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@JanDW
Created Aug 31, 2020
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Simulates the Boonie Conundrum
% Simulates the Boonie Conundrum
%
%
% Input(s)
% DispOn: Displays the graph of student and teacher rumor knowledge
% Modify simulation parameters in the code below
%
% Output(s)
% studentFraction: Fraction of student population that knows the rumor
% teacherFraction: Fraction of teacher population that knows the rumor
% Day: Day that Principal S. finally hears
%
% Example:
% boonieSim(true);
%
% See also:
%
%
% Dependencies: pubFig
%
%
% Written by: John Peach 17-Aug-2020
% Marakesh Sailing Analysis and Design
%
% Revisions:
function [studentFraction,teacherFraction,Day] = boonieSim(DispOn)
if ~nargin
DispOn = false;
endif
% Parameters
nStudents = 1500; % Number of students
nTeachers = 100; % Number of teachers
studentFriendship = 0.005; % Probability that a student knows another
studentOpportunity = 0.01; % Probability that rumor is passed between students
studentTeacherOpp = 0.001; % Probability that the student has a chance to tell and is willing
teacherFriendship = 0.05; % Probability that a teacher knows another
teacherOpportunity = 0.001; % Probability that rumor is passed between teachers
teacherPrincipalOpp = 0.01; % Probability that a teacher will tell Principal S.
% Student friendship matrix
S = sprand(nStudents, nStudents, studentFriendship) > 0;
S2S_friendship = S + S' + speye(nStudents);
% Teacher friendship matrix
T = sprand(nTeachers, nTeachers, teacherFriendship) > 0;
T2T_friendship = T + T' + speye(nTeachers);
% Initialize rumor knowledge vectors
studentKnows = false(nStudents,1);
studentKnows(1) = true; % Only Boonie knows initially
teacherKnows = false(nTeachers,1);
PrincipalKnows = false;
% Fractional knowledge vectors
studentFraction = zeros(1,100);
teacherFraction = zeros(1,100);
% Update rumor mill daily
Day = 0;
while not(PrincipalKnows)
% Students talk to each other during the day (opportunity matrix)
studentsTalk = sprand(nStudents, nStudents, studentOpportunity) > 0;
% Update student rumor knowledge vector
studentKnows = studentKnows | ...
(S2S_friendship .* studentsTalk) * studentKnows > 0;
% Information transmitted from students to teachers (opportunity)
studentsTalkToTeachers = sprand(nTeachers, nStudents, studentTeacherOpp) > 0;
teacherKnows = teacherKnows | ...
((studentsTalkToTeachers * studentKnows) > 0);
% Teachers talk among themselves
teachersTalk = sprand(nTeachers, nTeachers, teacherOpportunity) > 0;
teacherKnows = teacherKnows | ...
(T2T_friendship .* teachersTalk) * teacherKnows > 0;
% Teachers pass on rumor to the principal
T2P_crossover = rand(nTeachers,1) < teacherPrincipalOpp;
PrincipalKnows = any(teacherKnows & T2P_crossover);
% Update day counter
Day = Day + 1;
% Fraction of each population that knows the rumor
studentFraction(Day) = sum(studentKnows) / nStudents;
teacherFraction(Day) = sum(teacherKnows) / nTeachers;
endwhile
% Reduce student and teacher fraction vectors to length of number of days
studentFraction = studentFraction(1:Day);
teacherFraction = teacherFraction(1:Day);
% Plot fraction of students and teachers who have heard the rumor
if DispOn
figure;
plot(1:Day, 100*[studentFraction; teacherFraction]);
xlabel('Days')
ylabel('Rumor spread (%)')
legend({'Students','Teachers'},'Location','northwest')
title('The Boonie Rumor')
pubFig
endif
endfunction
%------------------------------------------------------------------------------
% Modifies figures to get ready for publication
%
%
% Input(s)
% None
%
% Output(s)
% Current figure revised, suitable for publication
%
% Example:
% t = linspace(0,2*pi);
% y = sin(t);
% figure;
% plot(t,y);
% xlabel('Time')
% ylabel('sin(t)')
% title('Sine function')
% pubFig
%
% See also:
%
%
% Dependencies: None
%
%
% Written by: John Peach 20-Aug-2020
% Marakesh Sailing Analysis and Design
%
% Revisions:
function pubFig
% Set standard units
figUnits=get(gcf,'Units');
set(gcf,'Units','inches');
% Linewidth, fonts, figure dimensions
linewidth = 1.5;
axisFont = 16; %12;
labelFont = 20; %14;
titleFont = 24; %16;
fontName = 'Arial';
figPos = get(gcf,'Position');
% Modify text
texts = findall(gcf,'Type','text');
for k = 1:numel(texts)
textParent = get(texts(k),'Parent');
if ~strcmp(get(textParent,'Tag'),'legend')
set(texts(k), ...
'FontSize',labelFont, ...
'FontWeight','bold',...
'FontName',fontName);
endif
endfor
% Set line widths
figLines = findall(gcf,'Type','line');
for k = 1:numel(figLines)
set(figLines(k),'LineWidth',linewidth);
endfor
% Adjust axes
figAxes = findall(gcf,'Type','axes');
for k = 1:numel(figAxes)
set(figAxes(k), ...
'LineWidth',linewidth, ...
'Fontsize',axisFont,...
'FontWeight','bold', ...
'FontName',fontName);
endfor
% Correct figure size
currPos = get(gcf,'Position');
newPos = [currPos(1:2) - (figPos(3:4) - currPos(3:4)) figPos(3:4)];
set(gcf,'Position',newPos)
set(gcf,'PaperPosition',[1 1 figPos(3:4)])
set(gcf,'Units',figUnits)
endfunction
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