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

LSM LSM – Liquid State Machine (Maass, 2002)

Typical model of VS

Our Model of Visual System „Readout” 100 – 2500 HH neurons „Liquid” 25 × HHLSM 600 HH neurons „Eye”(Retina) 100 HH neurons

SOC Phenomena SOC – Self Organizing Criticality Lots of complex systems in the Universe behave following the exponential law: We have analyzed the work of different readouts from 10x10 to 51x51 neurons

Readout Structure (PVC) N 20,20 N 20,21 N 20,22 N 20,23 N 20,24 N 20,25 N 20,26 N 20,27 N 20,28 N 20,29 N 20,30 N 21,20 N 21,22 N 21,23 N 21,24 N 21,25 N 21,26 N 21,27 N 21,28 N 21,29 N 21,30 N 22,20 N 22,21 N 22,22 N 22,23 N 22,24 N 22,25 N 22,26 N 22,27 N 22,28 N 22,29 N 22,30 N 23,20 N 23,21 N 23,22 N 23,23 N 23,24 N 23,25 N 23,26 N 23,27 N 23,28 N 23,29 N 23,30 N 24,20 N 24,21 N 24,22 N 24,23 N 24,24 N 24,25 N 24,26 N 24,27 N 24,28 N 24,29 N 24,30 N 25,20 N 25,21 N 25,22 N 25,23 N 25,24 N 25,25 N 25,26 N 25,27 N 25,28 N 25,29 N 25,30 N 26,20 N 26,21 N 26,22 N 26,23 N 26,24 N 26,25 N 26,26 N 26,27 N 26,28 N 26,29 N 26,30 N 27,20 N 27,21 N 27,22 N 27,23 N 27,24 N 27,25 N 27,26 N 27,27 N 27,28 N 27,29 N 27,30 N 28,20 N 28,21 N 28,22 N 28,23 N 28,24 N 28,25 N 28,26 N 28,27 N 28,28 N 28,29 N 28,30 N 29,20 N 29,21 N 29,22 N 29,23 N 29,24 N 29,25 N 29,26 N 29,27 N 29,28 N 29,29 N 29,30 N 30,20 N 30,21 N 30,22 N 30,23 N 30,24 N 30,25 N 30,26 N 30,27 N 30,28 N 30,29 N 30,30

Avalanches of Spike Potentials

Time of Simulation (1 processor)

33x33

Time of Simulation (6 processors) 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