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IV. Cosmomics: A Genome Code Self-Organizes Everywhere

C. Network Physics: A Cosmic Connectome

The first title phrase can serve to distinguish this 21st century scientific endeavor from a long, prior, necessary particle emphasis. It reports the elucidation of nature’s scale-free mode of dynamic interconnections everywhere, originally much due, circa 2000, to Albert-Laszlo Barabasi and Reka Albert, then University of Notre Dame physicists, search each name. In contrast to random graph, Poisson, or Erdos-Renyi networks, such as telephones, natural phenomena from galaxies to genomes, organisms, societies and languages, as these references attest, are connected by “preferential attachments and growth” of nodes and linkages. As such, they contain larger and smaller components or hubs with more or less connections and influence, for example neural nets, animal and human groupings, airports, Internet websites.

The initial model applied so well that it has, with much updating and expansion, been adopted by every scientific field and realm, as ALB notes in a 2012 Nature Physics article, and this section documents. Network Science textbooks by Mark Newman, Shlomo Havlin, Barabasi, and many others show how robust this realization of equally real interactions between parts, objects, elements, entities has become. A ubiquitous tendency is further found to form internal modules, communities, multiplex layers, and so on. In April 2016, one can find on the arXiv e-print site disparate postings such as The Network Behind the Cosmic Web (1604.03236) and Mapping Out Narrative Structures and Dynamics Using Networks (1604.03029), wherein both papers employ these same principles.

In just 15 worldwise years, a general, salutary surmise is lately possible. As a common structural topology and dynamic growth becomes evident at each phase and instance, it well implies an independent, universally exemplified, mathematical source. Moreover, if we might wonder what is being perceived, a novel genesis universe gains a vital anatomy and physiology, whence the archetypal networks from cosmos to brains to culture then become similar to genomes. Thus we add A Cosmic Connectomics as a subtitle.

NetSci2014. www.netsci2014.net. An International School and Conference on Network Science to be held in June at UC Berkeley, slated as “the biggest annual network science show.” An all star cast includes Reka Albert, Mark Newman, Dirk Helbing, Jessica Flack, Albert-Laszlo Barabasi, many more. Satellite symposia such as Temporal Networks, Human Dynamics and Social Physics, Complex Networks in Ecology, Urban Systems, and Information and Self-Organizing Dynamics, and Quantum Frontiers (search Faccin) are planned. I post this in May along with the Euro Evo Devo 2014 meeting above, as examples of a robust veracity across every ascendant phase along with their integral assembly, which much augurs for a natural genesis.

Watanabe, Akitomo, et al. Fractal and Small-World Networks Formed by Self-Organized Critical Dynamics. arXiv:1507.05716. Hokhaido University physicists theorize that nature’s pervasive networks achieve their serviceable form and function by way of this common dynamical tendency to critically poised states.

We propose a dynamical model in which a network structure evolves in a self-organized critical (SOC) manner and explain a possible origin of the emergence of fractal and small-world networks. Our model combines a network growth and its decay by failures of nodes. The decay mechanism reflects the instability of large functional networks against cascading overload failures. It is demonstrated that the dynamical system surely exhibits SOC characteristics, such as power-law forms of the avalanche size distribution, the cluster size distribution, and the distribution of the time interval between intermittent avalanches. During the network evolution, fractal networks are spontaneously generated when networks experience critical cascades of failures that lead to a percolation transition. (Abstract)

Aguirre, Jacobo, et al. On the Networked Architecture of Genotype Spaces and Its Critical Effects on Molecular Evolution. arXiv:1804.06835. Reviewed more in Genome Complex Systems, Charles III University of Madrid, Interdisciplinary Group of Complex Systems theorists J. Aguirre, Pablo Catalan, Jose Cuesta, and Susanna Manrubia contribution an inclusive synthesis that ranges across statistical physics, multiplex networks, nonlinear complexities, which then is seen to take on a computational guise.

Ahn, Yong-Yeol, et al. Link Communities Reveal Multiscale Complexity in Networks. Nature. 466/761, 2010. Researchers from the Center for Complex Network Research, Northeastern University; Center for Cancer Systems Biology at Harvard University; Institute for Quantitative Social Science, Harvard; and the College of Computer and Information Science, Northeastern, resolve a conceptual issue about how to allocate, describe, and understand nature’s ubiquitous relational form and fluidity. However then by such interdisciplinarity might it dawn that a grand genesis universe is revealed with a once and future, above and below, replication that we might avail for a better world? What time is it, whom altogether is learning, in translation are we reading a cosmic to child genetic code?

Networks have become a key approach to understanding systems of interacting objects, unifying the study of diverse phenomena including biological organisms and human society. One crucial step when studying the structure and dynamics of networks is to identify communities: groups of related nodes that correspond to functional subunits such as protein complexes or social spheres. (761) Here we reinvent communities as groups of links rather than nodes and show that this unorthodox approach successfully reconciles the antagonistic organizing principles of overlapping communities and hierarchy. In contrast to the existing literature, which has entirely focused on grouping nodes, link communities naturally incorporate overlap while revealing hierarchical organization. (761) Our results imply that link communities are fundamental building blocks that reveal overlap and hierarchical organization in networks to be two aspects of the same phenomenon. (761)

Albert, Reka. Scale-Free Networks in Cell Biology. Journal of Cell Science. 118/4947, 2005. The fields of genomics, transcriptomics and proteomics are providing a vast quantity of intracellular molecular data, which can now be mapped by interaction graphs. These structures are not random but take on the dynamic geometry of invariant, redundant relationships as seen everywhere else. With the many internal components of a cell being identified and interrelated, the presence of a universal interconnectivity becomes evident. A prime feature is a nested, hierarchical modularity of nets within nets. An editorial for this issue avers that a challenge for the new cell biology, set forth in a turn of the millennium editorial (113/749): ….to go beyond ‘toon’ (diagram) explanations, to understand the emergent, self-organizing properties of interdependent systems, is being fulfilled by such as the subject article. As a reflection, these advances, as they integrate the many cellular particles and pieces, via a collaborative humankind, they contribute to a cosmic Copernican Revolution from moribund machine to organic genesis. For a popular update, see "Networks in Motion" by Albert and Adilson Motter in Physics Today, April 2012.

