Dear Students,
welcome to the next lecture of Biological Modeling of Neural Networks.
We will touch two different topics today.
1. I have tried to insist in previous weeks that the mathematical tools of theoretical biology that we use in the class on Neural Networks are rather generic and can be applied to different fields. In fact there is a tight relation between dynamics of recurrent neural networks and dynamics of spreading of infectious diseases in networks of people.
I would encourage those who have not yet done so to have a look
at the lecture
https://drive.switch.ch/index.php/s/fIkyRGPbepHOoDc
The math that is applied in this lecture is the math of phase plane analysis, dynamics systems, and stability of fixed points. However, in the background of the SIR model that is discussed in the lecture, there is also the math of mean-field analysis that will be the topic of the lectures of NEXT week. And mean-field is also in the background of the Hopfield model that we discuss today as a second topic (even though I do not call it mean-field yet ... wait for next week to see the connections.
On the moodle the video lecture on epidemics is hosted in the week starting March 16.
The video is also linked to miniproject 2 (on epidemic networks). The first part of miniproject 2 comes as a graded theory exercise, see previous post of Valentin Schmutz.
2. We continue our discussion of the Hopfield model and attractor networks. The model of last is generalized in several directions. Instead of neurons that are deterministic binary switches, we generalize to neurons with a certain degree of stochasticity. We introduce the picture of an energy landscape and discuss its limitations. We then generalize to patterns which are no longer balanced with 50 percent plus and 50 percent minus, but have a much lower degree of activity. And finally we also discuss the transition to spiking neurons
I hope you will enjoy the lectures.
Exercise sessions again with slack as the basis for individual zoom interactions,
Let's get started!
Wulfram Gerstner
