Physics 313: Lecture 15
Wednesday, 10/15/08
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.
Read John Hopfield's 1982 paper
http://www.phy.duke.edu/~hsg/313/protected/
hopfield-pnas-82.pdf
More on Lyapunov Functionals
What is nonlinear term in the evolution equation
associated with the following 4th-order term in the
Lyapunov functional:
Introducing A Lyapunov Functional As A
Conceptual Strategy:
The Hopfield Model of Associatve Memory:
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The physical “state” of a brain is quite complicated:
channels, anatomy, connectivity, synaptic
strengths, internal dynamics related to genome.
Not known how many of these details can be
ignored or averaged over.
Conceptual rather abstract models have played
important role in trying to understand brains.
Neurons: Complicated Electrically
Excitable Cells
Songbird HVC Neurons
Brains Compute By Opening
Holes in Membranes
Intracellular Recordings of Projection
Neurons in a Non-behaving Locust
Laurent Group, Neuron 30:569 (2001)
Listen To Neurons During Behavior
Luo, Fee, Katz, Science 299:1196-1201 (2003)
Neurons Connect Via Excitatory or Inhibitory
Complex Nanomachines Called Synapses
Memory and learning achieved here!
Cell A
Capillary
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Cell B
Graham Knott
5µ m
Connectivity Does Not Determine Functionality
1 mm long
C. elegans adult has 959 cells, of which 302 are neurons, each distinct. These connect
via 5,000 chemical synapses, 600 gap junctions, 2,000 neuromuscular junctions.
Functionality not
known because
dynamics not
known, neurons
too small to
penetrate with an
electrode.
http://www.wormatlas.org