liquid state machines and large simulations of mammalian visual system grzegorz m. wójcik 14 xii...
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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
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LSM
• LSM – Liquid State Machine (Maass, 2002)
Typical model of VS
Our Model of Visual System
„„Readout”Readout”100 – 2500 HH 100 – 2500 HH
neuronsneurons
„„Liquid”Liquid”25 × HHLSM25 × HHLSM
600 HH 600 HH neuronsneurons
„„Eye”Eye”(Retina)(Retina)100 HH 100 HH neuronsneurons
SOC Phenomena
• SOC – Self Organizing Criticality• Lots of complex systems in the Universe
behave following the exponential law:
SSD ~)(
• 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)
400 600 800 1000 1200N um ber o f C e lls
0
200000
400000
600000
800000
1000000
Sim
ula
tion
Tim
e [s
]
Time of Simulation (1 processor)
0.4 0.80.6 10.2
Probab ility o f exocitosis
0
200000
400000
600000
800000
1000000
Sim
ulat
ion
time
[s]
33x33
Time of Simulation (6 processors)
0 0.4 0.80.2 0.6 1
P robab ility o f Exocitos is
0
400000
800000
1200000
1600000
Sim
ulat
ion
Tim
e
51x51
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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