User:Jrm228/Model Plan

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Table 1: State Variables

Variable Description Initial Value
v membrane potential Example
u membrane recovery variable Example

Table 2: Dependent Variables

Variable Description Default Value RS IB CH FS LTS RZ
a timescale of membrane recovery variable 0.02 0.02 0.02 0.02 0.1 0.02 0.1
b sensitivity of recovery variable to fluctuations in membrane potential 0.2 0.2 0.2 0.2 0.2 0.25 0.25
c after-spike reset value of potential -65 mV -65 mV -55 mV -50 mV -65 mV -65 mV -65 mV
d after-spike reset value of recovery 2 8 4 2 2 2 2

Table 3: Independent Variables

Variable Description Value
t time 0-1 seconds
  • Note: RS: Regular Spiking; IB: Intrinsically bursting; CH: Chattering; FS: Fast Spiking; LTS: Low Threshold Spiking; RZ: Resonator.

Hypothesis: Our paper hypothesizes that the minimum number of inhibitory neurons necessary in the model to prevent the network of 1000 randomly coupled spiking neurons from ever reaching a spike is between 250 and 300 inhibitory neurons.

To test our hypothesis, we shall need to first demonstrate an accurate model of a single neuron under regular firing conditions for the values of the dependent variables a, b, c, and d, as shown in Table 2. Next, we will demonstrate that the model remains accurate for the other five types of firing neurons by generating graphs to compare to Figure 2. Then we shall produce Figure 3 by altering our model for 1000 neurons, and make it possible to randomly select what type of firing neurons they are. Finally, we shall alter our model to make it a Manipulate with the number of inhibitory cortical cells out of the 1000 being the changing variable, and determine the point where the spikes no longer occur in our selected time window of 1 second.

Our timetable list out the remaining class days, with daily goals to be completed by the next class period. The intermediate goals and calculations are also part of the schedule;

  • March 23
    • Outline the necessary components of the model
    • Outline Benchmark 1: Introduction
    • Write Benchmark 1: Introduction
  • March 28 (Benchmark 1: Introduction due)
    • Create an accurate model of an individual neuron with the paper's equation
    • Replicate a graph from the paper in Figure 1 using DSolve and the model
    • Outline Model Description
  • March 30
    • Write Model Description
  • April 4 (Benchmark 2: Model Description due)
    • Edit model to accept different values for the dependent variables through
  • April 6
    • Replicate remaining graphs from the paper in Figure 1 using the new model
  • April 11
    • Edit model to randomly choose 1000 neuron types and graph
  • April 13
    • Replicate Figure 3 from paper
    • Outline Benchmark 3: Results
    • Write Benchmark 3: Results
  • April 18 (Benchmark 3: Results due)
    • Extend model to manipulate the random nature by selecting the number of inhibitory neurons and by use of the Manipulate function
  • April 20
    • Outline Benchmark 4: Discussion
    • Write Benchmark 4: Discussion
  • April 25 (Benchmark 4: Discussion due)
    • Create new graph that shows the result of the manipulate function
    • Analyze and interpret the new figure to determine the state of our hypothesis
    • Comment on other students Discussions and learn from their work (EC)
  • April 27
    • Present findings to class (EC)
    • Write Final Paper
  • May 1
    • Turn in Final Draft of Paper