% plotBEModeCurves b=1; % basal branching rate % The parameter E giving the dependence of branch rate on the number of terminal segments will varied scrsz = get(0,'ScreenSize'); figure(1) set(gcf,'Position',[1, 1 , scrsz(4) , scrsz(4) ]) clf hold on nplotrange=1:5:101; for E=0:0.25:1 % Calculate numerical solutions [T,Y,mun,sigman,validPoints]=cBEModel(b,E); % Plot top row: temporal development for the probabilities $p(n,t)$ for % $n=1,6,11,...,101$ and three different values of $E$: $E=0$ (left), % $E=\frac{1}{2}$ (middle) and $E=1$ (right) in all cases lower % $n$-values lead to earlier $p(n,t)$-peaks, while late peaking traces % might peak outside the window shown. subplot(3,3,1) if(E==0) plot(T(validPoints),Y(validPoints,nplotrange)) end axis([0,4,0,0.2]) subplot(3,3,2) if(E==0.5) plot(T(validPoints),Y(validPoints,nplotrange)) end axis([0,25,0,0.2]) subplot(3,3,3) if(E==1) plot(T(validPoints),Y(validPoints,nplotrange)) end axis([0,25,0,0.2]) % Plot middle row: expectation value and variance for the number of terminal % segments for three different values of $E$ (matching those in the top % row) calculated using the first 1000 $p(n,t)$'s while keeping % $p_{high}< 10^{-6}$. subplot(3,3,4) hold on if(E==0) plot(T(validPoints),mun(validPoints),'k-') plot(T(validPoints),sigman(validPoints),'k--') end axis([0,4,0,30]) subplot(3,3,5) hold on if(E==0.5) plot(T(validPoints),mun(validPoints),'k-') plot(T(validPoints),sigman(validPoints),'k--') end axis([0,10,0,30]) subplot(3,3,6) hold on if(E==1) plot(T(validPoints),mun(validPoints),'k-') plot(T(validPoints),sigman(validPoints),'k--') legend('\mu(n)','\sigma(n )','p_{high}10^7 ','Location','NorthWest') end axis([0,25,0,30]) % Plot bottom row left: comparison expectation value (solid grey lines) with % mean field prediction (dashed black lines) for five different $E$ % values: $E= 0,0.25, 0.5, 0.75, 1$; at $E$-values $0, 1$ the mean % field solutions coincide with the exact solution. subplot(3,2,5) hold on plot(T(validPoints),mun(validPoints),'k-') if(E==0) plot(T(validPoints),exp(T(validPoints)),'r--') else plot(T(validPoints),(E*T(validPoints)+1).^(1/E),'r--') legend('\mu(n)','\mu_{MF}(n)','Location','SouthEast') end axis([0,25,0,30]) % Plot bottom row right: comparison of mean field solution and numerical % results; after an initial growth of the relative error for % intermediate values of $E$ , i.e. $E= 0.25, 0.5, 0.75$, the % relative error attenuates. The standard deviation and mean for $E=0$ % and $E=1$ correspond within the numerical error with the exact % solutions. markers=['.';'+';'d';'o';'-']; subplot(3,2,6) hold on if(E==0 ) plot(T(validPoints),(exp(T(validPoints))./mun(validPoints)'),markers(1+round(E/0.25))) else plot(T(validPoints),((E*T(validPoints)+1).^(1/E)./mun(validPoints)'),markers(1+round(E/0.25))) end legend('E=0','E=0.25','E=0.50','E=0.75','E=1','Location','SouthEast') axis([0,25,0.99,1.1]) end %% Save figure to file (pdf) figure(1) saveas(gcf,'figures/BEModel.pdf')