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Physics 313: Lecture 16 Monday, 10/20/08 Announcements ● ● ● ● Please make an appointment to see me, to choose a project by Friday, October 24. Look at details of the course project http://www.phy.duke.edu/~hsg/313/homeworks/ Start reading Chapter 6 on amplitude equations. Please experiment with the Hopfield and Game of Life programs mentioned in today's lecture. Implications of Potential Dynamics Introducing A Lyapunov Functional As A Conceptual Strategy: The Hopfield Model of Associative Memory: ● ● The physical “state” of a brain is quite complicated: anatomy, channels, connectivity, synaptic strengths, internal dynamics related to genome. Not known how many of these immense details can be ignored or averaged over. Conceptual, often highly simplified models have played important roles in trying to understand brains. Attractor Model of Memory Hopfield Model ● ● ● ● ● ● Replace neurons by simple mathematical abstractions that sum input and switch binary state based on threshold. Connect neurons recursively in all-to-all network. (Real brain is small-world like.) Make strong non-biological assumption of symmetric connectivity matrix Tij that allows Lyapunov functional to be introduced. Algorithm is asynchronous, parallel, and robust. Many interesting analytical and numerical predictions of this model. Implies biological synapses encode how to approach a fixed point, not information itself. Exploring the Hopfield Model http://lcn.epfl.ch/tutorial/english/hopfield/html/index.html ● Does Hopfield network know about symmetries?