# 8.7 Mathematical modeling of hippocampal spatial memory with place

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This report summarizes work done as part of the Modeling Spatial Memory with Place Cells PFUG under Rice University's VIGRE program. VIGRE is a program of Vertically Integrated Grants for Research and Education in the Mathematical Sciences under the direction of the National Science Foundation. A PFUG is a group of Postdocs, Faculty, Undergraduates and Graduate students formed round the study of a common problem. This work was studied in the Rice University VIGRE program in the Summer of 2011. In this module, we mathematically model Kneirim's Double Rotation Experiment with a model given by Cox and Gabbiani and analytically discuss the relation between overlapping place fields and synaptic input weights.

## Biology

Spatial memory is what allows us to keep track of our location in space by making mental maps of each environment. Let's consider what happens in the brain during the process of forming these internal maps.

Connections, called synapses, between certain neurons strengthen or weaken–a process known as synaptic plasticity. The strength, or weight, of a synapse controls how much one neuron can affect another. Synaptic plasticity is necessary for memory formation [link] .

While many neurons are involved with spatial memory, our focus is upon neurons in the hippocampus called place cells [link] . Place cells have a unique firing pattern. When an environment becomes familiar, each place cell becomes associated with one area of the environment. In other words, after repeated exposure to one environment, a place cell will come to spike in only one area of the environment, which is called that cell's place field [link] . See [link] .

Due to place cells' characteristic firing pattern where a cell has a single place field in each environment, it is easy to test if a rat recognizes the environment they have been placed in by examining place cell activity.

## Motivation: double rotation experiment

Our research on place cells is based off of the Double Rotation Experiment (DRE) conducted by our collaborator Dr. Knierim [link] .

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research.net
kanaga
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
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Daniel
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Maciej
Abigail
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Anassong
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NANO
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are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
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Damian
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Tarell
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Virgil
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CYNTHIA
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NANO
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Harper
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s.
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for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
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Cied
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Cied
types of nano material
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Porter
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Porter
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Yasmin
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Cesar
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Uday
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Berger describes sociologists as concerned with
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