BORSUK-ULAM THEOREM ON A MÖBIUS STRIP

Arturo Tozzi
Center for Nonlinear Science, University of North Texas
1155 Union Circle, #311427
Denton, TX 76203-5017 USA
E-mail address: tozziarturo@libero.it
 
 
The Borsuk-Ulam theorem stands for a general principle able to describe a large amount of brain functions. However,
when managing the neurodata extracted from EEG and fMRI, the BUT method, based on projections and mappings
between different functional brain dimensions, in impractical and computationally expensive. Here we show how the
BUT’s antipodal features with matching description (say, two brain areas with the same values of entropy) can be
described in terms of closed paths on a Möbius strip. This allows to assess the dynamics of the nervous system in terms of trajectories taking place in a well-established, easily manageable phase space.
 
 

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of trajectories taking place in a well-established, easily manageable phase space.Arturo Tozzi
Center for Nonlinear Science, University of North Texas
1155 Union Circle, #311427
Denton, TX 76203-5017 USA
E-mail address: tozziarturo@libero.it
The Borsuk-Ulam theorem stands for a general principle able to describe a large amount of brain functions. However,
when managing the neurodata extracted from EEG and fMRI, the BUT method, based on projections and mappings
between different functional brain dimensions, in impractical and computationally expensive. Here we show how the
BUT’s antipodal features with matching description (say, two brain areas with the same values of entropy) can be
described in terms of closed paths on a Möbius strip. This allows to assess the dynamics of the nervous system in terms
of trajectories taking place in a well-established, easily manageable phase space.