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

1. Network Physics: A Vital Interlinked Anatomy and Physiology

Kivela, Mikko, et al. Multilayer Networks. Journal of Complex Networks. 2/3, 2014. In this new Oxford journal, systems mathematicians from the UK, Spain, France and Ireland, including Mason Porter, post a 59 page introductory survey with 376 references that has become, along with Stefano Boccaletti’s work (search), a prime document for this latest expansion of nature’s intrinsic vitalities.

In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications. Such systems include multiple subsystems and layers of connectivity, and it is important to take such "multilayer" features into account to try to improve our understanding of complex systems. The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science. In this paper, we discuss the history of multilayer networks (and related concepts) and review the exploding body of work on such networks. To unify the disparate terminology in the large body of recent work, we discuss a general framework for multilayer networks, construct a dictionary of terminology to relate the numerous existing concepts to each other, and provide a thorough discussion that compares, contrasts, and translates between related notions such as multilayer networks, multiplex networks, interdependent networks, networks of networks, and many others. (Abstract)

Kleineberg, Kij-Kolja, et al. Hidden Geometric Correlations in Real Multiplex Networks. Nature Physics. 12/11, 2016. University of Barcelona and Cyprus University of Technology researchers including Martin Boguna tease out nature’s intricate orderliness by way of deeply persistent topological interconnections. In this regard, such phenomena serves as an independent source which becomes exemplified in kind across every cosmos to creature scale and instance.

Real networks often form interacting parts of larger and more complex systems. Examples can be found in different domains, ranging from the Internet to structural and functional brain networks. Here, we show that these multiplex systems are not random combinations of single network layers. Instead, they are organized in specific ways dictated by hidden geometric correlations between the layers. We find that these correlations are significant in different real multiplexes, and form a key framework for answering many important questions. Specifically, we show that these geometric correlations facilitate the definition and detection of multidimensional communities, which are sets of nodes that are simultaneously similar in multiple layers. They also enable accurate trans-layer link prediction, meaning that connections in one layer can be predicted by observing the hidden geometric space of another layer. And they allow efficient targeted navigation in the multilayer system using only local knowledge, outperforming navigation in the single layers only if the geometric correlations are sufficiently strong. (Abstract)

Klimm, Florian, et al. Individual Node’s Contribution to the Mesoscale of Complex Networks. New Journal of Physics. 16/125006, 2014. After much identification and study of modules, hubs, and communities in living, interconnective systems, Humboldt University, Qatar Computing Research Institute, and Universitat Pompeu Fabra, Barcelona researchers including Jurgen Kurths, can now technically describe the place, importance and contribution of each discrete node, element, entity, in their relative dynamic network setting.

The analysis of complex networks is devoted to the statistical characterization of the topology of graphs at different scales of organization in order to understand their functionality. While the modular structure of networks has become an essential element to better apprehend their complexity, the efforts to characterize the mesoscale of networks have focused on the identification of the modules rather than describing the mesoscale in an informative manner. Here we propose a framework to characterize the position every node takes within the modular configuration of complex networks and to evaluate their function accordingly. For illustration, we apply this framework to a set of synthetic networks, empirical neural networks, and to the transcriptional regulatory network of the Mycobacterium tuberculosis. We find that the architecture of both neuronal and transcriptional networks are optimized for the processing of multisensory information with the coexistence of well-defined modules of specialized components and the presence of hubs conveying information from and to the distinct functional domains. (Abstract)

The representation of real systems as complex networks has become a successful practice in the literature across different scientific disciplines: biology, technology, sociology, climatology, etc. Graph analysis allows us to describe the topological organization of the constituents of a multi-component system and uncover their functional implications. This is of particular relevance in physiology whose central aim is to understand the biological function of the observed anatomical structures. For example, recent studies indicated that such networks are highly complex in terms of dynamic reorganization in multiple hierarchical levels, highlighting the necessity to treat the system in an integrative manner. Brain networks, both anatomical and functional, have properties supporting brains function. There is also growing evidence of how alterations in connectivity lead to brain malfunction or disease, and vice versa. (1)

Kojaku, Sadamori and Naoki Masuda. Finding Multiple Core-Periphery Pairs in Networks. arXiv:1702.06903. University of Bristol engineering mathematicians describe this common topological phenomena (search Porter) and then evince its presence across social, infrastructure and political settings.

