function [ws,wa] = hebb_trace(nn,sig)
 % self organization of idiothetic connections
   lrate=1;     % learning rate
   ws=zeros(nn); wa=zeros(nn,nn,2);
   r_trace=0; eta=0.9;

   %%%%%%% learning session
   for loc=1:nn; % counter-clockwise rotation
      r=in_signal_pbc(loc,1,sig,nn);
      r_trace=eta*r_trace+(1-eta)*r;
      dws=lrate.*r*r';
      dwa(:,:,1)=lrate.*r*r_trace';
      dwa(:,:,2)=0;
      ws=ws+dws;
      wa=wa+dwa;
   end
   r_trace=0; eta=0.9;
   for loc=nn:-1:1; % clockwise rotation
      r=in_signal_pbc(loc,1,sig,nn);
      r_trace=eta*r_trace+(1-eta)*r;
      dws=lrate.*r*r';
      dwa(:,:,1)=0;
      dwa(:,:,2)=lrate.*r*r_trace';
      ws=ws+dws;
      wa=wa+dwa;
   end
 return