?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.title=The+number+of+synaptic+inputs+and+the+synchrony+of+large+sparse+neuronal+networks&rft.creator=Golomb%2C+David&rft.creator=Hansel%2C+David&rft.subject=Computational+Neuroscience&rft.subject=Neural+Modelling&rft.subject=Neural+Modelling&rft.subject=Neurophysiology&rft.description=The+prevalence+of+coherent+oscillations+in+various+frequency+ranges+in+the+central+nervous+system+raises+the+question+of+the+mechanisms+that+synchronize+large+populations+of+neurons.+We+study+synchronization+in+models+of+large+networks+of+spiking+neurons+with+random+sparse+connectivity.+Synchrony+occurs+only+when+the+average+number+of+synapses%2C+M+that+a+cell+receives+is+larger+than+a+critical+value%2C+%24M_c%24.+Below+%24M_c%24%2C+the+system+is+in+an+asynchronous+state.+In+the+limit+of+weak+coupling%2C+assuming+identical+neurons%2C+we+reduce+the+model+to+a+system+of+phase+oscillators+which+are+coupled+via+an+effective+interaction%2C+%24%5CGamma%24.+In+this+framework%2C+we+develop+an+approximate+theory+for+sparse+networks+of+identical+neurons+to+estimate+%24M_c%24+analytically+from+the+Fourier+coefficients+of+%24%5CGamma%24.+Our+approach+relies+on+the+assumption+that+the+dynamics+of+a+neuron+depend+mainly+on+the+number+of+cells+that+are+presynaptic+to+it.+We+apply+this+theory+to+compute+%24M_c%24+for+the+integrate-and-fire+(%5CIF)+model+as+a+function+of+the+intrinsic+neuronal+properties+(%5Ceg+the+refractory+period+%24T_r%24)%2C+the+synaptic+time+constants+and+the+strength+of+the+external+stimulus%2C+%24%5CIapp%24.+When+the+neurons+are+inhibitory%2C+%24M_c%24+is+found+to+be+non-monotonous+with+the+strength+of+%24%5CIapp%24.+For+%24T_r%3D0%24%2C+we+estimate+the+minimum+value+of+%24M_c%24+over+all+the+parameters+of+the+model+to+be+%24363.8%24.+Above+%24M_c%24%2C+the+neurons+tend+to+fire+in%3A+1)+smeared+one+cluster+states+at+high+firing+rates+and+2)+smeared+two+or+more+cluster+states+at+low+firing+rates.+For+excitatory+interactions+synchrony+can+be+achieved+only+if+the+firing+rate+is+not+too+high.+However%2C+our+estimates+of+%24M_c%24+are%2C+in+general%2C+much+smaller+than+for+inhibitory+networks+for+similar+level+of+activity.+Above+%24M_c%24+excitatory+networks+settle+into+smeared+1-cluster+states.Refractoriness+decreases+%24M_c%24+at+intermediate+and+high+firing+rates.+These+results+are+compared+against+numerical+simulations.+We+show+numerically+that+systems+with+different+sizes%2C+%24N%24%2C+behave+in+the+same+way+provided+the+connectivity%2C+%24M%24%2C+is+such+a+way+that+%241%2F+%5CMeff+%3D+1+%2F+M+-+1+%2F+N%24+remains+constant+when+%24N%24+varies.+This+allows+one+to+extrapolate+the+large+%24N%24+behavior+of+a+network+from+numerical+simulations+of+networks+of+relatively+small+sizes+(%24N%3D800%24+in+our+case).+We+find+that+our+theory+predicts+with+remarkable+accuracy+the+value+of+%24M_c%24+and+the+patterns+of+synchrony+above+%24M_c%24%2C+provided+the+synaptic+coupling+is+not+too+large.+We+also+study+the+strong+coupling+regime+of+inhibitory+sparse+networks.+All+of+our+simulations+demonstrate+that+increasing+the+coupling+strength+reduces+the+level+of+synchrony+of+the+neuronal+activity.+Above+a+critical+coupling+strength%2C+the+network+activity+is+asynchronous.+We+point+out+that+there+is+a+fundamental+limitation+for+the+mechanisms+of+synchrony+relying+on+inhibition+alone%2C+if+heterogeneities+in+the+intrinsic+properties+of+the+neurons+and+spatial+fluctuations+in+the+external+input+are+also+taken+into+account.&rft.date=1999-05&rft.type=Preprint&rft.type=NonPeerReviewed&rft.format=application%2Fpostscript&rft.identifier=http%3A%2F%2Fcogprints.org%2F83%2F2%2Fsy28_4.ps&rft.identifier=++Golomb%2C+David+and+Hansel%2C+David++(1999)+The+number+of+synaptic+inputs+and+the+synchrony+of+large+sparse+neuronal+networks.++%5BPreprint%5D++++(Unpublished)++&rft.relation=http%3A%2F%2Fcogprints.org%2F83%2F