How to Make a Computer Think for You Jeff Knisley, The Institute for Quantitative Biology, East Tennessee State University ALABAMA MAA STATE DINNER AND LECTURE, Feb, 2006 Soma Dendrites Synapses Axon This is a Neuron Signals Propagate from Dendrites to Soma Signals Decay at
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Jeff Knisley, The Institute for Quantitative Biology, East Tennessee State University
ALABAMA MAA STATE DINNER AND LECTURE, Feb, 2006
AxonThis is a Neuron
Signals Propagate from
Dendrites to Soma
Signals Decay at
Soma if below a
If threshold exceeded,
then neuron “fires,”
sending a signal
along its axon.
Choose ith neuron at random and calculate its new stateHopfield Network
wij between ith
and jth neurons
Blue = 1
White = 0
Define the energy to be
Theorem: If the weights are symmetric, then the Energy
decreases each time a neuron fires.
The output layer may
consist of a single
(is usually much larger)
This tiny 3-Dimensional
Artificial Neural Network,
modeled after neural networks
in the human brain, is helping
machines better visualize
8Illustration: Colors = Terrains
we have a
0Train ANN to Classify Colors
Input OutputTerrain <R,G,B>
“No luck, so I’m a water forager.”
“I’m so good at getting water, I think I should go forage for pulp.”
“I have water!”
x1 = Gene 1
x2 = Gene 2
xn = Gene n
The output is the “physiological state” due to the relative gene expression levels used as inputs.
Separation using Hyperplanes
Remaining genes are most important in classifying experimentals versus controls
ajcorrespond to genes,
but do not directly depend
on a single gene.
Cybenko, G. Approximation by Superpositions of a sigmoidal function, Mathematics of Control, Signals, and Systems, 2(4),1989, p. 303-314.
De Freitas J. F. G., et. al. Sequential Monte Carlo Methods To Train Neural Network Models. Neural Computation, Volume 12, Number 4, 1 April 2000, pp. 955-993(39)
L. Glenn and J. Knisley, Solutions for Transients in Arbitrarily Branching and Tapering Cables, Modeling in the Neurosciences: From Biological Systems to Neuromimetic Robotics, ed. Lindsay, R., R. Poznanski, G.N.Reeke, J.R. Rosenberg, and O.Sporns, CRC Press, London, 2004.
A. Narayan, et. al Artificial Neural Networks for Reducing the Dimensionality of Gene Expression Data. Neurocomputing, 2004.