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\Large\bf DEFORMING THE HIPPOCAMPAL MAP\\[2em]

\normalsize
David S. Touretzky$^1$, Wendy E. Weisman$^2$, Mark C. Fuhs$^1$, 
William E. Skaggs$^3$, Andre A. Fenton$^{4,5}$, 
and Robert U. Muller$^{5,6}$\\[2em]
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$^1$ Computer Science Department \& Center for the Neural Basis of Cognition,
Carnegie Mellon University, Pittsburgh, PA

$^2$ 300 Woodlawn Avenue, Saint Paul, MN

$^3$ Arizona Research Laboratories, Division of Neural Systems, Memory, and Aging, 
Tucson, AZ

$^4$ Institute of Physiology, Academy of Sciences of the Czech Republic,
V\'{i}densk\'{a} 1083, 142 20 Prague 4, Czech Republic

$^5$ Dept. of Physiology and Pharmacology, State University of New York
Health Sciences Center at Brooklyn, Brooklyn, NY

$^6$ Medical Research Council Center for Synaptic Plasticity, Dept. of Anatomy,
University of Bristol, Bristol UK\\[1em]

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\noindent
Number of words in Abstract: 182\\
Number of text pages: 35\\
Number of figures: 10\\
Number of tables: 2\\~\\
Corresponding author:
\begin{quotation}
\noindent
David S. Touretzky\\
Computer Science Department\\
Carnegie Mellon University \\
Pittsburgh, PA 15213-3981 \\[1em]
phone: 412-268-7561\\
fax: 412-268-3608\\
e-mail: dst@cs.cmu.edu
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}
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\bf Funding Sources:
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\begin{itemize}
\item National Institutes of Health award MH59932 to
DST and WES

\item National Science Foundation REU supplement to
award IIS-9978403 to DST (to fund Wendy Weisman) 

\item National Science Foundation IGERT training grant DGE-9987588 to DST (support
for Mark Fuhs)

\item National Institutes of Health awards NS20686 and NS 37150
to RUM

\item Medical Research Council (UK) Grant to RUM 

\end{itemize}

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\centerline{\large\bf Abstract}
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To investigate conjoint stimulus control over place cells, 
Fenton et al. (2000a) recorded while rats foraged in a cylinder with
\mdeg{45} white and black cue cards on the wall.  Card centers were
\mdeg{135} apart. In probe trials the cards were rotated together or
apart by \mdeg{25}.  Firing field centers shifted during these trials,
stretching and shrinking the cognitive map.  Fenton et al. (2000b)
described this deformation with an {\em ad hoc} vector field equation.

We consider what sorts of neural network mechanisms might be capable
of accounting for their observations.  In an abstract, maximum
likelihood formulation, the rat's location is estimated by a conjoint
probability density function of landmark positions.  In an attractor
neural network model, recurrent connections produce a bump of activity
over a 2D array of cells; the bump's position is influenced by
landmark features such as distances or bearings.  If features are
chosen with appropriate care, the attractor network and maximum
likelihood models yield similar results, in accord with previous
demonstrations that recurrent neural networks can efficiently
implement maximum likelihood computations (Pouget et al., 1998; Deneve
et al., 2001).\\[3em]


\noindent
Keywords: {\bf place cell, attractor network, maximum likelihood, map deformation,
rodent hippocampus}


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