diff --git a/.DS_Store b/.DS_Store
deleted file mode 100644
index 487def8..0000000
Binary files a/.DS_Store and /dev/null differ
diff --git a/ExampleCode.m b/ExampleCode.m
old mode 100644
new mode 100755
index e7b0897..de550f3
--- a/ExampleCode.m
+++ b/ExampleCode.m
@@ -1,139 +1,90 @@
% Note: the following simulations use a GLM-based method to simulate V_low
-% and V_high, and the p-values are the analytical p-values from the
+% and V_high, and the p-values are the empirical bootstrapped p-values from the
% manuscript
%% Signal with neither PAC nor AAC
-[XX,P,Vlo,Vhi,t] = simfun(0,0,'GLM','theoretical','none',.05);
-figure(1)
-plot(t,Vlo + .08,t,Vhi,'LineWidth',2); axis off
-hold on;
-[pks, ipks] = findpeaks(Vlo);
-for i = 1:length(ipks)
- ind = ipks(i);
- plot([t(ind),t(ind)],[Vlo(ind)+.07,Vlo(ind)+.09],'r','LineWidth',2)
-end
-plot([8,8.1],[-.04,-.04],'k','LineWidth',2)
-legend('V_{low}','V_{high}')
-axis off
-set(gca,'FontSize',13)
-str = strcat({'R_PAC is '},{num2str(XX.rpac)},{' with p-value '},{num2str(P.rpac)}); disp(str);
-str = strcat({'R_AAC is '},{num2str(XX.raac)},{' with p-value '},{num2str(P.raac)}); disp(str);
-str = strcat({'R_CFC is '},{num2str(XX.rcfc)},{' with p-value '},{num2str(P.rcfc)}); disp(str);
-xlim([8,10])
+[XX] = simfun(0,0,'pink','none','none','none',.05);
+d = 5;
+XX.ampAXIS = XX.ampAXIS(1:d:end);
+XX.phi0 = XX.phi0(1:d:end);
+XX.PAC = XX.Phi_low(1:d:end,1:d:end); XX.AAC = XX.A_low(1:d:end,1:d:end); XX.CFC = XX.Phi_low_A_low(1:d:end,1:d:end);
-figure(2)
-surf(XX.ampAXIS,XX.phi0,XX.PAC,'EdgeColor','none','FaceAlpha',.8,'FaceColor',[35, 106, 185]/255);
-hold on;
-surf(XX.ampAXIS,XX.phi0,XX.AAC,'EdgeColor','none','FaceAlpha',.8,'FaceColor',[214, 26, 70]/255);
+surf(XX.ampAXIS,XX.phi0,XX.PAC,'FaceAlpha',.8,'FaceColor',[35, 106, 185]/255);
hold on;
-surf(XX.ampAXIS,XX.phi0,XX.CFC,'EdgeColor','none','FaceAlpha',.9,'FaceColor',[253, 220, 34]/255);
-
+surf(XX.ampAXIS,XX.phi0,XX.AAC,'FaceAlpha',.8,'FaceColor',[214, 26, 70]/255);
+surf(XX.ampAXIS,XX.phi0,XX.CFC,'FaceAlpha',.9,'FaceColor',[253, 220, 34]/255);
xlim([min(XX.ampAXIS),max(XX.ampAXIS)]); ylim([min(XX.phi0),max(XX.phi0)])
xlabel('A_{low}'); ylabel('\Phi_{low}'); zlabel('A_{high}')
-legend('PAC','AAC','CFC')
+legend('\phi_{low}','A_{low}','\phi_{low},A_{low}')
set(gca,'FontSize',13)
+set(gca,'YTick',-pi:pi:pi)
+set(gca,'YTickLabel',{'-\pi','0','\pi'})
+set(gca,'Ydir','reverse')
grid off
-zlim([.008,.02])
+zlim([.002,.02])
%% Signal with PAC
-[XX,P,Vlo,Vhi,t] = simfun(1,0,'GLM','theoretical','none',.05);
-figure(1)
-plot(t,Vlo + .08,t,Vhi,'LineWidth',2); axis off
-hold on;
-[pks, ipks] = findpeaks(Vlo);
-for i = 1:length(ipks)
- ind = ipks(i);
- plot([t(ind),t(ind)],[Vlo(ind)+.07,Vlo(ind)+.09],'r','LineWidth',2)
-end
-plot([8,8.1],[-.04,-.04],'k','LineWidth',2)
-legend('V_{low}','V_{high}')
