dorsal/arxiv
View SchemaTriangular lattice neurons may implement an advanced numeral system to precisely encode rat position over large ranges
| Authors | Yoram Burak, Ted Brookings, Ila Fiete |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0606005 |
| URL | https://arxiv.org/abs/q-bio/0606005 |
Abstract
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 hypothesis.
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"abstract": "We argue by observation of the neural data that neurons in area dMEC of rats,\nwhich fire whenever the rat is on any vertex of a regular triangular lattice\nthat tiles 2-d space, may be using an advanced numeral system to reversibly\nencode rat position. We interpret measured dMEC properties within the framework\nof a residue number system (RNS), and describe how RNS encoding -- which breaks\nthe non-periodic variable of rat position into a set of narrowly distributed\nperiodic variables -- allows a small set of cells to compactly represent and\nefficiently update rat position with high resolution over a large range. We\nshow that the uniquely useful properties of RNS encoding still hold when the\nencoded and encoding quantities are relaxed to be real numbers with built-in\nuncertainties, and provide a numerical and functional estimate of the range and\nresolution of rat positions that can be uniquely encoded in dMEC. The use of a\ncompact, `arithmetic-friendly\u0027 numeral system to encode a metric variable, as\nwe propose is happening in dMEC, is qualitatively different from all previously\nidentified examples of coding in the brain. We discuss the numerous\nneurobiological implications and predictions of our hypothesis.",
"arxiv_id": "q-bio/0606005",
"authors": [
"Yoram Burak",
"Ted Brookings",
"Ila Fiete"
],
"categories": [
"q-bio.NC"
],
"title": "Triangular lattice neurons may implement an advanced numeral system to precisely encode rat position over large ranges",
"url": "https://arxiv.org/abs/q-bio/0606005"
},
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