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SetInitialConditions.m
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250 lines (209 loc) · 13.8 KB
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%% Set Initial Conditions based on Connectivity+Model+Integrator
%
% ARGUMENTS:
% options -- usual options structure
%
% OUTPUT:
% options -- input structure updated with InitialConditions
%
% REQUIRES:
% Sigma() -- for BRRW and AFR Models
%
% USAGE:
%{
<example-commands-to-make-this-function-run>
%}
%
% MODIFICATION HISTORY:
% SAK(<dd-mm-yyyy>) -- Original.
% SAK(Nov 2013) -- Move to git, future modification history is
% there...
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function options = SetInitialConditions(options)
if isfield(options.Dynamics,'InitialConditions'),
options.Dynamics = rmfield(options.Dynamics,'InitialConditions');
end
%Set RandStream to a state consistent with InitialConditions.
options.Dynamics.InitialConditions.StateRand = 5489;
if isoctave(),
rand('seed', options.Dynamics.InitialConditions.StateRand);
temp = rand(625, 1); % This can't be the only way to simply seed a state...
rand('state', temp);
options.Dynamics.InitialConditions.ThisRandomStream.State = rand('state');
options.Dynamics.InitialConditions.StateRand = rand('state');
else %Presumably Matlab
options.Dynamics.InitialConditions.ThisRandomStream = RandStream.create('mt19937ar','seed', options.Dynamics.InitialConditions.StateRand);
RandStream.setDefaultStream(options.Dynamics.InitialConditions.ThisRandomStream);
options.Dynamics.InitialConditions.StateRand = options.Dynamics.InitialConditions.ThisRandomStream.State;
end
NumberOfNodes = options.Connectivity.NumberOfNodes;
NumberOfModes = options.Dynamics.NumberOfModes;
maxdelayiters = options.Integration.maxdelayiters;
%%
switch options.Dynamics.WhichModel
case {'BRRWtess'}%%% Populations Sigma() acts on don't seem to make sense, but this is what MB's code did... %%%
options.Dynamics.StateVariables = {'phi_e', 'dphi_e', 'V_e', 'dV_e', 'V_s', 'dV_s', 'V_r', 'dV_r'};
switch options.Dynamics.BrainState
case{'absence','petitmal'}
MagicNumber1 = 0.005;
MagicNumber2 = 0.004;
case{'tonicclonic','grandmal'}
MagicNumber1 = 0.010;
MagicNumber2 = 0.009;
case{'ec'}
MagicNumber1 = 0.0093;
MagicNumber2 = 0.0087;
case{'eo'}
MagicNumber1 = 0.0063;
MagicNumber2 = 0.0055;
otherwise
end
%Calculate at region level
rV = MagicNumber1 + 0.1e-3*rand(maxdelayiters,NumberOfNodes)./2;
SigrVi = Sigma(rV, options.Dynamics.Qmax, options.Dynamics.Theta_e, options.Dynamics.sigma_e, 'inverse');
options.Dynamics.InitialConditions.phi_e = rV;
options.Dynamics.InitialConditions.dphi_e = zeros(1,NumberOfNodes);
options.Dynamics.InitialConditions.V_e = SigrVi;
options.Dynamics.InitialConditions.dV_e = zeros(1,NumberOfNodes);
options.Dynamics.InitialConditions.V_s = vs(SigrVi, options);
options.Dynamics.InitialConditions.dV_s = zeros(1,NumberOfNodes);
options.Dynamics.InitialConditions.V_r = options.Dynamics.nu_re.*Sigma(Sigma(MagicNumber2, options.Dynamics.Qmax, options.Dynamics.Theta_e, options.Dynamics.sigma_e, 'inverse'), options.Dynamics.Qmax,options.Dynamics.Theta_r,options.Dynamics.sigma_r) ...