-axis off
-set(gca,'FontSize',13)
-str = strcat({'R_PAC is '},{num2str(XX.rpac)},{' with p-value '},{num2str(P.rpac)}); disp(str);
-str = strcat({'R_AAC is '},{num2str(XX.raac)},{' with p-value '},{num2str(P.raac)}); disp(str);
-str = strcat({'R_CFC is '},{num2str(XX.rcfc)},{' with p-value '},{num2str(P.rcfc)}); disp(str);
-xlim([8,10])
+[XX] = simfun(1,0,'pink','none','none','none',.05);
+d = 5;
+XX.ampAXIS = XX.ampAXIS(1:d:end);
+XX.phi0 = XX.phi0(1:d:end);
+XX.PAC = XX.Phi_low(1:d:end,1:d:end); XX.AAC = XX.A_low(1:d:end,1:d:end); XX.CFC = XX.Phi_low_A_low(1:d:end,1:d:end);
-figure(2)
-surf(XX.ampAXIS,XX.phi0,XX.PAC,'EdgeColor','none','FaceAlpha',.8,'FaceColor',[35, 106, 185]/255);
-hold on;
-surf(XX.ampAXIS,XX.phi0,XX.AAC,'EdgeColor','none','FaceAlpha',.8,'FaceColor',[214, 26, 70]/255);
+surf(XX.ampAXIS,XX.phi0,XX.PAC,'FaceAlpha',.8,'FaceColor',[35, 106, 185]/255);
hold on;
-surf(XX.ampAXIS,XX.phi0,XX.CFC,'EdgeColor','none','FaceAlpha',.9,'FaceColor',[253, 220, 34]/255);
-
+surf(XX.ampAXIS,XX.phi0,XX.AAC,'FaceAlpha',.8,'FaceColor',[214, 26, 70]/255);
+surf(XX.ampAXIS,XX.phi0,XX.CFC,'FaceAlpha',.9,'FaceColor',[253, 220, 34]/255);
xlim([min(XX.ampAXIS),max(XX.ampAXIS)]); ylim([min(XX.phi0),max(XX.phi0)])
xlabel('A_{low}'); ylabel('\Phi_{low}'); zlabel('A_{high}')
-legend('PAC','AAC','CFC')
+legend('\phi_{low}','A_{low}','\phi_{low},A_{low}')
set(gca,'FontSize',13)
+set(gca,'YTick',-pi:pi:pi)
+set(gca,'YTickLabel',{'-\pi','0','\pi'})
+set(gca,'Ydir','reverse')
grid off
-zlim([.008,.02])
-
+zlim([.002,.01])
%% Signal with AAC
-[XX,P,Vlo,Vhi,t] = simfun(0,1,'GLM','theoretical','none',.05);
-figure(1)
-plot(t,Vlo + .08,t,Vhi,'LineWidth',2); axis off
-hold on;
-[pks, ipks] = findpeaks(Vlo);
-for i = 1:length(ipks)
- ind = ipks(i);
- plot([t(ind),t(ind)],[Vlo(ind)+.07,Vlo(ind)+.09],'r','LineWidth',2)
-end
-plot([8,8.1],[-.04,-.04],'k','LineWidth',2)
-legend('V_{low}','V_{high}')
-axis off
-set(gca,'FontSize',13)
-str = strcat({'R_PAC is '},{num2str(XX.rpac)},{' with p-value '},{num2str(P.rpac)}); disp(str);
-str = strcat({'R_AAC is '},{num2str(XX.raac)},{' with p-value '},{num2str(P.raac)}); disp(str);
-str = strcat({'R_CFC is '},{num2str(XX.rcfc)},{' with p-value '},{num2str(P.rcfc)}); disp(str);
-xlim([8,10])
+[XX] = simfun(0,1,'pink','none','none','none',.05);
+d = 5;
+XX.ampAXIS = XX.ampAXIS(1:d:end);
+XX.phi0 = XX.phi0(1:d:end);
+XX.PAC = XX.Phi_low(1:d:end,1:d:end); XX.AAC = XX.A_low(1:d:end,1:d:end); XX.CFC = XX.Phi_low_A_low(1:d:end,1:d:end);
-figure(2)
-surf(XX.ampAXIS,XX.phi0,XX.PAC,'EdgeColor','none','FaceAlpha',.8,'FaceColor',[35, 106, 185]/255);
+surf(XX.ampAXIS,XX.phi0,XX.PAC,'FaceAlpha',.8,'FaceColor',[35, 106, 185]/255);
hold on;
-surf(XX.ampAXIS,XX.phi0,XX.AAC,'EdgeColor','none','FaceAlpha',.8,'FaceColor',[214, 26, 70]/255);
-hold on;
