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Traveling waves across scales: Different mechanisms but same canonical computation?

Code ↔ Paper

3 matches between paragraphs of the paper and lines of its authors' code, computed by the harvester (lexical-v1). Click a colored paragraph or line to see its counterpart.

The 3 matches
  1. [1] § A framework for contextualizing potential origins of first- and second-order traveling waves ↔ Model-TW-Fig2.m, lines 335–363 · score 0.59 · recipient structure, power law, propagation delay, postsynaptic
  2. [2] § A framework for contextualizing potential origins of first- and second-order traveling waves ↔ Model-TW-Fig2.m, lines 126–183 · score 0.52 · post synaptic, horizontal propagation, network, phase, cortical
  3. [3] § A framework for contextualizing potential origins of first- and second-order traveling waves ↔ Model-TW-Fig2.m, lines 335–363 · score 0.52 · power law exponent, recipient structure, convolution, NL, propagation, delay

Paper

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The authors' code

MATLAB · 380 lines · 13 KB · no license · 3 matches

  1. %% ------------------------------------------ PARAMETERS
  3. AFP=0.2;% parameter of the alpha function (for g1)
  4. GainFB=0.25 ; % parameter for the gain of the feedback
  5. NL=4;% power law to account for the non-linearity (inspired from estimation going from vsd to spike)
  7. x=0:0.001:0.5; % temporal axis
  9. a1=0.024; % time constant of the first area
  10. d_tc=0.004; % increase of time constant from area to areas
  12. colcol=parula(5);
  14. % ---------- INTEGRATIVE TIME CONSTANTS IN ALL AREAS
  16. tc_a=a1:d_tc:(a1+5*d_tc);
  18. % g1 is the first input (alpha function) to the first area
  19. g1= x.^AFP .* exp (-x./tc_a(1)) ./ tc_a(1); % alpha function of the first area (FF driven)
  20. g1=g1./sum(g1); % normalization
  22. clear TC
  23. for i=1:5
  24. gtemp= exp (-x./tc_a(i)) ./ tc_a(i); % integration time constant of the i-st area
  25. TC(i,:)=gtemp./sum(gtemp); % normalization
  26. end
  28. % ---------- DELAYS BETWEEN ALL AREAS
  30. clear del
  31. del(1,2)=0.002; % delays from area 1 to area 2
  32. del(2,1)=0.004; % delays from area 2 to area 1
  34. for i=1:5
  35. del(i+1, i+2)=del(1,2); % delays from area i+1 to area i+2
  36. del(i+2, i+1)=del(2,1); % delays from area i+2 to area i+1
  37. end
  41. %% ------------------------------------------ FIGURE 2A
  42. % In this figure, we take a simple response (yy) and add to it the effect
  43. % of delay yy_DL, then integration time constant (yy_DL_TC) and then
  44. % nonlinearity (yy_DL_TC_NL)
  46. figure(21)
  47. clf, set(gcf,'PaperPosition',[0.25 0.25 50 10]);
  49. % CortConv is a function simulating the cortical integration (see below)
  50. % the first step is thus to integrate an alpha function (g1)
  51. % depending on the parameter of the CortConv function :
  52. % (input, time constant, delay, time vector, power law exponent)
  54. yy = CortConv( g1 ,squeeze(TC(1,:)),0 ,x,NL);
  55. yy_DL = CortConv( yy ,zeros(1,501) , del(1,2),x,1 );
