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

Mumford, David, et al. Indra’s Pearls. Cambridge: Cambridge University Press, 2002. A visually impressive book to convey how fast computers can now give colorful exposition to the intricate mathematics of the early 20th century, especially those of Felix Klein. By these insights and methods, an intricate fractal self-similarity seems to pervade nature at every scale. These findings are next seen to affirm the ancient Buddhist vision of reality as a net or web of jewels whence the entire universe is reflected in each pearl. These equations and images convey a universally repeated interrelationship, a mutual identity, among every domain and member of the cosmos.

Making a statement equally faithful to both mathematics and religion, we can say that each part of our pictures contains within itself the essence of the whole. (xix)

Munoz, Miguel. Colloquium: Criticality and Dynamical Scaling in Living Systems.. Reviews of Modern Physics. 90/031001, 2018. After three decades of complexity studies since 1980s inklings, 1990s diversities, onto a 21st century expansive filling in from cosmos to culture, in these later 2010s we seem to be closing on the dream and goal of a common, iconic recurrence everywhere. Along with other entries herein, a University of Granada, Statistical Physics Group (ergodic.ugr.es for info and bio) theorist posts a 40 page, 700 reference tutorial which explains how nature self-organizes and emerges in a scale invariant way from phase transitions to genomes, cellular physiologies, animal groups, neural activity, and much more by a constant critical poise between order and disorder. By literary license, one could cite a cosmic, gender-like complementary criticality. For some 2017 comparisons see The Wisdom of Networks by Peter Csermely, Inequality in Nature and Society by Marten Steffen, et al, and Challenges in the Analysis of Complex Systems by Harold Hastings, Harold, et al. Altogether here is an epochal discovery by our intelligent humankinder in our midst which would serve us to recognize and implement. See also an editorial by Mark Buchanan in Nature Physics for February 2018 which cites this work as a significant exposition of this universal complementarity.

For later works see, for example, The excitatory-inhibitory branching process: cortical states, excitability, and criticality by M. Munoz and colleagues at arXiv:2203.16374, and his personal website.

A celebrated and controversial hypothesis conjectures that some biological systems - parts, aspects, or groups of them - may extract important functional benefits from operating at the edge of instability, halfway between order and disorder, i.e. in the vicinity of the critical point of a phase transition. Criticality has been argued to provide biological systems with an optimal balance between robustness against perturbations and flexibility to adapt to changing conditions, as well as to confer on them optimal computational capabilities, huge dynamical repertoires, unparalleled sensitivity to stimuli, etc. Criticality, with its concomitant scale invariance, can be conjectured to emerge in living systems as the result of adaptive and evolutionary processes that select for it as a template upon which higher layers of complexity can rest. (Abstract excerpt)

The hypothesis that living systems may operate in the vicinity of critical points, with concomitant scale-invariance, has long inspired scientists. From a theoretical viewpoint this conjecture is certainly appealing, as it suggests an overarching mechanism exploited by biological systems to derive important functional benefits essential in their strive to survive and proliferate. Throughout this essay we discussed dynamical aspects of criticality, meaning that in most of the discussed examples it is assumed – either directly or indirectly - that there is an underlying dynamical process at work, and that such a process – susceptible to be mathematically modeled – operates in the vicinity of a continuous phase transition, at the borderline between two alternative regimes. (27)

Nadeau, Robert and Menas Kafatos. The Non-Local Universe. New York: Oxford University Press, 1999. An innovative synthesis of physics and biology which describes the cosmos as a unified, organic whole. The results of sophisticated physical experiments where widely separated objects are in instant contact implies a seamless, holistic reality. Such a universe develops into levels of increasing complexity and sentience due to a complementary interplay of particle and wave, entity and relation, analysis and system, at each subsequent stage. These qualities then imply a reciprocity of the masculine and feminine principles. In its human phase the cosmos reaches self-awareness able to reflect on the primal consciousness it arose from.