-surf(XX.ampAXIS,XX.phi0,XX.CFC,'EdgeColor','none','FaceAlpha',.9,'FaceColor',[253, 220, 34]/255);
-
+surf(XX.ampAXIS,XX.phi0,XX.AAC,'FaceAlpha',.8,'FaceColor',[214, 26, 70]/255);
+surf(XX.ampAXIS,XX.phi0,XX.CFC,'FaceAlpha',.9,'FaceColor',[253, 220, 34]/255);
xlim([min(XX.ampAXIS),max(XX.ampAXIS)]); ylim([min(XX.phi0),max(XX.phi0)])
xlabel('A_{low}'); ylabel('\Phi_{low}'); zlabel('A_{high}')
-legend('PAC','AAC','CFC')
+legend('\phi_{low}','A_{low}','\phi_{low},A_{low}')
set(gca,'FontSize',13)
+set(gca,'YTick',-pi:pi:pi)
+set(gca,'YTickLabel',{'-\pi','0','\pi'})
+set(gca,'Ydir','reverse')
grid off
-zlim([.008,.02])
+zlim([.002,.01])
%% Signal with PAC and AAC
-[XX,P,Vlo,Vhi,t] = simfun(1,1,'GLM','theoretical','none',.05);
-figure(1)
-plot(t,Vlo + .08,t,Vhi,'LineWidth',2); axis off
-hold on;
-[pks, ipks] = findpeaks(Vlo);
-for i = 1:length(ipks)
- ind = ipks(i);
- plot([t(ind),t(ind)],[Vlo(ind)+.07,Vlo(ind)+.09],'r','LineWidth',2)
-end
-plot([8,8.1],[-.04,-.04],'k','LineWidth',2)
-legend('V_{low}','V_{high}')
-axis off
-set(gca,'FontSize',13)
-str = strcat({'R_PAC is '},{num2str(XX.rpac)},{' with p-value '},{num2str(P.rpac)}); disp(str);
-str = strcat({'R_AAC is '},{num2str(XX.raac)},{' with p-value '},{num2str(P.raac)}); disp(str);
-str = strcat({'R_CFC is '},{num2str(XX.rcfc)},{' with p-value '},{num2str(P.rcfc)}); disp(str);
-xlim([8,10])
+[XX] = simfun(1,1,'pink','none','none','none',.05);
+d = 5;
+XX.ampAXIS = XX.ampAXIS(1:d:end);
+XX.phi0 = XX.phi0(1:d:end);
+XX.PAC = XX.Phi_low(1:d:end,1:d:end); XX.AAC = XX.A_low(1:d:end,1:d:end); XX.CFC = XX.Phi_low_A_low(1:d:end,1:d:end);
-figure(2)
-surf(XX.ampAXIS,XX.phi0,XX.PAC,'EdgeColor','none','FaceAlpha',.8,'FaceColor',[35, 106, 185]/255);
+surf(XX.ampAXIS,XX.phi0,XX.PAC,'FaceAlpha',.8,'FaceColor',[35, 106, 185]/255);
hold on;
-surf(XX.ampAXIS,XX.phi0,XX.AAC,'EdgeColor','none','FaceAlpha',.8,'FaceColor',[214, 26, 70]/255);
-hold on;
-surf(XX.ampAXIS,XX.phi0,XX.CFC,'EdgeColor','none','FaceAlpha',.9,'FaceColor',[253, 220, 34]/255);
-
+surf(XX.ampAXIS,XX.phi0,XX.AAC,'FaceAlpha',.8,'FaceColor',[214, 26, 70]/255);
+surf(XX.ampAXIS,XX.phi0,XX.CFC,'FaceAlpha',.9,'FaceColor',[253, 220, 34]/255);
xlim([min(XX.ampAXIS),max(XX.ampAXIS)]); ylim([min(XX.phi0),max(XX.phi0)])
xlabel('A_{low}'); ylabel('\Phi_{low}'); zlabel('A_{high}')
-legend('PAC','AAC','CFC')
+legend('\phi_{low}','A_{low}','\phi_{low},A_{low}')
set(gca,'FontSize',13)
+set(gca,'YTick',-pi:pi:pi)
+set(gca,'YTickLabel',{'-\pi','0','\pi'})
+set(gca,'Ydir','reverse')
grid off
-zlim([.008,.02])
\ No newline at end of file
+zlim([.002,.013])
\ No newline at end of file
diff --git a/LICENSE b/LICENSE
new file mode 100644
index 0000000..f288702
--- /dev/null
+++ b/LICENSE
@@ -0,0 +1,674 @@
+ GNU GENERAL PUBLIC LICENSE
+ Version 3, 29 June 2007
+
+ Copyright (C) 2007 Free Software Foundation, Inc.