With a core-periphery structure of networks, core nodes are densely interconnected, peripheral nodes are connected to core nodes to different extents, and peripheral nodes are sparsely interconnected. Core-periphery structure composed of a single core and periphery has been identified for various networks. However, analogous to the observation that many empirical networks are composed of densely interconnected groups of nodes, i.e., communities, a network may be better regarded as a collection of multiple cores and peripheries. For example, we find distinct core-periphery pairs with different political leanings in a network of political blogs and separation between international and domestic subnetworks of airports in some single countries in a world-wide airport network. (Abstract)

Kostic, Daniel. Mechanistic and Topological Explanations. Synthese. 195/1, 2018. An introduction by a University of Paris Sorbonne scholar to this special issue, coedited by DK and Philip Huneman. We earlier entered in 2016 Kostic’s full paper, The Topological Realization, online in 2016, which argued that this current relational, network turn need be given a proper philosophical appreciation. With a notice of gene regulatory, physiological, neural nets, and more it is averred that such a basis is vital so to move beyond a prior particulate emphasis. See also herein Diversifying the Picture of Explanations in Biological Sciences by P. Huneman, Mechanisms Meet Structural Explanation by Laura Felline, and Network Representation and Complex Systems by Charles Rathkopf.

Kostic, Daniel. The Topological Realization. Synthese. Online October, 2016. A University of Paris philosopher attempts to give full notice to these heretofore unappreciated interconnective, network structural properties of natural and social systems, along with their prior nodal, discrete components. The special Synthese issue this paper is included in is now available as 195/1 January 2018, search DK for his Introduction and its contents.

In this paper, I argue that the newly developed network approach in neuroscience and biology provides a basis for formulating a unique type of realization, which I call topological realization. Some of its features and its relation to one of the dominant paradigms in the sciences, i.e. the mechanistic one, are already being discussed in the literature. But the detailed features of topological realization, its explanatory power and its relation to another prominent view, namely the semantic one, have not yet been discussed. I argue that topological realization is distinct from mechanistic and semantic ones because this framework is not based on local realisers, regardless of the scale but on global realizers. Furthermore, topological realization enables us to answer the “why” questions, which make it explanatory. (Edited Abstract)

Kostic, Daniel, et al. Unifying the Essential Concepts of Biological Networks. Philosophical Transactions of the Royal Society B. February, 2020. DR, University of Bordeaux, Claus Hilgetaf, University Medical Center Hamburg, and Marc Tittgemeyer, MPI Metabolism Research introduce a special issue with this integrative title. Its content is composed of both life science and philosophical considerations since both views need join together. For example, see General Theory of Topological Explanations and Explanatory Asymmetry by D. Kostic, Hierarchy and Levels by William Bechtel, Exploring Modularity by Maria Serban, and Network Architectures Supporting Learnability by Perry Zurn and Danielle Bassett, From Inert Matter to Global Society by David Chavalarias and Evolving Complexity by Richard Sole and Sergi Valverde (search for these last three).

Over the last decades, network-based approaches have become highly popular in diverse fields of biology, including neuroscience, ecology, molecular biology and genetics. While these approaches continue to grow very rapidly, some of their conceptual and methodological aspects still require a programmatic foundation. This challenge particularly concerns the question of whether a generalized account of explanatory, organizational and descriptive levels of networks can be applied universally across biological sciences. To this end, this highly interdisciplinary theme issue focuses on the definition, motivation and application of key concepts in biological network science, such as explanatory power of distinctively network explanations, network levels and network hierarchies. (Abstract)

Our organism constantly integrates information about the internal state with external environmental cues to adapt behavioural and autonomic responses to ensure physiological homeostasis. The Translational Neurocircuitry Group investigates how the human brain represents, integrates and prioritizes these internal and external signals to initiate adequate behavioural and physiological responses with a special focus on circuit-level models, metabolic mechanisms and human cognition. (Marc Tittgemeyer)

Kovacs, Istvan, et al. Community Landscapes: An Integrative Approach to Determine Overlapping Network Module Hierarchy, Identify Key Nodes and Predict Network Dynamics. PLoS One. 5/9, 2010. Cited more in Common Code, in this 100 page entry with bioinformatic programs and references, Semmelweis University, Budapest, living system scientists, including Peter Csermely, parse modular networks to uncover a ubiquitous topological feature. Indeed, nature seems intent on forming communal groupings of an appropriate size and populace at each and every strata and instance. Might one even broach an “ubuntu Universe.”