+options.Dynamics.nu_rs.*Sigma(options.Dynamics.nu_re.*Sigma(SigrVi, options.Dynamics.Qmax,options.Dynamics.Theta_r,options.Dynamics.sigma_r), options.Dynamics.Qmax,options.Dynamics.Theta_r,options.Dynamics.sigma_r);
options.Dynamics.InitialConditions.dV_r = zeros(1,NumberOfNodes);
%Map to surface
options.Dynamics.phi_n = 1e-3.*ones(options.Integration.iters,options.Connectivity.NumberOfVertices);
options.Dynamics.InitialConditions.dphi_e = zeros(1,options.Connectivity.NumberOfVertices);
options.Dynamics.InitialConditions.dV_e = zeros(1,options.Connectivity.NumberOfVertices);
options.Dynamics.InitialConditions.dV_s = zeros(1,options.Connectivity.NumberOfVertices);
options.Dynamics.InitialConditions.dV_r = zeros(1,options.Connectivity.NumberOfVertices);
tempphi_e = options.Dynamics.InitialConditions.phi_e ;
options.Dynamics.InitialConditions.phi_e = zeros(options.Integration.maxdelayiters,options.Connectivity.NumberOfVertices);
for n = 1:options.Connectivity.NumberOfNodes,
options.Dynamics.InitialConditions.phi_e(:,options.Connectivity.RegionMapping==n) = repmat(tempphi_e(:,n), [1 sum(options.Connectivity.RegionMapping==n)]);
end
clear tempphi_e
tempV_e = options.Dynamics.InitialConditions.V_e ;
options.Dynamics.InitialConditions.V_e = zeros(options.Integration.maxdelayiters,options.Connectivity.NumberOfVertices);
for n = 1:options.Connectivity.NumberOfNodes,
options.Dynamics.InitialConditions.V_e(:,options.Connectivity.RegionMapping==n) = repmat(tempV_e(:,n), [1 sum(options.Connectivity.RegionMapping==n)]);
end
clear tempV_e
tempV_s = options.Dynamics.InitialConditions.V_s ;
options.Dynamics.InitialConditions.V_s = zeros(options.Integration.maxdelayiters,options.Connectivity.NumberOfVertices);
for n = 1:options.Connectivity.NumberOfNodes,
options.Dynamics.InitialConditions.V_s(:,options.Connectivity.RegionMapping==n) = repmat(tempV_s(:,n), [1 sum(options.Connectivity.RegionMapping==n)]);
end
clear tempV_s
tempV_r = options.Dynamics.InitialConditions.V_r ;
options.Dynamics.InitialConditions.V_r = zeros(options.Integration.maxdelayiters,options.Connectivity.NumberOfVertices);
for n = 1:options.Connectivity.NumberOfNodes,
options.Dynamics.InitialConditions.V_r(:,options.Connectivity.RegionMapping==n) = repmat(tempV_r(:,n), [1 sum(options.Connectivity.RegionMapping==n)]);
end
clear tempV_r
options.Dynamics.InitialConditions.V_e = options.Dynamics.InitialConditions.V_e(end, :);
options.Dynamics.InitialConditions.V_r = options.Dynamics.InitialConditions.V_r(end, :);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
case {'BRRW'}%%% Populations Sigma() acts on don't seem to make sense, but this is what MB's code did... %%%
options.Dynamics.StateVariables = {'phi_e', 'dphi_e', 'V_e', 'dV_e', 'V_s', 'dV_s', 'V_r', 'dV_r'};
switch options.Dynamics.BrainState
case{'absence','petitmal'}
MagicNumber1 = 0.005;
MagicNumber2 = 0.004;
case{'tonicclonic','grandmal'}
MagicNumber1 = 0.010;
MagicNumber2 = 0.009;
case{'ec'}
MagicNumber1 = 0.0093;
MagicNumber2 = 0.0087;
case{'eo'}
MagicNumber1 = 0.0063;
MagicNumber2 = 0.0055;
otherwise
end
rV = MagicNumber1 + rand(maxdelayiters, NumberOfNodes) * ((options.Dynamics.Qmax - MagicNumber1) / 10.0);
SigrVi = Sigma(rV, options.Dynamics.Qmax, options.Dynamics.Theta_e, options.Dynamics.sigma_e, 'inverse');
options.Dynamics.InitialConditions.phi_e = rV;
options.Dynamics.InitialConditions.dphi_e = zeros(1,NumberOfNodes);
options.Dynamics.InitialConditions.V_e = SigrVi;
options.Dynamics.InitialConditions.dV_e = zeros(1,NumberOfNodes);
options.Dynamics.InitialConditions.V_s = vs(SigrVi, options);
options.Dynamics.InitialConditions.dV_s = zeros(1,NumberOfNodes);
options.Dynamics.InitialConditions.V_r = options.Dynamics.nu_re.*Sigma(Sigma(MagicNumber2, options.Dynamics.Qmax, options.Dynamics.Theta_e, options.Dynamics.sigma_e, 'inverse'), options.Dynamics.Qmax,options.Dynamics.Theta_r,options.Dynamics.sigma_r) ...
