What is it about?

Cochlear implants, perhaps the most successful brain machine interface, enables deaf patients to perceive pitch by stimulating specific areas, or places, in the cochlea. Though conceptually simple, this so-called place code actually involves the interaction of a vast number of neurons in the brain. This manuscript describes the mathematical rules for combining and modulating neural network activities that allow the brain to process sounds of varying frequencies and intensities.

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Why is it important?

Though the place code is a major scheme for representing sounds in the brain, the actual computations that can be performed has not been formally described. For example, two tones with different frequencies will each activate distinct populations of neurons. When the tones are presented simultaneously, the two populations will be separated if the frequency difference is large but may overlap if the difference is small. This study derives the algebraic operations for 'adding' and 'multiplying' neural representations of complex sounds. The rules can be used to describe results obtained with simulations and experiments and can potentially be applied to other sensory systems.


In neuroscience, the many uncontrolled variables associated with even simple experiments often lead to inconsistent results, which in turn lead to difficulties in developing general models. This study was inspired by physicist Paul Dirac who "..learned to distrust all physical concepts as the basis for a theory". I was curious whether a mathematical approach , with minimal reliance on experimental data, can be used as a skeleton for biologically-inspired models and for interpreting experimental data. I hope that the reader can look past the necessary formalism and appreciate that many of the operations are in the same spirit as those encountered in high school algebra.

Professor Alex Reyes
New York University

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This page is a summary of: Mathematical framework for place coding in the auditory system, PLoS Computational Biology, August 2021, PLOS,
DOI: 10.1371/journal.pcbi.1009251.
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