Krioukov, Dmitri, et al. Network Cosmology. Nature Scientific Reports. 2/793, 2012. . On occasion, a paper comes along of such unique, meritous content that it bodes for a significant breakthrough and synthesis. A team of five University of California, San Diego, systems scientists with Marian Boguna, a University of Barcelona physicist, proceed via sophisticated quantifications to discern the same nonlinear dynamics that infuse from proteins to cities within celestial topological networks. Its technical acumen and depth requires several excerpts. For example, Figure 2, “Mapping between the de Sitter universe and complex networks” illustrates many isomorphic affinities. As per Figure 4, “Degree distribution and clustering in complex networks and space time,” Internet, social network, brain anatomy, and hyperbolic spatial lineaments all graph on the same line, indicating common node and link geometries. As the quotes allude, a grand unification of universe, life, cognition, and humankind could be in the offing, a nascent witness of a biological genesis uniVerse.

Kumpula, Jussi, et al. Emergence of Communities in Weighted Networks. Physics Review Letters. 99/228701, 2007. As scale-free networks grow in intricacy, they reveal an inherent propensity to form modular and communal topologies. This “quite general paradigm” is then evident across a nested nature from metabolic to neural to societal systems, each amenable to this common physical explanation. And one might add, what is implied by such findings is an organic developing cosmos.

Network theory has undergone a remarkable development over the last decade and has contributed significantly to our understanding of complex systems, ranging from genetic transcriptions to the Internet and human societies. (228701-1) Understanding how the microscopic mechanisms translate into mesoscopic communities and macroscopic social systems is a key problem in its own right and one that is accessible within the scope of statistical physics. (228701-1)

Lalli, Margherita and Diego Gariaschelli. Geometry-free renormalization of directed networks: scale-invariance and reciprocity. arXiv:2403.00235. IMT School for Advanced Studies, Lucca, Italy physicists are able to demonstrate an effective integrity of this physical attribute with multiplex phenomena across diverse, practical instances. See also Renormalization of Complex Networks with Partition Functions by Jung, Sungwon, et al at arXiv:2403.07402

Recent research has tried to extend the concept of renormalization to more general networks with arbitrary topology. Here we show that the Scale-Invariant Model can be extended to directed networks without an embedding geometry or Laplacian structure. Moreover, it can account for the tendency of links to occur in mutual pairs more or less often than predicted by chance. By way of renormalization rules, we propose a multiscale international trade network with nontrivial reciprocity and an annealed model where positive reciprocity emerges spontaneously. (Excerpt)

Landry, Nicholas, et al. The simpliciality of higher-order networks. arXiv:2308.13918. University of Vermont and Grinnell College system theorists heighten our understandings as nature's vital connectivities ever expand and deepen. See also Topology and dynamics of higher-order multiplex networks by Sanjukta Krishnagopal and Ginestra Bianconi at arXiv:2308.14189.
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Higher-order networks are widely used to describe complex systems in which interactions can involve more than two entities at once. In this paper, we focus on inclusion within higher-order networks, referring to situations where specific entities participate in an interaction, and subsets of those entities also interact with each other. Traditional modeling approaches to higher-order networks tend to either not consider inclusion at all (e.g., hypergraph models) or explicitly assume perfect and complete inclusion (e.g., simplicial complex models). To allow for a more nuanced assessment of inclusion in higher-order networks, we introduce the concept of "simpliciality" and several corresponding measures. Contrary to current modeling practice, we show that empirically observed systems rarely lie at either end of the simpliciality spectrum. (Abstract)

A wide range of complex systems are shaped by interactions involving several entities at once: social networks are driven by group behavior [1], emails often have multiple recipients [2–4], molecular pathways in cells involve multi-protein interactions [5], and scientific articles in-
volve groups of co-authors [6]. Higher-order networks are a natural extension to networks explicitly designed to model such multiway relationships [7]

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