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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

$^2$ Wendy Weisman current address, Minnesota

$^3$ 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\\[2em]

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\noindent
Number of words in Abstract: 160\\
Number of text pages: 30\\
Number of figures: 10\\
Number of tables: 1\\~\\
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 present two other models of map deformation.  In a maximum
likelihood formulation, the rat's location is estimated by a conjoint
probability density function.  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.  The maximum likelihood and attractor network
models yield similar results, supporting previous conjectures (Deneve
et al., 2002) that maximum likelihood may be an appropriate framework
for describing attractor network behavior.\\[3em]


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


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