+options.Dynamics.nu_rs.*Sigma(options.Dynamics.nu_re.*Sigma(SigrVi, options.Dynamics.Qmax,options.Dynamics.Theta_r,options.Dynamics.sigma_r), options.Dynamics.Qmax,options.Dynamics.Theta_r,options.Dynamics.sigma_r);
options.Dynamics.InitialConditions.dV_r = zeros(1,NumberOfNodes);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
case {'AFR'}
options.Dynamics.StateVariables = {'phi', 'dphi', 'V', 'dV'};
MagicNumber1 = 0.012;
MagicNumber2 = 0.011;
rV = MagicNumber1 + rand(maxdelayiters,options.Connectivity.NumberOfVertices)./2;
SigrVi = Sigma(rV, options.Dynamics.Qmax, options.Dynamics.Theta_e, options.Dynamics.sigma_e, 'inverse');
options.Dynamics.InitialConditions.phi = rV;
options.Dynamics.InitialConditions.dphi = zeros(1,options.Connectivity.NumberOfVertices);
options.Dynamics.InitialConditions.V = SigrVi;
options.Dynamics.InitialConditions.dV = zeros(1,options.Connectivity.NumberOfVertices);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
case {'FHN'}
options.Dynamics.StateVariables = {'V', 'W'};
options.Dynamics.InitialConditions.V = rand(maxdelayiters,NumberOfNodes) + 0.5;
options.Dynamics.InitialConditions.W = rand(1,NumberOfNodes) - 0.5;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
case {'FHNtess'}
options.Dynamics.StateVariables = {'V', 'W'};
options.Dynamics.InitialConditions.V = rand(maxdelayiters, options.Connectivity.NumberOfVertices) + 0.5;
options.Dynamics.InitialConditions.W = rand(1, options.Connectivity.NumberOfVertices) - 0.5;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
case {'SNX'}
options.Dynamics.StateVariables = {'X'};
options.Dynamics.InitialConditions.X = randn(maxdelayiters,NumberOfNodes) .* 0.125;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
case {'ReducedFHN'}
options.Dynamics.StateVariables = {'Xi', 'Eta', 'Alfa', 'Btta'};
options.Dynamics.InitialConditions.Xi = rand(maxdelayiters,NumberOfNodes,NumberOfModes) - 0.5;
options.Dynamics.InitialConditions.Eta = rand(1,NumberOfNodes,NumberOfModes);
options.Dynamics.InitialConditions.Alfa = rand(1,NumberOfNodes,NumberOfModes) .*2 - 1.0;
options.Dynamics.InitialConditions.Btta = rand(1,NumberOfNodes,NumberOfModes) - 0.2;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
case {'ReducedFHNtess'}
options.Dynamics.StateVariables = {'Xi', 'Eta', 'Alfa', 'Btta'};
options.Dynamics.InitialConditions.Xi = rand(maxdelayiters,options.Connectivity.NumberOfVertices,NumberOfModes) - 0.5;
options.Dynamics.InitialConditions.Eta = rand(1,options.Connectivity.NumberOfVertices,NumberOfModes);
options.Dynamics.InitialConditions.Alfa = rand(1,options.Connectivity.NumberOfVertices,NumberOfModes) .*2 - 1.0;
