IV. Ecosmomics: Independent Complex Network Systems, Computational Programs, Genetic Ecode Scripts

1. Network Physics: A Vital Interlinked Anatomy and Physiology

Zheng, Muhua, et al. Geometric Origins of Self-Similarity in the Evolution of Real Networks. arXiv:1912.00704. MZ, Marian Boguna and Angeles Serrano, University of Barcelona, along with Guillermo Garcia-Perez, University of Turku contribute to integrations of nature’s universe to human multiplex connectivities with deeper physical principles.

One of the aspirations of network science is to explain the growth of real networks, often through the sequential addition of new nodes that connect to older ones. However, many real systems evolve through the branching of basic units, whether those be scientific fields, countries, or species. Here, we provide empirical evidence for self-similar branching growth in real networks and present the Geometric Branching Growth model, which is designed to predict evolution and symmetries. The model produces multiscale unfolding of a network in a sequence of scaled-up replicas. (Abstract excerpt)

In the context of network science, growth is often modeled through the sequential addition of new nodes that connect to older ones by preferential attachment. Here, we take an alternative approach and explore the relation between branching growth and geometric renormalization to explain self-similar network evolution. Renormalization in networks, based on statistical physics, acts as an inverse branching process by coarse-graining nodes. Thus, branching growth can be seen as an inverse renormalization transformation: an idea that was introduced in using a purely topological approach to reproduce the structure of fractal networks, where fractality was interpreted as an evolutionary drive towards robustness. (2)

Zheng, Muhua, et al. Geometric Renormalization of Weighted Networks. arXiv:2307.00879. MZ, Jiangsu University, G. Garcia-Perez, Algorithmiq, Ltd., Helsinki, and M. Boguna, M. A. Serrano, University of Barcelona post their latest contribution which proceeds to show how these title theories meld well into multiplex topologies so to further reveal common complexities.

The geometric renormalization technique for complex networks has successfully revealed the multiscale self-similarity of real network topologies and found to generate replicas at different length scales. In this letter, we extend the subject framework to weighted networks, wherein interactions play a crucial role in their structural organization and function. We present a theory that elucidates this invariant symmetry as it sustains this selection as a meaningful procedure. (Excerpt)

Zhuo, Zhao, et al. Accurate Detection of Hierarchical Communities in Complex Networks based on Nonlinear Dynamical Evolution. Chaos. Online April, 2018. University of Electronic Science and Technology of China and Arizona State University researchers propose a clever way to improve and advance studies and understandings of nature’s ubiquitous interconnections. In regard, a common mathematical topology appears to exist on its independent own, by virtue of its exemplary presence in kind everywhere.

One of the most challenging problems in network science is to accurately detect communities at distinct hierarchical scales. We articulate an alternative, dynamical evolution-based approach to the problem. The basic principle is to computationally implement a nonlinear dynamical process on all nodes in the network with a general coupling scheme, creating a networked dynamical system. Under a proper system setting and with an adjustable control parameter, the community structure of the network would “come out” or emerge naturally from the dynamical evolution of the system. As the control parameter is systematically varied, the community hierarchies at different scales can be revealed. Our method is computationally extremely efficient, eliminating completely the NP-hard difficulty associated with previous methods. (Abstract excerpt)

Zitnik, Marinka, et al.. Current and future directions in network biology. arXiv:2309.08478. Thirty-six scientists from across the USA and onto France, the UK and Brazil met last year to broadly scope out the cellular songs and melodies, as Siddhartha Mukherjee advises (2022), that we are learning serve to join living systems altogether.

Network biology, an interdisciplinary merger of computational and biological sciences, is vital understand cellular functioning and disease. A workshop on Future Directions in Network Biology was held at the University of Notre Dame in 2022, which brought together active researchers in this field. Typical topics were: inference and comparison of networks, multimodal data integration, heterogeneous, higher-order network analysis, machine learning, and network-based personalized medicine. Video recordings of the workshop presentations are publicly available on YouTube. This paper, co-authored mostly by the participants, summarizes the discussion and is expected to help shape short- and long-term visions for future computational and algorithmic research. (Excerpt)

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