Abstract:
:This review connects several lines of research to argue that hyperbolic geometry should be broadly applicable to neural circuits as well as other biological circuits. The reason for this is that networks that conform to hyperbolic geometry are maximally responsive to external and internal perturbations. These networks also allow for efficient communication under conditions where nodes are added or removed. We will argue that one of the signatures of hyperbolic geometry is the celebrated Zipf's law (also sometimes known as the Pareto distribution) that states that the probability to observe a given pattern is inversely related to its rank. Zipf's law is observed in a variety of biological systems - from protein sequences, neural networks to economics. These observations provide further evidence for the ubiquity of networks with an underlying hyperbolic metric structure. Recent studies in neuroscience specifically point to the relevance of a three-dimensional hyperbolic space for neural signaling. The three-dimensional hyperbolic space may confer additional robustness compared to other dimensions. We illustrate how the use of hyperbolic coordinates revealed a novel topographic organization within the olfactory system. The use of such coordinates may facilitate representation of relevant signals elsewhere in the brain.
journal_name
Curr Opin Neurobioljournal_title
Current opinion in neurobiologyauthors
Sharpee TOdoi
10.1016/j.conb.2019.07.008subject
Has Abstractpub_date
2019-10-01 00:00:00pages
101-104eissn
0959-4388issn
1873-6882pii
S0959-4388(18)30241-1journal_volume
58pub_type
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journal_title:Current opinion in neurobiology
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journal_title:Current opinion in neurobiology
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