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

5. Common Code: A Further Report of Reliable, Invariant Occasions

Yip, Jacky, et al. Cosmology with persistent homology. Journal of Cosmology and Astroparticle Physics.. September, 2024. We cite this paper to record and exemplify how the same mathematical methods such as the title case, algebraic topology, renormalization theories and so on are being readily applied across nature’s infinities. Another instance is cerebral architectures and cognition (D. Bassett). See also Cosmological Parameter Estimation from the Large-scale Structure by this collegial group at arXiv:2308.02636, which includes a neural net version.

Persistent homology naturally addresses the multi-scale topological characteristics of the large-scale structure as a distribution of clusters, loops, and voids. We apply this tool to dark matter halo catalogs to build a summary statistic for comparison with the joint power spectrum regarding their information content on cosmological parameters. We run a series of consistency checks to consolidate our results, and conclude that our findings motivate incorporating persistent homology into inference pipelines for cosmological survey data. (Excerpt)

Persistent homology is a method for computing topological features of a space at different spatial resolutions. More persistent features are detected over a wide range of spatial scales and are deemed more likely to represent true features of the underlying space.

Yu, Haiyuan and Mark Gerstein. Genomic Analysis of the Hierarchical Structure of Regulatory Networks. Proceedings of the National Academy of Sciences. 103/14724, 2006. Genomic systems employ a consistent network motif to achieve viable translation, which is found to be the same organization as present in human societies. Another contribution to the discovery of a natural genesis that recycles a common pattern and process from atom to cosmos.

A fundamental question in biology is how the cell uses transcription factors (TFs) to coordinate the expression of thousands of genes in response to various stimuli. The relationship between TFs and their target genes can be modeled in terms of directed regulatory networks. These relationships, in turn, can be readily compared with commonplace “chain-of-command” structures in social networks, which have characteristic layouts. (14724) In general, our results show that there is a pyramid-shaped hierarchical structure in regulatory networks, which is well organized in a clearly nonrandom manner. The decision making scheme in this hierarchy is a cogitation-like multistep process. (14730)

Zhang, Mengsen, et al. Connecting Empirical Phenomena and Theoretical Models of Biological Coordination across Scales. Journal of the Royal Society Interface. Online August, 2019. By way of sophisticated procedures, Center for Complex Systems and Brain Sciences, Florida Atlantic University researchers MZ, Chris Beetle, Scott Kelso and Emmanuelle Tognoli (search SK & ET) uncover intrinsic mathematic reciprocities which seem to imbue and guide small group social interactions. These patterns are then seen to suffuse organic and cerebral behaviors so at to reveal a broader scale-invariance. See also Critical Diversity: Divided or United States of Social Coordination by this group in PLoS One (April 4, 2018) which alludes to a chimeric dynamics.

Coordination in living systems—from cells to people—must be understood at multiple levels of description. Analyses and modelling of patterns of biological coordination often focus either on large-scale systems with many components, or on detailed dynamics in small-scale systems with few components. To bridge this gap, we have conducted a mid-scale human social experiment designed to reveal coordination at multiple levels (ensemble, subgroups and dyads) simultaneously. The present paper shows that a single system of equations captures key observations at all relevant levels. It also connects empirically validated models of both large- and small-scale biological coordination. Only by incorporating both of these features simultaneously can we reproduce the essential coordination behaviour observed in our experiment. (Abstract excerpt)

This cross-scale consistency of experimental observations may be explained by the scale-invariant nature of the critical coupling ratio, the transition point between monostability and multistability. The scale invariance suggests that experimental methods and conclusions for small-scale coordination dynamics have implications for multistability, phase transitions and metastability at larger scales, and enables a unified approach to biological coordination that meshes statistical mechanics and nonlinear dynamics. (7)

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