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Detecting structural complexity: from visiometrics to genomics and brain research. (English) Zbl 1397.00013

Emmer, Michele (ed.) et al., MATHKNOW. Mathematics, applied sciences and real life. Milano: Springer (ISBN 978-88-470-1121-2/hbk; 978-88-470-1122-9/ebook). MS&A. Modeling, Simulation and Applications 3, 167-181 (2009).
Summary: From visual inspection of complex phenomena to modern visiometrics, the quest for relating aspects of structural and morphological complexity to hidden physical and biological laws has accompanied progress in science ever since its origin. By using concepts and methods borrowed from differential and integral geometry, geometric and algebraic topology, and information from dynamical system analysis, there is now an unprecedented chance to develop new powerful diagnostic tools to detect and analyze complexity from both observational and computational data, relating this complexity to fundamental properties of the system. In this paper, we briefly review some of the most recent developments and results in the field. We give some examples, taken from studies on vortex entanglement, topological complexity of magnetic fields, DNA knots, by concluding with some comments on morphological analysis of structures present as far afield as in cosmology and brain research.
For the entire collection see [Zbl 1162.00010].

MSC:

00A05 Mathematics in general
57M25 Knots and links in the \(3\)-sphere (MSC2010)
92D10 Genetics and epigenetics
92B05 General biology and biomathematics
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