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
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diff --git a/Patient_Data.mat b/Patient_Data.mat
old mode 100644
new mode 100755
diff --git a/README.md b/README.md
index c90a8a2..8dac6af 100644
--- a/README.md
+++ b/README.md
@@ -1,16 +1,20 @@
# GLM-CFC
-A GLM based approach to measure CFC
+A GLM based approach to assess CFC.
-Code to measure cross-frequency coupling between two signals as described in this manuscript: [A statistical modeling framework to assess cross-frequency coupling while accounting for confounding effects]
+Code to measure cross-frequency coupling between two signals as described in this manuscript:
-simfun: code to simulate signals V_low, V_high, with induced cross-frequency coupling and measure output statistics R_PAC, R_AAC, and R_CFC, along with confidence intervals and p-values
+[A statistical framework to assess cross-frequency coupling while accounting for confounding analysis effects](https://www.biorxiv.org/content/10.1101/519470v2), J. Nadalin, L-E Martinet, E. Blackwood, M-S Lo, A. S. Widge, S. S. Cash, U. T. Eden, M. A. Kramer, 2019.
-glmfun: code to evaluate coupling statistics R_PAC, R_AAC, and R_CFC, along with confidence intervals and p-values, between two signals
+`ExampleCode.m`: Run the cells in this file to produce example voltage traces and surfaces in (Phi_low, A_low, A_high)-space (as in Figure 4 of the manuscript). Four simulations are present: (i) no CFC, (ii) PAC only, (iii) AAC only, and (iv) both PAC and AAC.
-ExampleCode: run to get example voltage traces and surfaces in Phi_low, A_low, A_high space (as in Figure 4). Four simulations are present: one with no CFC, one with PAC, one with AAC, and one with both PAC and AAC
+`simfun.m`: Code to simulate signals V_low, V_high, with induced cross-frequency coupling and measure output statistics R_PAC and R_AAC along with confidence intervals and p-values.
-glmfun_with_indicator: an example of how to update glmfun to test for effect of condition (e.g. pre and post stimuli) on coupling
+`glmfun.m`: Code to evaluate the coupling statistics R_PAC and R_AAC, along with confidence intervals and p-values, between two signals.
-The human data from figures 9 and 10 can be found in Patient_Data, and the rat data from figure 11 can be found at https://github.com/tne-lab/cl-example-data
+`glmfun_with_indicator.m`: Cn example of how to update glmfun to test for effect of condition (e.g. pre and post stimuli) on coupling
-Any questions/comments please direct to Jessica Nadalin (jnadalin@bu.edu)
+The voltage traces for the human data can be found in `Patient_Data.mat`, and the rodent data can be found at https://github.com/tne-lab/cl-example-data
+
+The [Chaotic System Toolbox](https://www.mathworks.com/matlabcentral/fileexchange/1597-chaotic-systems-toolbox) is required to generate surrogate data.
