Below you'll find the readings suggested for Peter Latham's presentation in class. Note that the papers and presentation covers somewhat more technical material than most of the earlier speakers. However, it's particularly interesting for providing a mathematical framework for testing theories concerning the presence of Hopfield networks in neural circuits by analyzing connectomic data. The presentation is also a good example of the sort of analyses featured in classes that Peter teaches at the Gatsby Institute for Computational Neuroscience Unit at University College London.
There are no slides associated with his presentation since Peter used the white-board for his lecture which is captured in the linked video (VIDEO). The video track is a little choppy; this is due to reducing the video refresh rate to eight frames per second in order to compress the file to a reasonable size while maintaining sufficient resolution so that Peter's writing on the white board is clearly legible. Here are Peter's comments on the linked readings:
PEL: My plan is to spend the first half of the lecture talking about randomly connected networks and Hopfield networks, and the second half on a back-of-the envelope calculation of the kind of connectome data one would need to detect Hopfield-like connectivity.Unfortunately, there aren't really any good papers for the first half, and none that I know of for the second half — thus the delay. However, I found a nice writeup by John Hertz [1] (PDF).
The students should read Chapters 3 and 4. Chapter 4 gets hard, and has more information than they need, so if they can absorb the material up to Eq. (1.42) I would be happy.
Optional papers are two of mine. I'm guessing reading the whole papers would be far too time consuming, so I'm providing the relevant sections:
Theory of randomly connected networks [3] (PDF). Read Results (p. 813), up to "Effect of adaptation on firing patterns" (p. 816).
Realistic Hopfield networks [2] (PDF). Read up to Eq. 2.5, and Appendix A.