% This function estimates the steady state distribution by time frame expansion technique for the T cell network.
% INPUT: 
%		threshold value: when the norm of the difference of the two adjancent distribution vectors are  below this value, then the loop will be broken;
%       M: the stochastic sequence length, e.g. M = 10000; 
%       p: the perturbation probability, e.g. p = 0.01;    
%          when there is no perturbation, p = 0. 
% OUTPUT: 
%       Output: The state distribution of the network for all the clock cycles.
%		Also state distributions of the last three clock cycles (t=period-2, t=period-1 and t=period) are plotted.
% Copyright @ The authors, 2012.


function Output = time_frame_expansion(threshold,M,p)

tic

%%   initialization

n = 12;          % gene numbers

Output1=zeros(1,2^n);
Output2=zeros(1,2^n);
Output3=ones(1,2^n);

%% time frame expansion


gn = zeros(2,n,M);

gn(1,1,:)=ones(1,M);
gn(1,7,:)=ones(1,M);
gn(1,8,:)=ones(1,M);
gn(1,10,:)=ones(1,M);
gn(1,11,:)=ones(1,M);

gup = zeros(1,n,M);
gdown = zeros(1,n,M);

period=0;
while (norm(Output1-Output2,2)>threshold)|(norm(Output2-Output3,2)>threshold)
    period=period+1
    
    norm(Output1-Output2,2)
    norm(Output2-Output3,2)
    
    Output3=Output2;
    Output2=Output1;
    Output1=zeros(1,2^n);
    
% generation of controlling sequences for muxes. It should be noted that in every time frame, the stochastic sequences for the muxes should be generated independently.
    e2=randomsequence(1,M,500);

    e6=randomsequence(1,M, 63);

    e9=randomsequence(1,M,500);


e110=zeros(1,1,M);
e111=zeros(1,1,M);
    
    while sum(e110)~=148;
        jj=int32(1+(length(e110)-1)*rand);
        e110(jj)=1;
        e111(jj)=1;
    end

    while sum(e110)~=(148+370);
        ii = int32(1+(length(e110)-1)*rand);
        if e110(ii)~=1
            e110(ii)=1;
        else
        end
    end
   
     while sum(e111)~=(148+185);
        ii = int32(1+(length(e111)-1)*rand);
        if or(e110(ii),e111(ii))~=1 
            e111(ii)=1;
        else
        end
    end
    
 
 
 % description of the network
    gup(1,1,:) = not(gn(1,6,:));

    f21 = or ( gn(1,3,:), gn(1,6,:) );
    f22 = or ( gn(1,2,:), gn(1,6,:) );
    gup(1,2,:) = mux2(f21,f22,e2);
  
    gup(1,3,:) = gn(1,2,:);
    
    gup(1,4,:) = not(gn(1,2,:));
    
    gup(1,5,:) = not(gn(1,3,:));

    
    f61 = and(not(gn(1,10,:)),or(or(gn(1,1,:),gn(1,9,:)),or(gn(1,11,:),gn(1,12,:))));
    f62 = not(gn(1,10,:));
    gup(1,6,:) = mux2(f61,f62,e6);
    

    gup(1,7,:) = gn(1,3,:);
    
    gup(1,8,:) = not(gn(1,5,:));
    
    f91 =  or(gn(1,4,:),gn(1,12,:));
    f92 =  or ( gn(1,5,:), gn(1,12,:) );
    gup(1,9,:) = mux2(f91,f92,e9);
    
    gup(1,10,:) = gn(1,11,:);
    
    f111 =  not(gn(1,6,:));     %%% 0.297
    f112 =  and(not(gn(1,6,:)), or ( gn(1,7,:), not(or(gn(1,4,:),gn(1,5,:))) ));   %%% 0.185
    f113 =  and ( not(or(gn(1,4,:),gn(1,5,:))), not(gn(1,6,:)) );                %%%    0.37
    f114 =  and (not(gn(1,6,:)),  gn(1,7,:));%0.148
    gup(1,11,:)  = mux4(f111,f112,f113,f114, e110, e111);
  
    gup(1,12,:)  = not(gn(1,8,:));
   