….profound complementarities have been disclosed in the study of relationships between parts and wholes in biological reality that are analogous to those previously disclosed in the study of the relationship between parts and wholes in physical reality. This not only suggests that complementarity is the logic of nature in biological reality. It could also provide a basis for better understanding how increasing levels of complexity in both physical and biological reality result from the progressive emergence of collections of parts that constitute new wholes that display properties and behavior that cannot be explained in terms of the sum of the parts. (103)

Newman, Mark. Modularity and Community Structure in Networks. Proceedings of the National Academy of Sciences. 103/8577, 2006. The recent discovery of the same network pattern and process from genomes to computers is distinguished by a prevalence of communal modules. University of Michigan physicist Newman here describes an improved mathematical method for their recognition and activity.

Newman, Stuart. Complexity in Organismal Evolution. Hooker, Cliff, ed. Philosophy of Complex Systems. Amsterdam: Elsevier, 2011. The New York Medical College mathematician begins with Immanuel Kant to trace an array of historical attempts to explain the intricate lineaments of genotype and phenotype. While any evocation of “design” is gauche, we ought not to let a past fixation on mechanism alone to keep us from the possibility that something is really going on. An overdue shift from point genes to dynamical forms, molecules to morphodynamics, is much underway, which augurs for a 21st century evolutionary synthesis at last able to include nature’s creative spontaneity.

Niazi, Muaz, editor. Complex Adaptive Systems Modeling: A Multidisciplinary Roadmap. Complex Adaptive Systems Modeling. 1/1, 2013. A new periodical from the SpringerOpen Journal and BioMed Central project, which are all in full online. This posting is an initial, thorough overview of CAS features, along with guidance for paper writing and entries, by its editor who is a computer scientist at Bahria University, Islamabad with a doctorate from the University of Stirling, UK. See also by Niazi and Amir Hussain, University of Stirling, a 2013 Springer Briefs in Cognitive Computation volume Cognitive Agent-Based Computing: A Unified Framework for Modeling Complex Adaptive Systems.

Keywords: agent-based models, agent-based simulation, artificial life, biological networks, Boolean networks, citation networks, complex adaptive systems, complex networks, computer networks, emergence, epidemiological networks, gene expression networks, gene regulatory networks, individual-based modeling, metabolic networks, multiagent systems, network modeling, nucleic acid networks, protein interaction networks, self-adaptation, self-assembly, self-healing, self-organization, signaling pathway networks, social network analysis, social networks, social simulation, systems biology.

The CAS concept is married to the interaction of a set of perhaps simple but numerous entities, components or agents which interact and adapt on the basis of interactions. This interaction is known to give rise to interesting and emergent phenomena. While it is rather difficult to contain all aspects of CAS in a single definition, our current understanding is that CAS are often found in nature and in nature-inspired artificial systems in close relation with or inspired by life in some way. CAS concepts are tied to an abstract concept of a society. As such, it can be noted that typical research articles with a focus in modeling CAS are ornate with the following concepts: 1. A large number of agents (e.g. Genes, societies, humans, animals, insects, software agents, data packets etc.). 2. Focus on somewhat simpler individual agents. 3. Focus on the nonlinear interaction between agents and global phenomena resulting from these interactions. (6-7)

Nitzan, Mor, et al. Revealing Physical Interaction Networks from Statistics of Collective Dynamics. Science Advances. 3/e1600396, 2017. (arXiv:1801.05598) Mor Nitzan, Hebrew University of Jerusalem, with Jose Casadiego and Marc Timme, MPI Dynamics and Self-Organization contribute to deeper rootings of life’s interconnective propensities within nature’s active physical substrate (which in turn appears as increasingly animate and conducive).

Revealing physical interactions in complex systems from observed collective dynamics constitutes a fundamental inverse problem in science. Current reconstruction methods require access to a system's model or dynamical data at a level of detail often not available. We exploit changes in invariant measures, in particular distributions of sampled states of the system in response to driving signals, and use compressed sensing to reveal physical interaction networks. Testing various nonlinear dynamic processes emerging on artificial and real network topologies indicates high reconstruction quality for existence as well as type of interactions. These results advance our ability to reveal physical interaction networks in complex synthetic and natural systems. (Abstract)

Many complex systems in physics and biology constitute networks of dynamically interacting units. Examples range from gene regulatory networks in the cell and neural circuits in the brain to food webs in ecosystems and power grids, as well as other supply systems of engineering. These systems’ interaction networks fundamentally underlie their collective dynamics and function, thus rendering the knowledge of their interaction topology essential. For instance, identifying new pathways in gene regulatory networks and understanding long-range feedback in engineering systems require exact knowledge of their physical interaction networks. (1)

Nonnemacher, Marcel, et al. Signatures of Criticality Arise from Random Subsampling in Simple Populations Models. PLOS Computational Biology. Online October, 2017. MPI Biological Cybernetics and University of Tubingen integrative neuroscientists contribute new ways to understand cognitive performance as best served by critically balanced state between static and rigor. This significant appreciation which began hesitantly a decade ago (search Dante Chialvo), is now well evident.