options.Dynamics.InitialConditions.Btta = rand(1,options.Connectivity.NumberOfVertices,NumberOfModes) - 0.2;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
case {'ReducedHMR'}
options.Dynamics.StateVariables = {'Xi', 'Eta', 'Tau', 'Alfa', 'Btta', 'Gamma'};
options.Dynamics.InitialConditions.Xi = rand(maxdelayiters,NumberOfNodes,NumberOfModes) - 0.7;
options.Dynamics.InitialConditions.Eta = rand(1,NumberOfNodes,NumberOfModes) - 0.5;
options.Dynamics.InitialConditions.Tau = rand(1,NumberOfNodes,NumberOfModes) + 2.5;
options.Dynamics.InitialConditions.Alfa = rand(1,NumberOfNodes,NumberOfModes) - 0.8;
options.Dynamics.InitialConditions.Btta = rand(1,NumberOfNodes,NumberOfModes) - 0.5;
options.Dynamics.InitialConditions.Gamma = rand(1,NumberOfNodes,NumberOfModes) + 2.25;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
case {'ReducedHMRtess'}
options.Dynamics.StateVariables = {'Xi', 'Eta', 'Tau', 'Alfa', 'Btta', 'Gamma'};
options.Dynamics.InitialConditions.Xi = rand(maxdelayiters,options.Connectivity.NumberOfVertices,NumberOfModes) - 0.7;
options.Dynamics.InitialConditions.Eta = rand(1,options.Connectivity.NumberOfVertices,NumberOfModes) - 0.5;
options.Dynamics.InitialConditions.Tau = rand(1,options.Connectivity.NumberOfVertices,NumberOfModes) + 2.5;
options.Dynamics.InitialConditions.Alfa = rand(1,options.Connectivity.NumberOfVertices,NumberOfModes) - 0.8;
options.Dynamics.InitialConditions.Btta = rand(1,options.Connectivity.NumberOfVertices,NumberOfModes) - 0.5;
options.Dynamics.InitialConditions.Gamma = rand(1,options.Connectivity.NumberOfVertices,NumberOfModes) + 2.25;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
otherwise
end
end %function SetInitialConditions()
%% Direct translation MB's code
function f=vs(V,options)
nmax = 30;
root = 0;
for j=1:nmax
x = options.Dynamics.nu_re.*Sigma(V, options.Dynamics.Qmax,options.Dynamics.Theta_r,options.Dynamics.sigma_r) ...
+options.Dynamics.nu_rs.*Sigma(root,options.Dynamics.Qmax,options.Dynamics.Theta_r,options.Dynamics.sigma_r);
ff = -root + options.Dynamics.nu_sn.*options.Dynamics.phi_n(1:options.Integration.maxdelayiters,:) ...
+ options.Dynamics.nu_se.*Sigma(V,options.Dynamics.Qmax,options.Dynamics.Theta_s,options.Dynamics.sigma_s) ...
+ options.Dynamics.nu_sr.*Sigma(x,options.Dynamics.Qmax,options.Dynamics.Theta_s,options.Dynamics.sigma_s);
fp = -1 + options.Dynamics.nu_sr.*options.Dynamics.nu_rs.*Sigma(x,options.Dynamics.Qmax,options.Dynamics.Theta_s,options.Dynamics.sigma_s, 'derivative').*Sigma(root,options.Dynamics.Qmax,options.Dynamics.Theta_s,options.Dynamics.sigma_s, 'derivative');
root = root - ff./fp;
end
f = root; %%% real(root); %HACK:TODO: NEED TO FIGURE OUT WHY WE'RE GETTING COMPLEX root HERE...
end