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EGR 183: Modeling Neural Networks  in silico Dr. Needham - Fall 2007 Daniel Calrin B.S.E. Daniel Cook Joshua Mendoza-Elias
Background: Neurons
Background: LTP and LTD ,[object Object]
Background continued: ,[object Object]
Short-term and Long-term Effects
The Basis of Hebbian Learning
Foundation for our Computer Model
Types of Neuron Inhibitory Neurons Input Neuron Output Neuron Neuron is voltage-clamped, presynaptic to all neurons in model Inhibitory neurons depress post-synaptic neurons Excitatory Neurons Average firing rates solved at each time step Learning rule determines change in synaptic strength inhibitory synapse excitatory synapse Key: 1 2 3 4 α  =  - 1 4
Synaptic strengths 1.0 1.0 t=t 0 t=t 0+1 + α In phase Out of phase + α Two neurons are firing full-speed: Strengths increase by factor of alpha 1.0 0.0 - β One neuron v i  is firing but v j  is not: Strengths decrease by factor of beta - β v i v j v i v j v i v j v i v j
Inhibitory Neurons t=t 0 t=t 0+1 Excitatory Inhibitory = ...+ w i,j v i  +... = ...- w i,j v i  +... An inhibitory neuron v i  is firing, depressing the post-synaptic neuron Weighted v i  is summed negatively into v j  Weighted v i  is summed positively into v j  An excitatory neuron v i  is firing, potentiating the post-synaptic neuron v i v j v j v i v i v j v i v j
[object Object],[object Object],Results
Phase components ,[object Object],Input Neuron Output Neuron Convergence In phase component Out of phase component time firing rate
Output Neuron Maxima & Minima Local max  near  minimum Local min  near  maximum Maximum at  maximum time firing rate Input Neuron
Further developments ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Biological parallel with  In Silico Starvoytov  et al.  2005 Light-drected stimulation of neurons on silicon wafers.  J Neurophysiol   93 : 1090-1098.
LDS in concert with Computer Simulation ,[object Object],[object Object],[object Object],[object Object]

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EGR 183 Final Presentation

  • 1. EGR 183: Modeling Neural Networks in silico Dr. Needham - Fall 2007 Daniel Calrin B.S.E. Daniel Cook Joshua Mendoza-Elias
  • 3.
  • 4.
  • 6. The Basis of Hebbian Learning
  • 7. Foundation for our Computer Model
  • 8. Types of Neuron Inhibitory Neurons Input Neuron Output Neuron Neuron is voltage-clamped, presynaptic to all neurons in model Inhibitory neurons depress post-synaptic neurons Excitatory Neurons Average firing rates solved at each time step Learning rule determines change in synaptic strength inhibitory synapse excitatory synapse Key: 1 2 3 4 α = - 1 4
  • 9. Synaptic strengths 1.0 1.0 t=t 0 t=t 0+1 + α In phase Out of phase + α Two neurons are firing full-speed: Strengths increase by factor of alpha 1.0 0.0 - β One neuron v i is firing but v j is not: Strengths decrease by factor of beta - β v i v j v i v j v i v j v i v j
  • 10. Inhibitory Neurons t=t 0 t=t 0+1 Excitatory Inhibitory = ...+ w i,j v i +... = ...- w i,j v i +... An inhibitory neuron v i is firing, depressing the post-synaptic neuron Weighted v i is summed negatively into v j Weighted v i is summed positively into v j An excitatory neuron v i is firing, potentiating the post-synaptic neuron v i v j v j v i v i v j v i v j
  • 11.
  • 12.
  • 13. Output Neuron Maxima & Minima Local max near minimum Local min near maximum Maximum at maximum time firing rate Input Neuron
  • 14.
  • 15. Biological parallel with In Silico Starvoytov et al. 2005 Light-drected stimulation of neurons on silicon wafers. J Neurophysiol 93 : 1090-1098.
  • 16.