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

4. Universality Affirmations: A Critical Complementarity

Wang, Zhen, et al. Evolutionary Games on Multilayer Networks. arXiv:1504.04359. An introduction to a special issue of the European Physical Journal B, by an international team, including Matjaz Perc, with postings in China, Hungary, Slovenia, and Saudi Arabia. In regard, the paper surveys the progress of complexity science from the late 1980s to today. As the quote advises, nature’s creative course by which many discrete agents arrange into viable collectives is seen as most distinguished by interlinking network topologies. A novel reality is thus revealed and quantified of organically nested systems which repeat the same patterns and dynamics at every strata and species. It is then stated that keen insights can be gained if this developmental phenomena is seen as a strategic, decision-making game activity.

The hallmark property of a complex system is that a large number of simple units give rise to fascinating collective phenomena that could not be anticipated from an individual unit. Social order, biological complexity, brain power, ant colonies, and economic interconnectedness are all prime examples of topics one might attempt to study with a complex system at the heart of the research endeavor. But what is behind the emergent complexity? What turns people to societies and simple cells like neurons to a brain? The answer is, primarily, the network. Although phenomena such as self-organization and pattern formation might play a pivotal role too, it is mainly the way the simple units that form the complex system are connected with each other that makes them so much more than just the sum of their parts. (1)

Williams, Steven and Larry Yaeger. Evolution of Neural Dynamics in an Ecological Model. Geosciences. 7/3, 2017. In this MDPI online journal, Indiana University informaticians draw widely removed parallels between brains and ecosystems. By so doing, one more portal is opened as nature’s phenomenal genesis avails the same iconic, archetypal bicameral source at each and every instance and scale. A further notice is here made of a preferred bicameral criticality between control and freedom.

What is the optimal level of chaos in a computational system? If a system is too chaotic, it cannot reliably store information. If it is too ordered, it cannot transmit information. A variety of computational systems exhibit dynamics at the “edge of chaos”, the transition between the ordered and chaotic regimes. In this work, we examine the evolved neural networks of Polyworld, an artificial life model consisting of a simulated ecology populated with biologically inspired agents. As these agents adapt to their environment, their initially simple neural networks become increasingly capable of exhibiting rich dynamics. Dynamical systems analysis reveals that natural selection drives these networks toward the edge of chaos until the agent population is able to sustain itself. After this point, the evolutionary trend stabilizes, with neural dynamics remaining on average significantly far from the transition to chaos. (Abstract)

Wilting, Jens and Viola Priesemann. 25 Years of Criticality in Neuroscience. arXiv:1903.05129. MPI Dynamics and Self-Organization researchers begin with 1990s inklings that cerebral activity spontaneously seem to take on “dynamic reverberations” and ”power-law distributed avalanches” between reciprocal tighter or looser, more or less controlled, open or closed states. The survey is braced by some 90 references over the time span. See also Criticality Signatures in a Self-Organizing Recurrent Neural Network by Bruno Del Papa, et al in PLoS One (May 26, 2017) with Viola P. as a coauthor. We also note 25 Years of Self-Organized Criticality in Astrophysics in (Aschwanden, 2015) as this common propensity becomes known from universe to human.

Twenty-five years ago, Dunkelmann and Radons (1994) proposed that neural networks should self-organize to a critical state. In models, criticality offers a number of computational advantages. Thus this hypothesis, and in particular the experimental work by Beggs and Plenz (2003), has triggered an avalanche of research, with thousands of studies referring to it. Nonetheless, experimental results are still contradictory. How is it possible, that a hypothesis has attracted active research for decades, but nonetheless remains controversial? We discuss the experimental and conceptual controversy, and then present a parsimonious solution that (i) unifies the contradictory experimental results, (ii) avoids disadvantages of a critical state, and (iii) enables rapid, adaptive tuning of network properties to task requirements. (Abstract)

Wolchover, Natalie. The Universal Law that Aims Time’s Arrow. Quanta. August 1, 2019. A new look at a ubiquitous phenomenon has uncovered unexpected fractal behavior that could give us clues about the early universe and the arrow of time. The science journalist reports on a confluence of findings which seem to quantify and affirm an intrinsic cosmic self-similarity. By way of a natural philosophia view, if of a mind to perceive, a worldwide human quest may at last be closing on a phenomenal discovery. As long intimated, an infinite recurrence of the same pattern and process in kind really does exist and emerge on its own. As a nascent sapiensphere can prove and realize this, organic nature’s genome-like source code can reach, as planned, our intentional, procreative furtherance.

Notable papers are Prescaling and Far from Equilibrium Hydrodynamics in the Quark-Gluon Plasma by Alekson Mazeliauskas and Jurgen Berges in Physical Review Letters (122/122301, 2019), Universal Dynamics Far from Equilibrium by C. M. Schmied, et al at arXiv:1810.08143, Observation of Universal Dynamics in a Spinor Gas by Max Prufer, et al in Nature (563/217, 2018) and Prescaling in a Far from Equilibrium Bose Gas by C. M. Schmied, et al in Physical Review Letters (122/170404, 2019). See also Bubble Experiment finds Universal Laws by Charlie Wood in Quanta for July 31, 2019.

In the new work, researchers see far-from-equilibrium systems undergoing fractal-like universal scaling across both time and space. Take the birth of the universe. After cosmic inflation, the hypothetical oscillating, space-filling condensate would have quickly transformed into a dense field of quantum particles all moving with the same characteristic speed. (Jurgen) Berges and his colleagues conjecture that these non-equilibrium particles then exhibited fractal scaling governed by universal scaling exponents as they began the thermal evolution of the universe.

Wu, J. H. and Q. Jia. A Universal Mechanism of Extreme Events and Critical Phenomena. Nature Scientific Reports. 6/21612, 2016. Nanjing University of Posts and Telecommunications of China, and Hohai University, Nanjing, researchers propose a “general probability density distribution” by which a seemingly chaotic situation can become mathematically predictable. While self-organized criticalities are rife from finance markets and climate change to neural activity and seismicity, in this way a reliable anticipation can be possible.

The occurrence of extreme events and critical phenomena is of importance because they can have inquisitive scientific impact and profound socio-economic consequences. Here we show a universal mechanism describing extreme events along with critical phenomena and derive a general expression of the probability distribution without concerning the physical details of individual events or critical properties. The general probability distribution unifies most important distributions in the field and demonstrates improved performance. The shape and symmetry of the general distribution is determined by the parameters of the fluctuations. Our work sheds judicious insights into the dynamical processes of complex systems with practical significance and provides a general approach of studying extreme and critical episodes in a combined and multidisciplinary scheme. (Abstract)

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)

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