+
+Any questions/comments please direct to Jessica Nadalin (jnadalin@bu.edu) or Mark Kramer (mak@bu.edu)
\ No newline at end of file
diff --git a/glmfun.m b/glmfun.m
old mode 100644
new mode 100755
index 4a1912f..2bfda8e
--- a/glmfun.m
+++ b/glmfun.m
@@ -1,25 +1,23 @@
-function [XX,P] = glmfun(Vlo, Vhi,pval,ci,varargin)
+function [XX,P] = glmfun(Vlo, Vhi,pval,ci,AIC,varargin)
%INPUTS:
% Vlo: Low frequency signal
% Vhi: High frequency signal
-% nCtlPts: number of control points, for spline phase
% pval: 'theoretical' gives analytic p-values for R
% 'empirical' gives bootstrapped p-values for R
% ci: 'ci' gives confidence intervals, 'none' gives no confidence intervals
+% AIC: 'AIC' computes number of control points for spline
+% phase via AIC minimization
% varargin: optionally, include the parameter q indicating which quantiles
% of AmpLo you'd like to fit over
%OUTPUTS:
-% XX.rpac: R_PAC value, confidence intervals XX.rPAC_CI
-% XX.raac: R_AAC value, confidence intervals XX.rAAC_CI
-% XX.rcfc: R_CFC value, confidence intervals XX.rCFC_CI
-% XX.null: 3D surface for null model in Phi_low, A_low, A_high space
-% XX.PAC: 3D surface for PAC model in Phi_low, A_low, A_high space
-% XX.AAC: 3D surface for AAC model in Phi_low, A_low, A_high space
-% XX.CFC: 3D surface for CFC model in Phi_low, A_low, A_high space
-% P.rpac: p-value for RPAC statistic
-% P.raac: p-value for RAAC statistic
-% P.rcfc: p-value for RCFC statistic
+% XX.rpac: R_PAC value, confidence intervals XX.rPAC_CI
+% XX.raac: R_AAC value, confidence intervals XX.rAAC_CI
+% XX.Phi_low: 3D surface for Phi_low model in Phi_low, A_low, A_high space
+% XX.A_low: 3D surface for A_low model in Phi_low, A_low, A_high space
+% XX.Phi_low_A_low: 3D surface for Phi_low,A_low model in Phi_low, A_low, A_high space
+% P.rpac: p-value for RPAC statistic
+% P.raac: p-value for RAAC statistic
nCtlPts = 10;
@@ -28,23 +26,49 @@
amp = abs(hilbert(Vhi));
ampLO = abs(hilbert(Vlo));
+ if exist('AIC','var') && strcmp(AIC, 'AIC')
+
+ Y = amp';
+ CtlPts = (4:1:30);
+ %Compute the AIC.
+ AIC1 = zeros(size(CtlPts));
+ for k=1:length(CtlPts) %for each suggested # knots
+ nCtlPts = CtlPts(k);
+ X1 = spline_phase0(phi',nCtlPts);%low frequency phase
+ [~, dev1, ~] = glmfit(X1, Y, 'gamma', 'link', 'log', 'constant', 'off'); %Phi_low model
+ AIC1(k) = dev1 + 2*nCtlPts; %compute AIC
+ end
+ %Select the # control points from AIC, and plot the AIC.
+ [~, imn1] = min(AIC1);
+ nCtlPts1 = CtlPts(imn1);
+
+ figure(1); clf();
+ plot(CtlPts, AIC1, 'k', 'LineWidth',2)
+ hold on
+ plot([nCtlPts1, nCtlPts1], [min(AIC1) max(AIC1)], 'r', 'LineWidth', 2)
+ hold off
+ axis tight
+ xlabel('# control points')
+ ylabel('AIC')
+ set(gca,'FontSize',13)
+ fprintf(['Suggested number of control points is ' num2str(nCtlPts1) '\n'])
+ nCtlPts = nCtlPts1;
+ end
+
%Define variables for GLM procedure.
Y = amp'; %high frequency amplitude
X1 = spline_phase0(phi',nCtlPts); %low frequency phase
X2 = [ones(size(Y)),ampLO']; %low frequency amplitude
X3 = [X1,ampLO',sin(phi').*ampLO',cos(phi').*ampLO']; %low frequency phase, low frequency amplitude, interaction terms
- XC = ones(size(Y)); %ones (null)
%Perform GLM.
[b1, dev1, stats1] = glmfit(X1, Y, 'gamma', 'link', 'log', 'constant', 'off'); %PAC
[b2, dev2, stats2] = glmfit(X2, Y, 'gamma','link','log','constant','off'); %AAC
[b3, dev3, stats3] = glmfit(X3, Y, 'gamma','link','log','constant','off'); %CFC
- [bC, dev0, statsC] = glmfit(XC, Y, 'gamma', 'link', 'log', 'constant', 'off'); %null
%Chi^2 test between nested models (theoretical p-values)
- chi0 = 1-chi2cdf(dev0-dev3,12);
- chi1 = 1-chi2cdf(dev1-dev3,3); %Between PAC and PACAAC Model, if low AAC is present
- chi2 = 1-chi2cdf(dev2-dev3,11); %Between AAC and PACAAC Model, if low PAC is present
+ chi1 = 1-chi2cdf(dev1-dev3,3); %Between Phi_low and Phi_low,A_low Model, if low AAC is present
+ chi2 = 1-chi2cdf(dev2-dev3,11); %Between A_low and Phi_low,A_low Model, if low PAC is present
%create 3d model surfaces
phi0 = linspace(-pi,pi,100);
@@ -54,45 +78,39 @@
ind = find(ampLO>quantile(ampLO,q) & ampLOXX.rpac)))/length(M.rpac);
P.raac = max(.5,length(find(M.raac>XX.raac)))/length(M.raac);
- P.rcfc = max(.5,length(find(M.rcfc>XX.rcfc)))/length(M.rcfc);
elseif exist('pval','var') && strcmp(pval, 'theoretical')
P.rpac = chi2; %use theoretical p-values
P.raac = chi1;
- P.rcfc = chi0;
else
P = 'No p-values output';
end
@@ -103,43 +121,56 @@
Amax = max(ampSORT); Amin = min(ampSORT); stepsize = (Amax-Amin)/99;
X2eval = Amin:stepsize:Amax; %evaluate on all amplitudes
X2eval = [ones(size(phi0))',X2eval'];
- %Determine CI for the measure RPAC.
