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					    Liquid State Machines
             and
      Large Simulations
of Mammalian Visual System


       Grzegorz M. Wójcik
          14 XII 2004
                Introduction
•   Neuron
•   Brain
•   Visual System and Visual Cortex
•   Hodgkin-Huxley Model
•   Liquid State Machine
•   Self Organizing Criticality
•   Results and plans for the future
                  Neuron
• Soma, axon, synapses, dendrites
• Role of ion channels
The Brain
Visual System and Visual Cortex
          Hodgkin-Huxley Model
• Neuron – Set of electric circuits
      dVm ( Em  Vm )                      (Vm  Vm ) (Vm'  Vm )
                                             '           '
   Cm                 [(Ek  Vm )Gk ]       '
                                                                  I inject.
       dt     Rm        k                      Ra          Ra

                                                GNa  g Na m3 h
                                                GK  g K n 4
                                                dm
                                                     m (V )(1  m)   m (V ) m
                                                dt

                                                dh
                                                     h (V )(1  h)   h (V ) h
                                                dt

                                                dn
                                                     n (V )(1  n)   n (V ) n
                                                dt
                  LSM




• LSM – Liquid State Machine (Maass, 2002)
Typical model of VS
   Our Model of Visual System




     „Eye”           „Liquid”       „Readout”
    (Retina)      25 × HHLSM      100 – 2500 HH
100 HH neurons   600 HH neurons      neurons
           SOC Phenomena
• SOC – Self Organizing Criticality
• Lots of complex systems in the Universe
  behave following the exponential law:


                   D( S ) ~ S 

 • We have analyzed the work of different
   readouts from 10x10 to 51x51 neurons
Readout Structure (PVC)
 N20,20   N20,21   N20,22   N20,23   N20,24   N20,25   N20,26   N20,27   N20,28   N20,29   N20,30

 N21,20   N21,22   N21,23   N21,24   N21,25   N21,25   N21,26   N21,27   N21,28   N21,29   N21,30


 N22,20   N22,21   N22,22   N22,23   N22,24   N22,25   N22,26   N22,27   N22,28   N22,29   N22,30


 N23,20   N23,21   N23,22   N23,23   N23,24   N23,25   N23,26   N23,27   N23,28   N23,29   N23,30


 N24,20   N24,21   N24,22   N24,23   N24,24   N24,25   N24,26   N24,27   N24,28   N24,29   N24,30


 N25,20   N25,21   N25,22   N25,23   N25,24   N25,25   N25,26   N25,27   N25,28   N25,29   N25,30


 N26,20   N26,21   N26,22   N26,23   N26,24   N26,25   N26,26   N26,27   N26,28   N26,29   N26,30

 N27,20   N27,21   N27,22   N27,23   N27,24   N27,25   N27,26   N27,27   N27,28   N27,29   N27,30


 N28,20   N28,21   N28,22   N28,23   N28,24   N28,25   N28,26   N28,27   N28,28   N28,29   N28,30


 N29,20   N29,21   N29,22   N29,23   N29,24   N29,25   N29,26   N29,27   N29,28   N29,29   N29,30


 N30,20   N30,21   N30,22   N30,23   N30,24   N30,25   N30,26   N30,27   N30,28   N30,29   N30,30
Avalanches of Spike Potentials
Avalanches of Spike Potentials
Time of Simulation (1 processor)
                          1000000




                           800000
    Simulation Time [s]




                           600000




                           400000




                           200000




                               0
                                    400   600        800          1000   1200
                                                Number of Cells
Time of Simulation (1 processor)
                          1000000

                                                                      33x33
                           800000
    Simulation time [s]




                           600000




                           400000




                           200000




                               0
                                    0.2                  0.6                  1
                                          0.4                          0.8
                                          Probability of exocitosis
Time of Simulation (6 processors)
                      1600000


                                                                  51x51
                      1200000
    Simulation Time




                       800000




                       400000




                            0
                                    0.2                  0.6                1
                                0         0.4                         0.8
                                          Probability of Exocitosis
               Summary
• In the model of primary visual cortex some
  SOC phenomena occur
• They may be connected i.e. with visual
  consciousness
• Parallelization dramatically shortens the
  time of simulation
                  Future Plans
• We are creating more sophisticated model of the
  mammalian visual system
• We will continue on the investigation of SOC phenomena
• Parallel version of GENESIS (for the MPI environment)
  will then be applied
• As a part of CLUSTERIX model we will simulate large
  biological neural networks consisting up to half million
  artificial cells
• This will help us to understand some processes
  occurring in the brain
• GRID tests for numerical solving of nonlinear differential
  equations will be conducted as well
THE END

				
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