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TestParam4paperEI_chaos.m
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TestParam4paperEI_chaos.m
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%% Test Parameters - From NeuroElectro.com
%% Priors
% --------------------
% --- Expectations ---
% --------------------
close all; clear M P P0;
P.ang = pi;
% --- Conectivity matrices ---
P.A(1).M = [ -32 log(2); % excitatory
-32 -32];
P.A(2).M = [-32 -32; % inhibitory
log(1) -32];
P.A(3).M = [ -32 -32; % excitatory
-32 log(.15)];
P.A(4).M = [log(.5) -32; % inhibitory
-32 -32];
P.C(1).M = [log(.1) log(8)]'; % excitatory exogenous input
P.C(2).M = [log(.1) log(.1)]'; % inhibitory exogenous input
P.C(3).M = [-32 -32]';
P.C(4).M = [-32 -32]';
% --- CA1 inhibitory interneurons ---
P.P(1).C = log(.084); % [nF] Cell capacitance
P.P(1).Vl = -62; % [mV] Leak reversal portential
P.P(1).gl = P.P(1).C -log(.012); % [nF/s] = [nS] Leak conductance
P.P(1).Vt = -55; % [mV] Spike threshold voltage
P.P(1).Vr = -70; % [mV] Reset voltage
P.P(1).Rt = log(1/1000); % [s] Refractory time
P.P(1).Vg = [0,-70,0,-70]; % [mV] Reversal portential of the families of synaptic channels
P.P(1).T = log([16,5,16,5]/1000); % [s] Decay time constants for the synaptic conductances
P.P(1).D = log(2000); % (1/2*sigma^2) [(mV^2)/ms] Membrane noise term
P.P(1).d = log(1/1000);
% --- CA1 excitatory pyramidal cells ---
P.P(2).C = log(.150); % [nF] Cell capacitance
P.P(2).Vl = -65; % [mV] Leak reversal portential
P.P(2).gl = P.P(2).C - log(0.030); % [nF/s] = [nS] Leak conductance
P.P(2).Vt = -48; % [mV] Spike threshold voltage
P.P(2).Vr = -70; % [mV] Reset voltage
P.P(2).Rt = log(8/1000); % [s] Refractory time
P.P(2).Vg = [0,-70,0,-70]; % [mV] Reversal portential of the families of synaptic channels
P.P(2).T = log([16,5,16,5]/1000); % [s] Decay time constants for the synaptic conductances
P.P(2).D = log(4000); % (1/2*sigma^2) [(mV^2)/s] Membrane noise term
P.P(2).d = log(1/1000);
% -------------------
% --- Covariances ---
% -------------------
CP.ang = 10*pi;
CP.A(1).M = exp([ -32 4;
-32 -32]);
CP.A(2).M = exp([-32 -32;
4 -32]);
CP.A(3).M = exp([ -32 -32;
-32 4]);
CP.A(4).M = exp([4 -32;
-32 -32]);
CP.C(1).M = exp([2 4]');
CP.C(2).M = exp([2 2]');
CP.C(3).M = exp([-32 -32]');
CP.C(4).M = exp([-32 -32]');
% --- inhibitory interneurons ---
CP.P(1).C = log(8); % [nF] Cell capacitance
CP.P(1).Vl = 3; % [mV] Leak reversal portential
CP.P(1).gl = log(8); % [pF/ms] = [nS] Leak conductance
CP.P(1).Vt = 100; % [mV] Spike threshold voltage
CP.P(1).Vr = exp(-32); % [mV] Reset voltage
CP.P(1).Rt = log(4); % [s] Refractory time
CP.P(1).Vg = [100,100,100,100];% [mV] Reversal portential of the families of synaptic channels
CP.P(1).T = log([8,8,8,8]); % [s] Decay time constants for the synaptic conductances
CP.P(1).D = log(16); % (1/2*sigma^2) [(mV^2)/ms] Membrane noise term
% --- excitatory pyramidal cells ---
CP.P(2).C = log(8); % [nF] Cell capacitance
CP.P(2).Vl = 4; % [mV] Leak reversal portential
CP.P(2).gl = log(8); % [pF/ms] = [nS] Leak conductance
CP.P(2).Vt = 50; % [mV] Spike threshold voltage
CP.P(2).Vr = exp(-32); % [mV] Reset voltage
CP.P(2).Rt = log(4); % [s] Refractory time
CP.P(2).Vg = [100,100,100,100];% [mV] Reversal portential of the families of synaptic channels
CP.P(2).T = log([8,8,8,8]); % [s] Decay time constants for the synaptic conductances
CP.P(2).D = log(16); % (1/2*sigma^2) [(mV^2)/ms] Membrane noise term
%%
M.opt.N = 4000; % Maximum time points for time integration
M.opt.dttol = 1e-3;
M.opt.LCtol = 1e-3;
M.opt.r = 1;
M.opt.popCurrents = [2 10; 2 -70; 1 10; 1 -70]; % Pop and Voltage clamp values [mV]
