Topological adventures in neuroscience. (English) Zbl 1451.92071
Baas, Nils (ed.) et al., Topological data analysis. Proceedings of the Abel symposium 2018, Geiranger, Norway, June 4–8, 2018. Cham: Springer. Abel Symp. 15, 277-305 (2020).
This is a summary of recent work at the interface of topology and neuroscience, primarily related to the Blue Brain Project. The first part relates to the algebraic topology of brain structure and function. A number of digitally reconstructed microcircuits from rat brains are studied, and directed flag complexes constructed from the directed networks of neurons. Statistics are calculated and compared with random models. Functional insights related to correlated activity between neurons at either end of a connection, and the time dependence of Betti numbers, are discussed. The second part discusses an objective topological descriptor of neuron morphologies. To each neuron morphology is associated a topological signature in the form of a persistence diagram. Populations of neurons are studied by statistical analysis of the associated sets of persistence diagrams.
For the entire collection see [Zbl 1448.62008].
For the entire collection see [Zbl 1448.62008].
Reviewer: Carlo Laing (Auckland)
MSC:
| 92C20 | Neural biology |
| 92B20 | Neural networks for/in biological studies, artificial life and related topics |
| 55N31 | Persistent homology and applications, topological data analysis |
| 92-02 | Research exposition (monographs, survey articles) pertaining to biology |
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