1. Tutorial 1

Konrad Kording
What model: Description of Data - No promises about meaning
How Model: Mechanistic Understanding
Why Model: Which things matter, what’s optimized ecologically or evolutionarily

Steinmetz dataset: Neuropixels - rodent is moving on

  1. What Models — Understand the data very well. What is its type, shape? How can I access and load it correctly?

Our dataset is a collection of neuronal activities. It’s an array of arrays of differing shapes representing firing activity for a single neuron. The entries are interspiking times (Floats).

np.ptp()
np.concatenate()

Important observation: Taking an interval of say (5, 15) sec we see that the percentage of neuronal firing in this interval is same as this duration as a percentage of the experiment interval (~0.33% of 2700 sec). This suggests that our interval is representative.

Heavy-Tailed Distributions are seen in neuroscience where a small number of neurons have extremely high number of spikes (>120000) whereas a good percentage is below mean (~8000).

plt.eventplot()

This is used to make a “raster” plot. The histogram in a given interval is a cumulative of a raster plot where each row is summed across.

np.diff()

Finds discrete differences along an array.

What does it mean for a What model to be good? It should describe the data well. Check exponential, linear and inverse fits to the ISI distribution.

2. Tutorial 2

Integrate and Fire (IF) model of neurons. This model is not enough because it doesn’t fit our data quite well. From a “How” perspective we see that it becomes quite regular but this is not what we see in actual physiology.

Leaky Integrate and Fire (LIF) model: Balanced excitation and inhibition. Random number of spikes that increase your voltage and also random spikes that decrease your voltage.

3. Tutorial 3

We want to describe theoretically obtained interspike distribution. We don’t want to describe how the brain does it, but rather why doing it this way is more efficient. “What is the optimal way for a neuron to fire in order to maximize its ability to communicate information?”

If interspike duration was deterministic, no information could be conveyed.

Theorem: Uniform distribution is the distribution with the highest entropy.

Proof: Follows from Jensen’s Inequality. is a concave function. Consider such that But uniform distribution also doesn’t fit. So we reform the optimization problem: “Each neuron can only fire a limited number of times. Energy is required for firing and there is a refractory period.”

The exponential has the highest entropy if the number of firings are constrained.

To convert histogram to PMF, just normalize by the total number of firings.