- M = 10000;
- bMC = b1*ones(1,M) + sqrtm(stats1.covb)*normrnd(0,1,nCtlPts,M);
- splineMC = glmval(bMC,X0,'log',stats1,'constant', 'off');
- mx = zeros(M,1);
- for k=1:M
- mx(k) = max(abs(1-splineMC(:,k)./splineC));
- end
- r_CI = quantile(mx, [0.025, 0.975]);
- XX.rpac_ci = r_CI;
-
- %and for rAAC
- M = 10000;
- bMC = b2*ones(1,M) + sqrtm(stats2.covb)*normrnd(0,1,2,M);
- splineMC = glmval(bMC,X2eval,'log',stats2,'constant', 'off');
- mx = zeros(M,1);
- for k=1:M
- mx(k) = max(abs(1-splineMC(:,k)./splineC));
- end
- r2_CI = quantile(mx, [0.025, 0.975]);
- XX.raac_ci = r2_CI;
-
- %and for rCFC
- M = 10000;
- [m,~] = max(abs(1-XX3./XXC)); %find point of maximum distance between null, CFC models
- [~,j] = max(m); %j ampLO, I(j) phiLO
- bMC = b3*ones(1,M) + sqrtm(stats3.covb)*normrnd(0,1,nCtlPts+3,M);
- Y1 = spline_phase0(phi0',nCtlPts); %model 1, function of phiLo
- Y2 = [Y1,ampAXIS(j)*ones(size(phi0))']; %model 2, function of phiLo, ampLo
- Y3 = [Y2,ampAXIS(j)*sin(phi0'),ampAXIS(j)*cos(phi0')];
- splineMC = glmval(bMC,Y3,'log',stats3,'constant', 'off');
- mx = zeros(M,1);
- for k=1:M
- mx(k) = max(abs(1-splineMC(:,k)./splineC));
- end
- r3_CI = quantile(mx, [0.025, 0.975]);
- XX.rcfc_ci = r3_CI;
+
+ [m] = max(abs(1-Xtemp'./XX3)); %find point of maximum distance between A_low and Phi_low,A_low models
+ [~,j] = max(m); %j ampLO index
+ [m2] = max(abs(1-Xtemp'./XX3),[],2);
+ [~,j2] = max(m2); %j2 phiLO index
+ phiLOW = phi0(j2);
+ M = 10000;
+ bMC = b3*ones(1,M) + sqrtm(stats3.covb)*normrnd(0,1,nCtlPts+3,M);
+ %Phi_low,A_low model at fixed Phi_low
+ Y_phi = spline_phase0(phiLOW*ones(size(phi0)),nCtlPts); %Phi_low model
+ AmpLOW = [Amin:stepsize:Amax]';
+ Y_phi = [Y_phi,AmpLOW]; %A_low model
+ Y_phi = [Y_phi,AmpLOW*sin(phiLOW'),AmpLOW*cos(phiLOW')];
+ spline_phi = glmval(bMC,Y_phi,'log',stats3,'constant', 'off'); %Phi_low,A_low model, constant in phi_low dim
+ %Phi_low,A_low model at fixed A_low
+ Y_a = spline_phase0(phi0',nCtlPts); %Phi_low model
+ Y_a = [Y_a,ampAXIS(j)*ones(size(phi0))']; %A_low model
+ Y_a = [Y_a,ampAXIS(j)*sin(phi0'),ampAXIS(j)*cos(phi0')];
+ spline_a = glmval(bMC,Y_a,'log',stats3,'constant','off'); %Phi_low,A_low model, constant in A_low dimension
+ %A_low model at fixed A_low
+ bMC = b2*ones(1,M) + sqrtm(stats2.covb)*normrnd(0,1,2,M);
+ X2eval_fixed_A = [ones(size(phi0))',ones(size(phi0))'*ampAXIS(j)];
+ splineMC = glmval(bMC,X2eval_fixed_A,'log',stats2,'constant', 'off');
+ splineAAC_a = splineMC;
+ %A_low model at fixed Phi_low
+ M = 10000;
+ bMC = b2*ones(1,M) + sqrtm(stats2.covb)*normrnd(0,1,2,M);
+ splineMC = glmval(bMC,X2eval,'log',stats2,'constant', 'off');
+ splineAAC_phi = splineMC;
+ %Phi_low model at fixed A_low
+ M = 10000;
+ bMC = b1*ones(1,M) + sqrtm(stats1.covb)*normrnd(0,1,nCtlPts,M);
+ splinePAC_a = glmval(bMC,X0,'log',stats1,'constant', 'off');
+ %Phi_low model at fixed Phi_low
+ X0_eval_fixed_Phi = spline_phase0(phiLOW*ones(size(phi0)),nCtlPts);
+ bMC = b1*ones(1,M) + sqrtm(stats1.covb)*normrnd(0,1,nCtlPts,M);
+ splinePAC_phi = glmval(bMC,X0_eval_fixed_Phi,'log',stats1,'constant', 'off');
+
+ mx_pac = zeros(M,1); mx_aac = zeros(M,1);
+ for k = 1:M