  56. yy_DL_TC = CortConv( yy ,squeeze(TC(1,:)), del(1,2),x,1 );
  57. yy_DL_TC_NL = CortConv( yy ,squeeze(TC(1,:)), del(1,2),x,NL);
  59. subplot(1,5,1) % ---------- plot of yy
  60. plot(x,yy,'color',colcol(1,:),'linewidth',4);
  61. hold on
  62. [HWg(1)]=find(yy>=max(yy/2),1);
  63. plot(x(HWg(1)),yy(HWg(1)),'o','color',colcol(1,:),'linewidth',2,'MarkerSize',15,'MarkerFaceColor','w');
  64. line([ 0 0],[0 0.005],'color',colcol(1,:),'linewidth',2)
  66. xlim([-0.005 0.10])
  67. ylim([-0.001 0.025])
  68. xlabel('Time ms')
  69. ylabel('Activity (au)')
  70. grid;
  71. Figure_appearance
  74. subplot(1,5,2) % ---------- plot of y_DL
  75. plot(x,yy_DL,'color',colcol(2,:),'linewidth',4);
  76. hold on
  77. [HWg(2)]=find(yy_DL>=max(yy_DL/2),1);
  78. plot(x(HWg(2)),yy_DL(HWg(2)),'o','color',colcol(2,:),'linewidth',2,'MarkerSize',15,'MarkerFaceColor','w');
  79. line([ (del(1,2)) (del(1,2))],[0 0.005],'color',colcol(1,:),'linewidth',2)
  81. xlim([-0.005 0.10])
  82. ylim([-0.001 0.025])
  83. title('+ D')
  84. grid;
  85. Figure_appearance
  87. subplot(1,5,3) % ---------- plot of yy_DL_TC
  88. plot(x,yy_DL_TC,'color',colcol(2,:),'linewidth',4);
  89. hold on
  90. [HWg(3)]=find(yy_DL_TC>=max(yy_DL_TC/2),1);
  91. plot(x(HWg(3)),yy_DL_TC(HWg(3)),'o','color',colcol(2,:),'linewidth',2,'MarkerSize',15,'MarkerFaceColor','w');
  92. line([ (del(1,2)) (del(1,2))],[0 0.005],'color',colcol(1,:),'linewidth',2)
  93. xlim([-0.005 0.10])
  94. ylim([-0.001 0.025])
  95. title('+ D+TC')
  96. grid;
  97. Figure_appearance
  99. subplot(1,5,4) % ---------- plot of yy_DL_TC_NL
  100. plot(x,yy_DL_TC_NL,'color',colcol(2,:),'linewidth',4);
  101. hold on
  102. [HWg(4)]=find(yy_DL_TC_NL>=max(yy_DL_TC_NL/2),1);
  103. plot(x(HWg(4)),yy_DL_TC_NL(HWg(4)),'o','color',colcol(2,:),'linewidth',2,'MarkerSize',15,'MarkerFaceColor','w');
  104. line([ (del(1,2)) (del(1,2))],[0 0.005],'color',colcol(1,:),'linewidth',2)
  106. xlim([-0.005 0.10])
  107. ylim([-0.001 0.025])
  108. title('+ NL + D + TC')
  109. grid;
  110. Figure_appearance
  113. subplot(1,5,5) % ---------- plot of phase estimations across all 4 conditions
  114. hold on
  115. plot(1000*del(1,2)*0,1000*x(HWg(1)),'o','color',colcol(1,:),'linewidth',2,'MarkerSize',10,'MarkerFaceColor','w');
  117. for z=2:4 % times steps
  118. plot(1000*del(1,2),1000*x(HWg(z)),'o','color',colcol(2,:),'linewidth',2,'MarkerSize',10,'MarkerFaceColor','w');
  119. end
  121. grid; Figure_appearance
  122. xlim([0 3])
  123. ylim([0 20])
  126. %% ------------------------------------------ FIG 2B
  127. % figure illustrating the case of horizontal propagation within one area
  129. delH=0.01; % delay from each node sample along the horizontal network
  130. tab=[1 1; 2 2; 3 3; 4 4; 5 5 ]; % receiving layer / time step
  131. ER(1,1,:)=CortConv( g1 ,squeeze(TC(1,:)),0,x,NL); % CortConv is a function for the cortical integration
  133. clear HPSI % horizontal post-synaptic integration
  134. for z=1:size(tab,1) % times steps
  135. j=tab(z,1); k=tab(z,2);
  136. if j>1,
  137. HPSI(j,k,:)=CortConv( squeeze(ER(1,1,:)) ,squeeze(TC(j,:)), delH*(j-1),x,NL); % Horizontal PostSynaptic Integration (PSI) of layer j (Time constant j) of FF input (coming from layer j-1) , step k