The architectural features of molecular interaction networks are shared to a large degree by other complex systems ranging from technological to social networks. (4953)

Albert, Reka and Albert-Laszlo Barabasi. Statistical Mechanics of Complex Networks. Reviews of Modern Physics. 74/1, 2002. The initial theoretical explanation of scale-free networks, which are a major advance beyond random-graph, Erdos-Renyi, percolation models and a true depiction of nature’s actual prolific, nested intricacy. Technical definitions appear on Google, but in general as opposed to telephones, elemental nodes (proteins, neurons, prairie dogs, websites) are linked (webs, axons, groups, Internet) by power law preferential attachments to more or less connected hubs. They further grow in size and density akin to fractal self-similarities. An original 1999 paper by the authors is Emergence of Scaling in Random Networks in Science for October 15, 1999, and a popular view is Scale-Free Networks by Barabasi and Eric Bonabeau in Scientific American for May 2003.

Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems have been modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks are governed by robust organizing principles. This article reviews the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, the authors discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, the emerging theory of evolving networks, and the interplay between topology and the network’s robustness against failures and attacks. (Abstract)

Aleta, Alberto and Yamir Moreno. Multllayer Networks in a Nutshell. arXiv:1804.03488. University of Zaragoza Institute for Biocomputation and Physics of Complex Systems researchers provide a succinct tutorial for this appreciation of nature’s dynamically interconnective anatomy and physiology from galactic clusters to multiplex brains. After a general review, their vital presence in ecosystems, biological organisms, trade transport, cerebral processes, economic commerce, and onto game theory is surveyed.

Complex systems are characterized by many interacting units that give rise to emergent behavior. A particularly advantageous way to study these systems is through the analysis of the networks that encode the interactions among the system's constituents. During the last two decades, network science has provided many insights in natural, social, biological and technological systems. However, real systems are more often than not interconnected, with many interdependencies that are not properly captured by single layer networks. To account for this source of complexity, a more general framework, in which different networks evolve or interact with each other, is needed. These are known as multilayer networks. Here we provide an overview of the basic methodology used to describe multilayer systems as well as of some representative dynamical processes that take place on top of them. (Abstract)

Arenas, Alex and Manlio De Domenico. Nonlinear Dynamics on Interconnected Networks. Physica D. 323-324/3, 2016. An introduction to a special issue on the latest finesses of ubiquitous, animate network properties. Some entries are Cascades in Interdependent Flow Networks, Random Walk Centrality in Interconnected Multilayer Networks, and On Degree-Degree Correlations in Multilayer Networks.

Arora, Viplove and Mario Ventresca. Action-Based Modeling of Complex Networks. Nature Scientific Reports. 7/6673, 2017. Purdue University engineers advance a better generic method to analyze and design real-world interconnective systems, which is shown to apply across a wide range of applications from airports, power grids, and social media to neural and protein webs. See Csoma, et al herein for a similar 2017 take.

Complex networks can model a wide range of complex systems in nature and society, and many algorithms (network generators) capable of synthesizing networks with few and very specific structural characteristics (degree distribution, average path length, etc.) have been developed. However, there remains a significant lack of generators capable of synthesizing networks with strong resemblance to those observed in the real-world, which can subsequently be used as a null model, or to perform tasks such as extrapolation, compression and control. In this paper, a robust new approach we term Action-based Modeling is presented that creates a compact probabilistic model of a given target network, which can then be used to synthesize networks of arbitrary size. (Abstract)

Aste, Tomaso, et al. Complex, Inter-Networked Economic and Social Systems. European Physical Journal Special Topics. 225/10, 2016. n introduction to this subject issue as the ubiquitous presence of generic network phenomena becomes found in every cultural aspect. Papers vary from generic features in Discretized Kinetic Theory on Scale-Free Networks, and On the Convergence of the Fitness-Complexity Algorithm to practical examples in A Generation-Attraction Model for Renewable Energy Flows in Italy, and Interests Diffusion on a Semantic Multiplex.

Bagrow, James and Dirk Brockmann. Natural Emergence of Clusters and Bursts in Network Evolution. Physical Review X. 3/021016, 2013. We cite this entry by Northwestern University mathematicians as a quantification of what seems to be a universal source of self-organizing, complex adaptive systems that exists on their independent own, as they manifest everywhere from cosmos to culture.

Barabasi, Albert-Laszlo. Linked: The New Science of Networks. Cambridge, MA: Perseus Books, 2002. In the past few years, sparked by this University of Notre Dame physicist and colleagues, a significant finding has been made that complex networks are not random geometries but exhibit a nested, scale-free topology of how their nodes (agents) and links (local relations) are interconnected and weighted. A well-written story of nested, dynamic natural networks of great consistency everywhere from genes to galaxies and especially the World Wide Web. (This review was written a decade ago. Since this early work by its main founder, as this section attests natural networks abound and connect everywhere in an intricate cosmos.)

A string of recent breathtaking discoveries has forced us to acknowledge that amazingly simple and far-reaching natural laws govern the structure and evolution of all the complex networks that surround us. (6) Taken together, the similar large-scale topology of the metabolic and the protein interaction networks indicate the existence of a high degree of harmony in the cell’s architecture: Whichever organizational level we examine, a scale-free topology greets us. (189)

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