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

4. Universality Affirmations: A Critical Complementarity

yang, Ruochen and Paul Bogdan. Controlling the Multifractal Generating Measures of Complex Networks. Nature Scientific Reports. 10/5541, 2020. In this special year, University of Southern California computer scientists (search PB) add to confirmations of a common presence of self-similar forms and functions across nature’s array from geologic to genomic, cerebral and onto our behavioral activities. See also in regard Quantifying Emergence and Self-Organization of Microbial Communities by V. Balaban, et al (USC) in NSR (8/12416, 2018).

Self-repeating patterns and multifractality exist in many real-world complex systems such as brain, genetic, geoscience, and social networks. To better comprehend the multifractal behavior in the real networks, we propose the weighted multifractal graph to model the spatiotemporal complexity and heterogeneity encoded in interaction weights. We apply this approach to two specific complex systems, namely (i) the chromosome interactions of yeast cells in quiescence and in exponential growth, and (ii) the brain networks of healthy people and patients exhibiting mild cognitive impairment leading to Alzheimer disease. We find that our method provides a novel way to understand the self-similar structure of complex networks and to discriminate network structures. (Abstract excerpt)

From a geometrical perspective, many large-scale complex networks from sociology and biology exhibit self-similar and multifractal characteristics. Multifractal geometric analysis makes it possible to capture the heterogeneous and multiscale interaction rules of large networks . It efficiently characterizes large-scale complex systems and can be employed to measure nodes similarity and detect community structures. For instance, the multifractality of geochemistry mapping explains the element concentration values distribution and spatial covariance structure in rock samples. (1)

Youn, Hyejin, et al. Scaling and Universality in Urban Economic Diversification. Journal of the Royal Society Interface. Vol.13/Iss.114, 2016. A premier team of Youn and Geoffrey West, Oxford University, Luis Bettencourt, Santa Fe Institute, Jose Lobo and Deborah Strumsky, Arizona State University, and Horacio Samaniego, Universidad Austral de Chile, attest to the presence of a common, complex adaptive, self-similar system that distinguishes in kind every aspect, topology, degree, function, dynamic of citified human habitation from local neighborhoods to a megametropolis. See also Invention as a Combinatorial Process: Evidence from US Patents by team members in this journal (Vol.12, Iss.106). Circa 2015, some 50 years after general systems theory and 30 years since SFI began, here is a robust achievement of their quest to find a constant repetition of the same archetypal pattern and process at each and every scale and instance. As a result, an implied independent, universal mathematic source code becomes strongly evident.

Understanding cities is central to addressing major global challenges from climate change to economic resilience. Although increasingly perceived as fundamental socio-economic units, the detailed fabric of urban economic activities is only recently accessible to comprehensive analyses with the availability of large datasets. Here, we study abundances of business categories across US metropolitan statistical areas, and provide a framework for measuring the intrinsic diversity of economic activities that transcends scales of the classification scheme. A universal structure common to all cities is revealed, manifesting self-similarity in internal economic structure as well as aggregated metrics (GDP, patents, crime). We present a simple mathematical derivation of the universality, and provide a model, together with its economic implications of open-ended diversity created by urbanization, for understanding the observed empirical distribution. (Abstract)

Zakharaova, Anna. Chimera Patterns in Networks. International: Springer, 2020. In a chimera state, a network spontaneously splits into two parts with different dynamics separated in space: one demonstrating coherent behavior and the other exhibiting incoherent behavior. (2) After some years of collegial papers (Google), a Technical University of Berlin theoretical physicist has written the first book length treatment of this newly recognized natural systemic propensity to reside at a dynamic poise of more or less relative order or stability. Typical subjects are Coherence-Incoherence Patterns with Topologies, Power-Law Coupling, Fractal Connectivities, and Multiplex Networks. Such synchronization phenomena is lately being detected in kind across quantum, chemical, and biologic areas onto neural and socio-economic domains, in a way as akin to self-organizing criticalities.

For main prior references the author recommends, Scholl, Eckehard. Synchronization Patterns and Chimera States in Complex Networks by Eckehard Scholl in European Physical Journal Special Topics (225/891, 2016) and Chimera States: Coexistence of Coherence and Incoherence in Networks by Mark Panaggio and Daniel Abrams in Nonlinearity (28/R67, 2015).

This is the first book devoted to chimera states - peculiar partial synchronization patterns in networks. Providing an overview of the state of the art in research on this topic, it explores how these hybrid states, which are composed of spatially separated domains of synchronized and desynchronized behavior, arise surprisingly in networks of identical units and symmetric coupling topologies. The book not only describes various types of chimeras, but also discusses the role of time delay, stochasticity, and network topology for these synchronization-desynchronization patterns. Moreover, it addresses the question of robustness and control of chimera states, which have various applications in physics, biology, chemistry, and engineering.

