A topological approach unveils system invariances and broken symmetries in the brain

Journal of Neuroscience Research
Arturo Tozzi, James F Peters

Abstract

Symmetries are widespread invariances underscoring countless systems, including the brain. A symmetry break occurs when the symmetry is present at one level of observation but is hidden at another level. In such a general framework, a concept from algebraic topology, namely, the Borsuk-Ulam theorem (BUT), comes into play and sheds new light on the general mechanisms of nervous symmetries. The BUT tells us that we can find, on an n-dimensional sphere, a pair of opposite points that have the same encoding on an n - 1 sphere. This mapping makes it possible to describe both antipodal points with a single real-valued vector on a lower dimensional sphere. Here we argue that this topological approach is useful for the evaluation of hidden nervous symmetries. This means that symmetries can be found when evaluating the brain in a proper dimension, although they disappear (are hidden or broken) when we evaluate the same brain only one dimension lower. In conclusion, we provide a topological methodology for the evaluation of the most general features of brain activity, i.e., the symmetries, cast in a physical/biological fashion that has the potential to be operationalized. © 2016 Wiley Periodicals, Inc.

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Citations

May 26, 2016·Neuroscience Letters·James F PetersSheela Ramanna
Feb 1, 2017·Integrative Psychological & Behavioral Science·Arturo Tozzi, James F Peters
Feb 17, 2017·Frontiers in Human Neuroscience·James F PetersEbubekir İnan
Nov 18, 2017·Cognitive Neurodynamics·Eva DéliJames F Peters
Jun 1, 2017·Cognitive Neurodynamics·Arturo Tozzi, James F Peters
Aug 2, 2017·Cognitive Neurodynamics·James F PetersEbubekir İnan
Oct 1, 2019·Cognitive Neurodynamics·Arturo Tozzi, James F Peters
Dec 16, 2019·Progress in Biophysics and Molecular Biology·Arturo Tozzi, David Papo
Aug 16, 2019·Progress in Biophysics and Molecular Biology·William B MillerFrantišek Baluška
Apr 16, 2021·Cognitive Neurodynamics·Arturo TozziJames F Peters

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