[Comp-neuro] paper on encoding of rat position by triangular lattice neurons

Ila Fiete prasad at kitp.ucsb.edu
Tue Jun 6 18:14:05 CEST 2006

Our paper on the encoding of rat position by triangular 
lattice neurons (grid cells) in the rat brain is now 
available for download from the q-bio arXiv, at:


The title and abstract are given below.

We welcome your comments!

Best regards,
Ila Fiete

Triangular lattice neurons may implement an advanced 
numeral system to precisely encode rat position over large 

Authors: Yoram Burak, Ted Brookings, Ila Fiete

We argue by observation of the neural data that neurons in 
area dMEC of rats, which fire whenever the rat is on any 
vertex of a regular triangular lattice that tiles 2-d 
space, may be using an advanced numeral system to 
reversibly encode rat position. We interpret measured dMEC 
properties within the framework of a residue number system 
(RNS), and describe how RNS encoding -- which breaks the 
non-periodic variable of rat position into a set of 
narrowly distributed periodic variables -- allows a small 
set of cells to compactly represent and efficiently update 
rat position with high resolution over a large range. We 
show that the uniquely useful properties of RNS encoding 
still hold when the encoded and encoding quantities are 
relaxed to be real numbers with built-in uncertainties, 
and provide a numerical and functional estimate of the 
range and resolution of rat positions that can be uniquely 
encoded in dMEC. The use of a compact, 
`arithmetic-friendly' numeral system to encode a metric 
variable, as we propose is happening in dMEC, is 
qualitatively different from all previously identified 
examples of coding in the brain. We discuss the numerous 
neurobiological implications and predictions of our 

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