The rise of large-scale recordings of neuronal activity has fueled the hope to gain new insights into the collective activity of neural ensembles. One attempt to interpret such data builds upon analogies to the behaviour of collective systems in statistical physics. Here, we connect “signatures of criticality”, and in particular the divergence of specific heat, back to statistics of neural population activity commonly studied in neural coding: firing rates and pairwise correlations. We show that the specific heat diverges whenever the average correlation strength does not depend on population size. To analyze these simulations, we develop efficient methods for characterizing large-scale neural population activity with maximum entropy models. Thus, previous reports of thermodynamical criticality in neural populations based on the analysis of specific heat can be explained by average firing rates and correlations. We conclude that a reliable interpretation of statistical tests for theories of neural coding is possible only in reference to relevant ground-truth models. (Abstract excerpts)

Novak, Miroslav, ed. Complexus Mundi: Emergent Patterns in Nature. Singapore: World Scientific, 2006. A collection from the international Fractals 2006 conference (check Google for paper abstracts). More than another theory or science of nonlinear dynamic systems, what is implied, upon reflection, is a new kind of animate natural genesis distinguished by its iterative, emergent similarity from cosmos to civilizations. Salient papers are (Scale Free) Structure of Genetic Regulatory Networks by L. S. Liebovitch, et al; Bruce West’s Modeling Fractal Dynamics; and Complexity in Nature and Society by Klaus Mainzer.

The dynamics of complex systems can clarify the creation of structures in Nature. This creation is driven by the collective interaction of constitutive elements of the system. Such interactions are frequently nonlinear and are directly responsible for the lack of prediction in the evolution process. The self-organization accompanying these processes occurs all around us and is constantly being rediscovered, under the guise of a new jargon, in apparently unrelated disciplines. (Back cover)
But, in general, the theory of complex dynamic systems deals with profound and striking analogies which have been discovered in the self-organized behavior of quite different systems in physics, chemistry, and biology. (Mainzer, 117)

Novak, Miroslav, ed. Emergent Nature. Singapore: World Scientific, 2001. Many papers on self-similar nonlinear dynamics being found in diverse systems such as heartbeats, peptide structures, ecosystems, solar magnetic fields, neural networks, and architecture.

Novak, Miroslav, ed. Thinking in Patterns. Singapore: World Scientific, 2005. Proceedings of the Fractal 2004 conference, an international biannual meeting which considers the many facets of a self-similar universe. Its website is www.kingston.ac.uk/fractal/. Typical papers are Selected Topics in Mathematics, Physics, and Finance Originating in Fractal Geometry by its founder, Benoit Mandelbrot, and Nicoletta Sala’s Fractal Geometry in the Arts.

The abundance of papers and the range of topics appearing here confirm the underlying similarity between subjects such as finance, road profiles, sound diffusion, image decompression, cognitive processes, biological aging, …epidermal ridges, fluctuations of sea levels, solar magnetic fields and arts across cultures. (Preface)

Oltvai, Zoltan and Albert-Laszlo Barabasi. Life’s Complexity Pyramid. Science. 298/763, 2002. A synoptic report on new research results and evidence about how nature is arrayed in an emergent scale where the same form and dynamics are in effect everywhere.

At the lowest level, these components form genetic-regulatory motifs or metabolic pathways (level 2), which in turn are the building blocks of function modules (level 3). These modules are nested, generating a scale-free hierarchical architecture (level 4). Although the individual components are unique to a given organism, the topologic properties of cellular networks share surprising similarities with those of natural and social networks. This suggests that universal organizing principles apply to all networks, from the cell to the World Wide Web. (763)

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