.

Interconnected ensembles of biological entities are some of the most complex systems that modern science has encountered so far. Many biological networks are now known to be constructed in a hierarchical way with two main properties: short average paths that join two distant nodes (neuronal, species, or protein patches) and a high proportion of nodes in modular aggregations. Here we show that network modularity is vital for the formation of self-organising patterns of functional activity. We show that spatial patterns at the modular scale can develop in this case, which may explain how spontaneous order in biological networks follows their modular structures. We test our results on real-world networks to confirm the important role of modularity for macro-scale patterns. (Abstract excerpt)

Siew, Cynthia, et al. Cognitive Network Science: A Review of Research on Cognition through the Lens of Network Representations, Processes, and Dynamics. Complexity. Art. 2108423, 2019. Within a special issue on this subject, University of Warwick. Basel, Wisconsin, and Pennsylvania including Nicole Beckage contribute to this 2010s revolution (see Barabasi 2012) by an observance of how a common, representative form and utility, as if a natural anatomy and physiology, is now well in place. By so doing (second quote) it can then join the prior pieces altogether. As a topical example, their occasion even in literary syntactic and informational content is confirmed. Again by turns, we note that an independent, universal network reality would be deeply textual in kind. See also From Topic Networks to Distributed Cognitive Maps by Akexander Mehler, et al in this issue.

Network science provides a set of quantitative methods to investigate complex systems, including human cognition. Although cognitive theories in different domains are strongly based on a network perspective, the application of network methodologies to quantitatively study cognition has so far been limited. This review shows how such approaches have been applied to the study of human cognition and can uniquely provide novel insight on important questions related to the complexity of cognitive systems. Drawing on the literature in cognitive network science, with a focus on semantic and lexical networks, we argue three points. (i) Network science provides aquantitative approach to represent cognitive systems. (ii) This method enables cognitive scientists to achieve a deeper understanding of how the neural network processes interact to produce behavioral phenomena. (iii) Network science provides a quantitative framework to model the dynamics of cognitive systems as structural changes on different timescales and resolutions. (Abstract)

Networks are composed of two elements: nodes that represent the conceptual entities of interest (e.g., persons, websites, or words) and edges that represent the relationships among those units (e.g., friendship, hyperlinks, or semantic similarity). While additional aspects can be considered as is done in bipartite and multiplex networks, identifying these two basic elements in the system of study is sufficient to formalize the system as a network and to employ the powerful tools provided by network science. Network science approaches often capitalize on the fact that relationships between nodes (i.e., edges) can be as important as the nodes themselves. A challenge in studying cognitive systems as networks is to represent these systems in a meaningful way in terms of nodes and edges. (2)

Song, Chaoming, et al. Self-Similarity of Complex Networks. Nature. 433/392, 2005. The power-law scaling which distinguishes small world networks is found to exhibit a self-repeating fractal geometry. This is achieved by a renormalization procedure that ‘coarse-grains’ the system into a nest of nodes and modules. This novel work is introduced by Steven Strogatz in the same issue (365) with the title Romanesque Networks since this property is ideally displayed by broccoli of this name.

Here we show that real complex networks, such as the world-wide web, social, protein-protein interaction networks and cellular networks are invariant or self-similar under a length-scale transformation. (392) These fundamental properties help to explain the scale-free nature of complex networks and suggest a common self-organization dynamics. (392)

Sorek, Matan, et al. Stochasticity, Bistability and the Wisdom of Crowds: A Model for Associative Learning in Genetic Regulatory Networks. PLoS Computational Biology. 9/8, 2013. With Nathalie Balaban and Yonatan Loewenstein, Hebrew University of Jerusalem neuroscientists identify deep similarities between a brain’s neural networks and genomic interactive systems. Once again nature uses the same universal and independent communicative dynamics in these separate realms. Might we imagine in turn that our thought processes are somehow “genetic” in kind?

It is generally believed that associative memory in the brain depends on multistable synaptic dynamics, which enable the synapses to maintain their value for extended periods of time. However, multistable dynamics are not restricted to synapses. In particular, the dynamics of some genetic regulatory networks are multistable, raising the possibility that even single cells, in the absence of a nervous system, are capable of learning associations. Here we study a standard genetic regulatory network model with bistable elements and stochastic dynamics. We demonstrate that such a genetic regulatory network model is capable of learning multiple, general, overlapping associations. The capacity of the network, defined as the number of associations that can be simultaneously stored and retrieved, is proportional to the square root of the number of bistable elements in the genetic regulatory network. Moreover, we compute the capacity of a clonal population of cells, such as in a colony of bacteria or a tissue, to store associations. We show that even if the cells do not interact, the capacity of the population to store associations substantially exceeds that of a single cell and is proportional to the number of bistable elements. Thus, we show that even single cells are endowed with the computational power to learn associations, a power that is substantially enhanced when these cells form a population. (Abstract)

Sporns, Olaf and Richard Betzel. Modular Brain Networks. Annual Review of Psychology. 67/613, 2016. Indiana University neuroscientists emphasize a propensity of generic network phenomena is to form modules, aka communities, as nature’s way of gaining and maintaining a robust performance.

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