+ m_a = max(abs(1-splineAAC_a(:,k)./spline_a(:,k))); %fixed A
+ m_phi = max(abs(1-splineAAC_phi(:,k)./spline_phi(:,k))); %fixed Phi
+ mx_pac(k) = max(m_a,m_phi);
+
+ m_a = max(abs(1-splinePAC_a(:,k)./spline_a(:,k))); %fixed A
+ m_phi = max(abs(1-splinePAC_phi(:,k)./spline_phi(:,k))); %fixed Phi
+ mx_aac(k) = max(m_a,m_phi);
+ end
+ XX.rpac_ci = quantile(mx_pac,[0.025,0.975]);
+ XX.raac_ci = quantile(mx_aac,[0.025,0.975]);
end
end
@@ -147,16 +178,15 @@
% Bootstrapped p-values
function M = minvals(Vlo,Vhi)
K = 100;
- RPAC = zeros(1,K); RCFC = zeros(1,K); RAAC = zeros(1,K);
+ RPAC = zeros(1,K); RAAC = zeros(1,K);
N = zeros(1,K); L = zeros(1,K);
for i = 1:K
Vhi_prime = AAFT(Vhi,1);
- [XX] = glmfun(Vlo,Vhi_prime','none'); %compute R statistics between Vhi and shifted Vlo
+ [XX] = glmfun(Vlo,Vhi_prime','none','none','none',.05); %compute R statistics between Vhi and shifted Vlo
RPAC(i) = XX.rpac;
- RCFC(i) = XX.rcfc;
RAAC(i) = XX.raac;
end
- M.rpac = RPAC; M.rcfc = RCFC; M.raac = RAAC; M.shiftN = N; M.shiftL = L;
+ M.rpac = RPAC;M.raac = RAAC;
end
% Generate a design matrix X (n by nCtlPts) for a phase signal (n by 1)
diff --git a/simfun.m b/simfun.m
old mode 100644
new mode 100755
index 93cff38..fc0b8f6
--- a/simfun.m
+++ b/simfun.m
@@ -1,4 +1,4 @@
-function [XX,P,Vlo,Vhi,t] = simfun(pac_mod,aac_mod,sim_method,pval,ci,varargin)
+function [XX,P,Vlo,Vhi,t] = simfun(pac_mod,aac_mod,sim_method,pval,ci,AIC,varargin)
%INPUTS:
% pac_mod: Intensity of PAC (I_PAC in paper)
% aac_mod: Intensity of AAC (I_AAC in paper)
@@ -8,23 +8,22 @@
% 'empirical' gives bootstrapped p-values for R
% ci: 'ci' gives confidence intervals for R
% 'none' gives no confidence intervals (faster)
+% AIC: 'AIC' computes number of control points for spline
+% phase via AIC minimization
% varargin: optionally, include the parameter q indicating which quantiles
% of AmpLo you'd like to fit over
%
%OUTPUTS:
-% XX.rpac: R_PAC value, confidence intervals XX.rPAC_CI
-% XX.raac: R_AAC value, confidence intervals XX.rAAC_CI
-% XX.rcfc: R_CFC value, confidence intervals XX.rCFC_CI
-% XX.null: 3D surface for null model in Phi_low, A_low, A_high space
-% XX.PAC: 3D surface for PAC model in Phi_low, A_low, A_high space
-% XX.AAC: 3D surface for AAC model in Phi_low, A_low, A_high space
-% XX.CFC: 3D surface for CFC model in Phi_low, A_low, A_high space
-% P.rpac: p-value for RPAC statistic
-% P.raac: p-value for RAAC statistic
-% P.rcfc: p-value for RCFC statistic
-% Vlo: simulated low-frequency signal
-% Vhi: simulated high-frequency signal
-% t: time
+% XX.rpac: R_PAC value, confidence intervals XX.rPAC_CI
+% XX.raac: R_AAC value, confidence intervals XX.rAAC_CI
+% XX.Phi_low: 3D surface for Phi_low model in Phi_low, A_low, A_high space
+% XX.A_low: 3D surface for A_low model in Phi_low, A_low, A_high space
+% XX.Phi_low_A_low: 3D surface for Phi_low,A_low model in Phi_low, A_low, A_high space
+% P.rpac: p-value for RPAC statistic
+% P.raac: p-value for RAAC statistic
+% Vlo: simulated low-frequency signal
+% Vhi: simulated high-frequency signal
+% t: time
dt = 0.002; Fs = 1/dt; fNQ = Fs/2; % Simulated time series parameters.
