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8.7 Mathematical modeling of hippocampal spatial memory with place  (Page 31/6)

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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.

Background: place cells in the hippocampus

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] .

The place field of one place cell. As a rat explored the square environment, experimenters monitored the activity of one place cell.ÊThe black line is the rat's trajectory, and each red dot represents a location that the place cell has become active. The place field of the particular place cell that was monitored is the area of the environment marked densely by red dots [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] .

The Double Rotation Experiment (DRE). Rats were trained to walk clockwise around the track, and the place fields corresponding to specific locations on the track were monitored. During the learning phase, the place fields experienced a backward shift. During double rotation runs of the experiment, the local cues were rotated backward (counterclockwise), and the place fields shifted backward as well. Thus the place fields seemed to favor following the local cues. Perhaps the natural backward shift seen in the learning phase predisposes the place fields to wanting to follow cues that move backwards [link] .

Questions & Answers

what does the ideal gas law states
Joy Reply
Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
Kate Reply
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Kate Reply
what is the change in momentum of a body?
Eunice Reply
what is a capacitor?
Raymond Reply
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
Maria Reply
please solve
Sharon
8m/s²
Aishat
What is Thermodynamics
Muordit
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
Saheed Reply
50 m/s due south east
Someone
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
Ramon Reply
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
Someone
definitely of physics
Haryormhidey Reply
how many start and codon
Esrael Reply
what is field
Felix Reply
physics, biology and chemistry this is my Field
ALIYU
field is a region of space under the influence of some physical properties
Collete
what is ogarnic chemistry
WISDOM Reply
determine the slope giving that 3y+ 2x-14=0
WISDOM
Another formula for Acceleration
Belty Reply
a=v/t. a=f/m a
IHUMA
innocent
Adah
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
Nassze Reply
how do lnternal energy measures
Esrael
Two bodies attract each other electrically. Do they both have to be charged? Answer the same question if the bodies repel one another.
JALLAH Reply
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you. Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Robert
like charges repel while unlike charges atttact
Raymond
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Source:  OpenStax, The art of the pfug. OpenStax CNX. Jun 05, 2013 Download for free at http://cnx.org/content/col10523/1.34
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