The Mines of Moria (It’s a deep dark place where bad things happened) Ocular Dominance Araya, Joy,...
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Transcript of The Mines of Moria (It’s a deep dark place where bad things happened) Ocular Dominance Araya, Joy,...
The Mines of Moria(It’s a deep dark place where bad things happened)
Ocular Dominance
Araya, Joy, and Angela
Visual information is transmitted from cells in the retina to cells in the visual cortex.
Cells in the visual cortex receive nerve terminals from both right and left eyes.
Competition occurs between the right synapses and the left synapses such that there exists spatial bands of cells responding to the right eyes interlacing with bands of cells responding to the left eyes. This is called the Ocular Dominance Column.
Introducing the Question
The Rule Interaction between same-eye-type synapses is stimulatory
within the radius of 200 m.
Interaction between different-eye-type synapses is inhibitory within the radius of 200 m.
Interaction between same-eye-type synapses is inhibitory with the radius of 200-600 m.
Interaction between different-eye-type synapses is stimulatory with the radius of 200-600 m.
The Difference EquationRandomize initial condition for each cells
So..
cell’s state (t+1) := cell’s state (t) + change
Let Rn = fraction of the right synapses
So, Ln = fraction of the left synapses
= 1 - Rn
Defining Change
The “change” depends on – The state of the neighboring cells
• Random initialization
– The distance of the neighboring cells from the cell of interest.
• …. Using the Mexican Hat Function
The Mexican Hat FunctionThis is the 2nd derivative of the Gaussian
distribution with =0 and =20.
80022800
2222
630033239835.0329593425.1
kaka
ekae
Cellular Automata Simulator
Made minor modifications to Tomas’ CA simulator for Maple
‘MexFlat’ placeholder
It Worked!!!
Beautiful striped pattern as excepted
Right result – Wrong reason– We’re still using our ‘MexFlat’
placeholder function
Incorporating MexHat
Right Reason, Wrong Result– No more stripes, everything to one
state
Right Tool, Right Result – The problem was lack of
computational power– Took too long to run a large enough
simulation– Neighborhood size of 81 cells