Zarepour, Mahdi, et al. Universal and Non-Universal Neural Dynamics on Small World Connectomes. arXiv:1905.05280. Five Argentine complexity theorists including Dante Chialvo propose novel ways to quantify and understand nature’s propensity to seek and reside at a critically poised state. As the Abstract notes, this advance is achieved by joining active cerebral phenomena with common network topologies which serves to reveal optimal invariant behaviors. If to view altogether within this “connect-omic” motif, it well suggests that the uniVerse to us course is essentially genetic in kind.

Evidence of critical dynamics has been recently found in both experiments and models of large scale brain dynamics. The understanding of the nature and features of such critical regime is hampered by the relatively small size of the available connectome, which prevent among other things to determine its associated universality class. To circumvent that, here we study a neural model defined on a class of small-world network that share some topological features with the human connectome. We found that varying the topological parameters can give rise to a scale-invariant behavior belonging either to mean field percolation universality class or having non universal critical exponents. Overall these results shed light on the interplay of dynamical and topological roots of the complex brain dynamics. (Abstract)

Zeraati, Roxana, et al. Self-organization toward Criticality by Synaptic Plasticity. arXiv:2010.07888. RZ, MPI Biological Cybernetics, Viola Priesemann, MPI Dynamics and Self-organization, and Anna Levina, University of Tubingen theorists add to a flow of timely papers which identify and affirm that life’s evolution and development seems to prefer and tend to this malleable condition for both brains and bodies because it can achieve an optimum responsiveness by being critically poised between relatively closed, fixed and open, fluid states. As this section and elsewhere documents, into the later 2010s and 2020, so many various studies are coming to and realizing nature’s universal preference for this optimum balance. See also Online Adaptation in Robots as Biological Development Provides Phenotypic Plasticity by Michele Braccini, et al at 2006.02367.

Self-organized criticality has been proposed as a universal mechanism for the emergence of scale-free dynamics in many complex systems, and in the brain. While such scale-free patterns appear many neural recordings, the biological principles behind their presence remained unknown. By way of network models and experimental observations, synaptic plasticity was proposed as a mechanism to drive self-organized brain dynamics towards a critical point. We discuss how biological plasticity rules operate across timescales and how they alter the network's dynamical state through modification of the connections between neurons. Overall, the concept of criticality helps to shed light on brain function and self-organization, whence living neural networks also avail their criticality for computation. (Abstract excerpt)

Synaptic plasticity is the biological process by which specific patterns of synaptic activity result in changes in synaptic strength and is thought to contribute to learning and memory. (Nature Research) In neuroscience, synaptic plasticity is the ability of synapses to strengthen or weaken over time, in response to increases or decreases in their activity. (Wikipedia)

Thus instead of self-organizing precisely to criticality, the brain could make use of the divergence of processing capabilities around the critical point. Thereby, each brain area might optimize its computational properties by tuning itself towards and away from criticality in a flexible, adaptive manner. In the past decades, the community has revealed the local plasticity rules that would enable such a tuning and adaption of the working point. Criticality has been very inspiring to understand brain dynamics and function. We assume that being perfectly critical is not an optimal solution for many brain areas, during different task epochs. (16)

Zhang, Jiang, et al. Scaling Behaviors in the Growth of Networked Systems and Their Geometric Origins. Nature Scientific Reports. 5/9767, 2015. Into the 2010s, Beijing Normal University and Arizona State University systems scientists contribute to realizations of ubiquitous, generic interlinking, relational phenomena that recurs in similar kind across a wide expanse from microbes to brains to cities. Such a network nature bears witness to “simple underlying mechanisms” that must exist independently of any specific instance.

Two classes of scaling behaviours, namely the super-linear scaling of links or activities, and the sub-linear scaling of area, diversity, or time elapsed with respect to size have been found to prevail in the growth of complex networked systems. Despite some pioneering modelling approaches proposed for specific systems, whether there exists some general mechanisms that account for the origins of such scaling behaviours in different contexts, especially in socioeconomic systems, remains an open question. We address this problem by introducing a geometric network model without free parameter, finding that both super-linear and sub-linear scaling behaviours can be simultaneously reproduced and that the scaling exponents are exclusively determined by the dimension of the Euclidean space in which the network is embedded. By virtue of these general findings concerning scaling behaviour, our models with simple mechanisms gain new insights into the evolution and development of complex networked systems. (Abstract)

Sub-linear scaling as another type of scaling behavior with exponent smaller than 1 is also prevalent in complex networked systems. For instance, the area and road volume of a city are found to scale sub-linearly with its population. In online communities, the number of distinct tags scales sub-linearly with the system size. In information retrieval or in linguistics, the general Heap’s law captures a sub-linear scaling between the number of distinct words and the total number of words. In ecological communities, the diversity of higher taxa scales sub-linearly with the number of species. The sub-linear scaling is also found in river networks, various combinatorial systems and etc. (1)

Zhang, Xiaoge, et al. A Biologically Inspired Network Design Model. Nature Scientific Reports. 5/10794, 2015. As the quotes explain, scientists from China, the UK, USA, and Greece, including Andrew Adamatzky and Xin-She Yang, draw upon nature’s original wisdom by way of a universal repetition of the same effective complex adaptive systems. In this case its presence is noted in the multifarious behaviors of fungi, from which a common algorithm can be identified. Further topological exemplars are cited across the animal kingdoms. As this genome-like agency may pass to human cognizance, it can be intentionally availed to create a much better, organic, homeostatic civilization.

