Physics 313: Lecture 16
Monday, 10/20/08
Announcements
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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:
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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
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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
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Does Hopfield network know about symmetries?