File: examples-frompapers_Guetig_Sompolinsky_2009.txt

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.. currentmodule:: brian

.. index::
   pair: example usage; subplot
   pair: example usage; plot
   pair: example usage; run
   pair: example usage; figure
   pair: example usage; show
   pair: example usage; title
   pair: example usage; xticks
   pair: example usage; colors
   pair: example usage; xlabel
   pair: example usage; yticks
   pair: example usage; append
   pair: example usage; axis

.. _example-frompapers_Guetig_Sompolinsky_2009:

Example: Guetig_Sompolinsky_2009 (frompapers)
=============================================

Implementation of the basic model (no speech recognition, no learning) 
described in:
Gutig and Sompolinsky (2009): "Time-Warp-Invariant Neuronal Processing"
PLoS Biology, Vol. 7 (7), e1000141

::

    from brian import *
    
    class TimeWarpModel(object):
        '''
        A simple neuron model for testing the "time-warp invariance" with 
        conductance based or current based synapses. The neuron receives balanced
        excitatory and inhibitory input from a random spike train. The same spike
        train can be fed into the model with different time warps.
        ''' 
        def __init__(self, conductance_based=True):
            '''
            Create a new model with conductance based or current based synapses
            '''
            # Model parameters
            E_e = 5
            E_i = -1
            E_L = 0
            g_L = 1/(100.0*msecond)
            tau_syn = 1*ms
            N_ex = 250
            N_inh = 250
            self.N = N_ex + N_inh
                    
            # Equations
            if conductance_based:
                eqs = '''
                    dV/dt = -(V - E_L) * g_L - I_syn  : 1
                    I_syn = I_ge + I_gi  : second**-1
                    I_ge = (V - E_e) * g_e : second**-1
                    I_gi = (V - E_i) * g_i : second**-1
                    dg_e/dt = -g_e/tau_syn : second**-1
                    dg_i/dt = -g_i/tau_syn : second**-1
                    '''
            else:
                eqs = '''
                    dV/dt = -(V - E_L) * g_L - I_syn  : 1
                    I_syn = -5 * g_e + g_i : second**-1
                    dg_e/dt = -g_e/tau_syn : second**-1
                    dg_i/dt = -g_i/tau_syn : second**-1
                    '''        
            
            # for simpler voltage traces: no spiking
            neuron = NeuronGroup(1, model=eqs, threshold=None)
                
            # every input neuron fires once in a random interval
            self.unwarped_spiketimes = [(i, t * 250 * ms) for i, t in 
                                        zip(range(0, self.N), rand(self.N))]
            
            # final spiketimes will be set in the run function
            self.input = SpikeGeneratorGroup(self.N, [])
                    
            e_input = self.input.subgroup(N_ex)
            i_input = self.input.subgroup(N_inh)        
            e_conn = Connection(e_input, neuron, 'g_e',
                                      weight=6 / (N_ex * tau_syn))
            i_conn = Connection(i_input, neuron, 'g_i',
                                      weight=5 * 6 / (N_ex * tau_syn)) 
            
            # record membrane potential
            self.monitor = StateMonitor(neuron, varname='V', record=True)
    
            # putting everything together
            self.net = Network(neuron, self.input, e_conn, i_conn, self.monitor)
    
        def run(self, beta=1.0):
            ''' 
            Run the network with the original spike train warped by a certain factor
            beta. Beta > 1 corresponds to an extended and beta < 1 to a shrinked
            input spike train.
            '''
            self.net.reinit()
            
            #warp spike train in time        
            self.input.spiketimes = [(i, beta*t) 
                                     for i, t in self.unwarped_spiketimes]        
            self.net.run(beta * 250*ms)
            
            #Return the voltage trace
            return (self.monitor.times, self.monitor[0])
    
    
    if __name__ == '__main__':
        cond_model = TimeWarpModel(True)
        curr_model = TimeWarpModel(False)
        N = cond_model.N    
        
        # #########################################################################
        # Reproduce Fig. 2 from Gütig and Sompolinsky (2009)
        # #########################################################################
        beta = 2.0
        times1, v1 = cond_model.run(beta=1.0)
        times2, v2 = cond_model.run(beta=beta)
        maxtime = 250 * beta
        subplot(4, 1, 1)
        (neurons, times) = zip(*cond_model.unwarped_spiketimes)
        plot(array(times) / ms, neurons, 'g.')
        axis([0, maxtime, 0, N])
        xticks([])
        yticks([])
        title('Time-warp-invariant voltage traces (conductance-based)')
        
        subplot(4, 1, 2)
        plot(times1 / ms, v1, 'g')
        axis([0, maxtime, -1.5, 1.5])
        xticks([])
        yticks([])
        
        subplot(4, 1, 3)
        plot(array(times) * beta / ms, neurons, 'b.')
        axis([0, maxtime, 0, N])
        xticks([])
        yticks([1, 500])
        
        subplot(4, 1, 4)
        plot(times2 / ms, v2, 'b')
        plot(times1 / ms * beta, v1, 'g')
        axis([0, maxtime, -1.5, 1.5])
        xlabel('Time (ms)')
        xticks([0, 250, 500])
        yticks([-1, 1])
        show()
        # #########################################################################
        # Reproduce Fig. 3(C) from Gütig and Sompolinsky (2009), but for random
        # spike trains and not in a speech recognition task
        # #########################################################################
    
        betas = arange(0.2, 3.1, 0.1)
        #betas = array([1.0, 2.0])
        cond_results = []
        curr_results = []
        for beta in betas:
            print 'Testing warp factor %.1f' % beta
            cond_results.append(cond_model.run(beta))
            curr_results.append(curr_model.run(beta))
        
        figure()
        colors = mpl.cm.gist_earth((betas - betas[0]) / (betas[-1] - betas[0]))
        lookup = dict(zip(betas, colors))
        for beta, cond_result, curr_result in zip(betas, cond_results, 
                                                  curr_results):
            times_cond, v_cond = cond_result
            times_curr, v_curr = curr_result 
            subplot(1,2,1)
            plot(times_cond / ms / beta, v_cond, color=lookup[beta])
            axis([0, 250, -1.5, 1.5])
            subplot(1,2,2)
            plot(times_curr / ms / beta, v_curr, color=lookup[beta])
            axis([0, 250, -1.5, 1.5])
        subplot(1,2,1)
        title('conductance based')
        subplot(1,2,2)  
        title('current based')
        show()