    
%% perturbation
    
   ee1=randomsequence(1,M,M*p);
   ee2=randomsequence(1,M,M*p);
   ee3=randomsequence(1,M,M*p);
   ee4=randomsequence(1,M,M*p);
   ee5=randomsequence(1,M,M*p);
   ee6=randomsequence(1,M,M*p);
   ee7=randomsequence(1,M,M*p);
   ee8=randomsequence(1,M,M*p);
   ee9=randomsequence(1,M,M*p);
   ee10=randomsequence(1,M,M*p);
   ee11=randomsequence(1,M,M*p);
   ee12=randomsequence(1,M,M*p);


    
   gdown(1,1,:) = xor(gn(1,1,:),ee1);
   gdown(1,2,:) = xor(gn(1,2,:),ee2);
   gdown(1,3,:) = xor(gn(1,3,:),ee3);
   gdown(1,4,:) = xor(gn(1,4,:),ee4);
   gdown(1,5,:) = xor(gn(1,5,:),ee5);
   gdown(1,6,:) = xor(gn(1,6,:),ee6);
   gdown(1,7,:) = xor(gn(1,7,:),ee7);
   gdown(1,8,:) = xor(gn(1,8,:),ee8);
   gdown(1,9,:) = xor(gn(1,9,:),ee9);
   gdown(1,10,:) = xor(gn(1,10,:),ee10);
   gdown(1,11,:) = xor(gn(1,11,:),ee11);
   gdown(1,12,:) = xor(gn(1,12,:),ee12);
   
   sel = or(or(or(or(or(or(or(or(or(or(or(ee1,ee2),ee3),ee4),ee5),ee6),ee7),ee8),ee9),ee10),ee11),ee12);
   gn(2,1,:) = mux2(gup(1,1,:),gdown(1,1,:),sel);
   gn(2,2,:) = mux2(gup(1,2,:),gdown(1,2,:),sel);
   gn(2,3,:) = mux2(gup(1,3,:),gdown(1,3,:),sel);
   gn(2,4,:) = mux2(gup(1,4,:),gdown(1,4,:),sel);
   gn(2,5,:) = mux2(gup(1,5,:),gdown(1,5,:),sel);
   gn(2,6,:) = mux2(gup(1,6,:),gdown(1,6,:),sel);
   gn(2,7,:) = mux2(gup(1,7,:),gdown(1,7,:),sel);
   gn(2,8,:) = mux2(gup(1,8,:),gdown(1,8,:),sel);
   gn(2,9,:) = mux2(gup(1,9,:),gdown(1,9,:),sel);
   gn(2,10,:) = mux2(gup(1,10,:),gdown(1,10,:),sel);
   gn(2,11,:) = mux2(gup(1,11,:),gdown(1,11,:),sel);
   gn(2,12,:) = mux2(gup(1,12,:),gdown(1,12,:),sel);
   
    
    
%% compute the distribution at each time point    
      for k = 1:M
        
        j = 1;
        
        for kkk = 1:n
            
           j = j + gn(2,kkk,k)*2^(kkk-1);  
              
        end
        Output1(j) = Output1(j) + 1/M;
      end

      gn(1,:,:)=gn(2,:,:);
   
end
figure;
hold on;
    subplot(3,1,1) 
    stem([1:4096],Output1);
    subplot(3,1,2) 
    stem([1:4096],Output2);
    subplot(3,1,3) 
    stem([1:4096],Output3);

Output=Output3;
toc

end

function c=randomsequence(c1,c2,c3)      % randomsequence sequence generator
  
c=zeros(1,c1,c2);
  
  irandom=0;
  
  while irandom ~= c3
      x=int32(1+(length(c)-1)*rand);
      if c(x)~=1
         c(x)=1;
         irandom=irandom+1;
      end
  end
end