A network design problem is to select a subset of links in a transport network that satisfy passengers or cargo transportation demands while minimizing the overall costs of the transportation. We propose a mathematical model of the foraging behaviour of slime mould P. polycephalum to solve the network design problem and construct optimal transport networks. In our algorithm, a traffic flow between any two cities is estimated using a gravity model. The flow is imitated by the model of the slime mould. The algorithm model converges to a steady state, which represents a solution of the problem. We validate our approach on examples of major transport networks in Mexico and China. By comparing networks developed in our approach with the man-made highways, networks developed by the slime mould, and a cellular automata model inspired by slime mould, we demonstrate the flexibility and efficiency of our approach. (Abstract)

When we design a transportation network we should, ideally, make it fault tolerant, capable to cope with traffic accidents, terrorist attack, and emergency road maintenance. Fault tolerance and high performance attract higher building and maintenance costs. How to make a tradeoff between the overall cost, the fault tolerance, and the performance is the problem worthwhile to investigate. During their evolution living creatures optimised their transportation networks over million of years: vascular systems of plants and animals, foraging patterns of social insects migration trails by birds and animals, hunting routes of predators. It is therefore often very fruitful to apply natural solutions in designs of human-made artifacts. (1-2)

Zhang, Yuanzhao and Adilson Motter. Mechanism for Strong Chimeras. arXiv:2101.12230. Northwestern University systems physicists (search AM) provide a deeply technical explanation of why so many natural phenomena are found to exhibit this optimum state of both order and disorder at once.

Chimera states have attracted significant attention as symmetry-broken states exhibiting the unexpected coexistence of coherence and incoherence. Despite the valuable insights gained from analyzing specific systems, an understanding of the general physical mechanism underlying the emergence of chimeras is still lacking. Here, we show that many stable chimeras arise because coherence in part of the system is sustained by incoherence in the rest of the system. Recognizing this mechanism offers a new meaning to the interpretation that chimeras are a natural link between coherence and incoherence. (Abstract)

Zuev, Konstantin, et al. Emergence of Soft Communities from Geometric Preferential Attachment. Nature Scientific Reports. 5/9421, 2015. In that context, the decay of initial attractiveness Λ that we found in the Internet must be analogous to the decay of cosmological constant Λ in modern cosmological theories. (6) In a paper that could exemplify a 2015 proof of nature’s repetitive universality, Zuev and Dmitri Krioukov, Northeastern University, Martin Boguna, University of Barcelona, and Ginestra Bianconi, Queen Mary University of London course from cosmos to culture to find a constant self-similarity. Whether interstellar or world web media, the same network node and link topologies and dynamics persist. From perennial metaphysics, 1960s general systems theory, complex self-organization sciences, to this global synthesis, it is said that a natural iterative correspondence can at last be confirmed. See also Scaling Behaviors in the Growth of Networked Systems and Their Geometric Origins by Jiang Zhang (Nature Scientific Reports, 2015) and Evolutionary Games on Multilayer Networks by Zhen Wang, et al (arXiv:1504.04359) for companion entries.

All real networks are different, but many have some structural properties in common. There seems to be no consensus on what the most common properties are, but scale-free degree distributions, strong clustering, and community structure are frequently mentioned without question. Surprisingly, there exists no simple generative mechanism explaining all the three properties at once in growing networks. Here we show how latent network geometry coupled with preferential attachment of nodes to this geometry fills this gap. We call this mechanism geometric preferential attachment (GPA), and validate it against the Internet. GPA gives rise to soft communities that provide a different perspective on the community structure in networks. The connections between GPA and cosmological models, including inflation, are also discussed. (Abstract)

In summary, hyperbolic network geometry, combining popularity and similarity forces driving network evolution, and coupled with preferential attachment of nodes to this geometry (GPA), naturally yields scale-free, strongly clustered growing networks with emergent soft community structure. (6)

Zur Bonsen, Alexander, et al. Chimera States in Networks of Logistic Maps with Hierarchical Connectivities. arXiv:1711.03287. Technical University of Berlin system physicists including Anna Zakharova and Eckehard Scholl go on to describe fractal self-similar bifurcations which these node/link scalar topologies seem to be attracted to.

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