Learning how and why crossover happens.

[bcipolli]

In order to better control interactions between tasks and networks, we've needed to understand relationships between crossover frequencies and: # connections, image size. We hoped these would be consistent and smoothly varying.

Here, I made code changes that enabled this. Indeed, the interactions are smooth. I found:

• when you increase # connections, peaks & crossover shifts right (lower frequencies).
• when you increase image size (keep same cpi & sigma), crossover shift left (higher frequencies)

These are not surprises; we know that as the connection density decreases, the curve flattens and raises, so interactions push right (lower frequencies).

A few key code changes:

• Update crossover computation to handle multiple crosses
• Update crossover computation to interpolate (linearly) where the crossing actually happened (between the measured frequencies).
• Migrate code to be more consistent with what's in the core de code:
  • Use de_MakeDataset('gratings'), instead of the raw mfe_gratings call.
  • Don't do input normalization (was done in multiple places)

Some supporting figures:

[bcipolli]

@vishaalprasad I did this by running different sizes one at a time, tweaking nConns to see how things varied. Then moving up to the next image size, etc.

[vishaalprasad]

All the changes look good to me. The only concern is with the way multiple crossover points are being detected.