M.opt.popFiringRates = [2; 1]; % Pop for fring rates
M.opt.dpsize = 10^-6; % For DCM
M.opt.svdtol = 10^-6; % For LC perturbation
M.opt.Drawplots = 0; % Progress plots of pdfs and conductances
M.opt.vmin = -16; % For DCM
M.opt.vmax = 8; % For DCM
M.opt.vini = -4; % For DCM
M.opt.Nmax = 32; % For DCM
M.opt.sigma = 0; % For DCM
Vp = 0*spm_vec(P); Vp = [Vp Vp]; Vp(4,1) = 1; Vp(4,2) = -1; % For DCM tests
% Vp = spm_svd(diag(spm_vec(CP)),exp(-32));
%% Data
M.pE = P;
M.pC = CP;
M.hE = 0*[3 9 -3 -3 3 3 3 9]' + 15;
M.hC = eye(length(M.hE))*.01;
M.Ep = P;
M.opt.Ncoefs = 100; % For DCM
M.converged = 0; % For DCM
M.F = -Inf; % For DCM
M.opt.LCtol = .1; % Convergence tolerance for LC
M.opt.Drawprogress = 1; % For DCM
% if ~isfield(M.opt,'dttol'); M.opt.dttol = 10^-3; end;
% if ~isfield(M.opt,'dt'); M.opt.dt = .001; end;
% if ~isfield(M.opt,'T0max'); M.opt.T0max = .12; end;
% if ~isfield(M.opt,'svdtol'); M.opt.svdtol = 10^-6; end;
% if ~isfield(M.opt,'dpsize'); M.opt.dpsize = exp(-3); end;
% if ~isfield(M.opt,'Ncoefs'); M.opt.Ncoefs = 1000; end;
% if ~isfield(M.opt,'LCtol'); M.opt.LCtol = 10^-3; end;
% M.Gv0 = zeros(M.np,M.np);
% M.LFP = zeros(M.np,M.opt.N);
% M.Currents = zeros(size(M.opt.popCurrents,1),M.opt.N);
%
% P = spm_ExpP(Ep);
% M = spm_lifpopsys_LC_prepare(P,M);
% M.opt.Drawplots = 1;
% M = spm_DCM_lifpopsys_LC_int(P,M);
%
% clear Ang I n phaseshift y y0 y2 yf yf0 ans Vp CP P
%% Parameter Initialization
%
% M.P.C(1).M = [log(.1) log(8)]';
% M.P.C(2).M = [log(.1) log(.1)]';
% M.P.C(3).M = [-32 -32]';
% M.P.C(4).M = [-32 -32]';
%
P0 = P; % Save original parameters
P = spm_ExpP(P0); % Adapt parameters for integration
M = spm_lifpopsys_LC_prepare(P,M); % Complete M structure
cflag = 0; % convergence flag for Fixed point search
%% --- Coment this section if modeling more than 2 populations ---
[~, ~, M, cflag] = fx_LIFpopMEJpar(P,M); % Try to find a fixed point
% --- end of comented section ---
if cflag
M = spm_perturb_fp(P,M); % Kick the system out of the fixed point
end
M.opt.Drawplots = 1; % Option for drawing progress plots
%% This will integrate the model until a limit cycle (or Nmax) is reached
% if ~cflag || max(real(M.J.S))>10e-4
%
% M = spm_DCM_lifpopsys_LC_int(P,M);
%
% ts = timeseries( squeeze(M.Currents(1,(1:M.opt.Kend))), M.opt.t(1:M.opt.Kend));
% ts1 = resample(ts,0:.001:M.opt.t(M.opt.Kend)); % resample to 1KHz
% figure
% plot(ts1)
% fprintf('LC frequency: %f Hz \n', 1/M.opt.T0)
% else
% fprintf('Stable Fixed Point')
% end
% The structure M will have the results of the integration
% figure
% TFanalysis(squeeze(ts1.data)',40,200,16,500,1000,.000001);
%% Scheme benchmark
M.opt.Drawplots = 0;
M.opt.dttol = 1e-3;
tic
M = spm_DCM_lifpopsys_LC_int(P,M);
toc
%%
% try
% k = M.opt.Kend;
% catch
% k = 2;
% end
k = 2;
nstates = 0;
sumS = zeros(M.np,1);
clear S
for l = 1:M.np % cycle through populations
P1 = M.P(l);
SSS2 = [reshape(M.SS(l).SS(:,k-1),[],1,1); squeeze(M.GV(l,:,k-1))'];
S(nstates+1 : nstates + M.P(l).LVV + M.nc) = SSS2;
nstates = nstates + M.P(l).LVV + M.nc;
sumS(l) = 1/M.P(l).Vres; % sum constrain on pdf's
end
y = S';
odefun = @(a,b) fx_LIFpopMEJparOdeFun(0,b,P,M);
opt=[];
% opt.RelTol = M.opt.dttol;
% opt.RelTol = 10^(-0);
tic
[T,Y] = ode15s(odefun,[0 M.opt.t(M.opt.Kend)],y,opt);
% [T,Y] = ode45(odefun,[0 M.opt.t(M.opt.Kend)],y,opt);
toc
%%
figure;
plot(T,Y(:,M.P(1).LVV+1),'c.')
hold on
plot(M.opt.t(1:M.opt.Kend),squeeze(M.GV(1,1,1:M.opt.Kend)),'.')
% plot(T1,Y1(:,201),'y.')
% plot(M1.opt.t(1:M1.opt.Kend),squeeze(M1.GV(1,1,1:M1.opt.Kend)),'k.')
% plot(M2.opt.t(1:M2.opt.Kend),squeeze(M2.GV(1,1,1:M2.opt.Kend)),'m.')
% plot(M3.opt.t(1:M3.opt.Kend),squeeze(M3.GV(1,1,1:M3.opt.Kend)),'g.')