N = 20/dt+4000; % # steps to simulate, making the duration 20s
@@ -77,16 +76,41 @@
end
s = s/max(s); % Normalize so it falls between 0 and 1
-if exist('sim_method','var') && strcmp(sim_method, 'GLM')
- Ahi = (1+pac_mod*s)'; % Define Ahi.
- Vhi = (0.01* Ahi .* cos(angle(hilbert(Vhi'))))';% ... and use PhiHi to get Vhi.
-elseif exist('sim_method','var') && strcmp(sim_method, 'pink')
- Vhi = Vhi.*(1+pac_mod*s); % Modulate high freq activity by modulation envelope.
+if exist('sim_method','var')
+
+ switch sim_method
+
+ case 'GLM'
+ Ahi = (1+pac_mod*s)'; % Define Ahi.
+ Vhi = (0.01* Ahi .* cos(angle(hilbert(Vhi'))))';% ... and use PhiHi to get Vhi.
+ Vhi = Vhi.*(1+aac_mod*AmpLo/max(AmpLo));
+
+ case 'pink'
+ Vhi = Vhi.*(1+pac_mod*s); % Modulate high freq activity by modulation envelope.
+ Vhi = Vhi.*(1+aac_mod*AmpLo/max(AmpLo));
+
+ case 'spiking' % Add a spiking model.
+ N = 20/dt; % # steps to simulate, making the duration 20s
+ t = (1:N)*dt; % Time axis.
+ Alo = 1+(sin(2*pi*t*0.1)+1)/2; % Slow modulation of low frequency envelope.
+ Philo = pi*sawtooth(2*pi*t*4); % Low frequency phase is periodic (4 Hz).
+ Vlo = Alo.*cos(Philo);
+
+ Philo_star = pi + Alo*pi; % Target phase depends on low frequency envelope.
+ sigma = 0.01;
+ lambda = 1/sqrt(2*pi*sigma) * exp( -(1+sawtooth(Philo - Philo_star,1/2)).^2 / (2*sigma^2) );
+ lambda = (0.001+0.3*lambda/max(lambda));
+ Vhi = 1*binornd(1,lambda); % When low freq phase is near target phase, produce a spike.
+
+ Vlo =(Vlo)+0.1*randn(size(Vlo)); % Define Vlo and Vhi directly for this sim.
+ Vhi =(Vhi)+0.1*randn(size(Vlo));
+ end
+
else
return
end
-Vhi = Vhi.*(1+aac_mod*AmpLo/max(AmpLo));
+if exist('sim_method','var') && ~strcmp(sim_method, 'spiking')
Vpink2 = make_pink_noise(1,N,dt); % Create additional pink noise signal
noise_level = 0.01;
@@ -116,11 +140,13 @@
filtwts = firls(filtorder,f,m); % get FIR filter coefficients
Vhi = filtfilt(filtwts,1,V1); % Define high freq band activity.
+end
+
if isempty(varargin)
- [XX,P] = glmfun(Vlo, Vhi, pval,ci);
+ [XX,P] = glmfun(Vlo, Vhi, pval,ci,AIC);
else
q = varargin{1};
- [XX,P] = glmfun(Vlo, Vhi, pval,ci,q);
+ [XX,P] = glmfun(Vlo, Vhi, pval,ci,AIC,q);
end
end