  138. ER(j,k,:)=squeeze(HPSI(j,k,:));
  139. end
  140. end
  143. figure(22)
  144. clf, set(gcf,'PaperPosition',[0.25 0.25 50 10]);
  147. for z=2:size(tab,1) % t---------- Times steps
  148. j=tab(z,1);
  150. subplot(1,size(tab,1),z-1) % plot the hPSI at each step
  151. clcl=1;
  153. plot(x,squeeze(ER(j,j,:)),'color',colcol(clcl,:),'linewidth',4);
  154. hold on
  156. [HWz(j,j)]=find(ER(j,j,:)>=max(squeeze(ER(j,j,:)))/2,1); % extract and plot an approximation of the phase (half height) HWz
  157. plot(x(HWz(j,j)),squeeze(ER(j,j,HWz(j,j))),'o','color',colcol(clcl,:),'linewidth',2,'MarkerSize',15,'MarkerFaceColor','w');
  159. line([ delH*(j-1) delH*(j-1)],[0 0.005],'color',colcol(clcl,:),'linewidth',2)
  161. xlim([-0.005 0.25])
  162. ylim([-0.001 0.025])
  163. grid;
  164. Figure_appearance
  166. end
  168. [HWz(1,1)]=find(ER(1,1,:)>=max(squeeze(ER(1,1,:)))/2,1); % extract an approximation of the phase (half height) HWz
  171. subplot(1,5,5) % ---------- final plot of the evolution of the phase (HWz) across all steps
  172. hold on
  173. line([0 40],1000*x(HWz(1,1))+[0 40],'color','k','linewidth',3,'linestyle',':')
  174. line([0 40],1000*x(HWz(1,1))+[0 80],'color','k','linewidth',2,'linestyle',':')
  175. line([0 40],1000*x(HWz(1,1))+[0 120],'color','k','linewidth',1,'linestyle',':')
  176. plot(0,1000*x(HWz(1,1)),'o','color',colcol(1,:),'linewidth',2,'MarkerSize',10,'MarkerFaceColor','w');
  177. for z=2:5 % times steps
  178. j=z+(k-1)*2;
  179. plot(1000*(z-1).*delH,1000*x(HWz(z,z)),'o','color',colcol(1,:),'linewidth',2,'MarkerSize',10,'MarkerFaceColor','w');
  180. end
  182. ylim([0 90])
  183. grid; Figure_appearance
  187. %% ------------------------------------------ INTER-CORTICAL SIMULATION OF EVOKED RESPONSE (ER)
  188. % ER IS CALCULATED AS SUM OF POSTSYNAPTIC INTEGRATION (PSI) FROM Feedforward (FF) AND Feedback (FB)
  190. clear ER tab PSI
  193. % ER(i,j,:) is Evoked Response in time for hierarchical level i, and cycle step j
  195. ER(1,1,:)=CortConv( g1 ,squeeze(TC(1,:)),0,x,NL); % CortConv is a function for the cortical integration (see below)
  196. % the first step is thus to integrate an alpha function (g1)
  197. ER(2,1,:)=x.*0; % ER for downstream areas is set to 0 when no activity yet reached this level
  198. ER(3,1,:)=x.*0;
  199. ER(4,2,:)=x.*0;
  200. ER(5,3,:)=x.*0;
  201. ER(6,4,:)=x.*0;
  203. % tab is defining, for each time step z, the corresponding hierarchical level (tab(z,1)) and the cycle step (tab(z,2))
  204. tab=[2 2; 1 3; 3 3; 2 4; 4 4; 1 5 ;3 5 ;5 5; 2 6 ; 4 6 ; 1 7 ; 3 7 ; 5 7; 2 8 ; 4 8 ; 1 9 ; 3 9 ; 5 9 ; 4 10 ]; % receiving layer / time step
  206. for z=1:size(tab,1) % times steps
  207. j=tab(z,1); k=tab(z,2);
  208. if j>1,
  209. % PostSynaptic Integration (PSI) of layer j (Time constant j) of FF input (ER coming from layer j-1) , step k
  210. PSI(j-1,j,k,:)=CortConv( squeeze(ER(j-1,k-1,:)) ,squeeze(TC(j,:)), del(j-1,j),x,NL);
  211. % PostSynaptic Integration (PSI) of layer j (Time constant j) of FB input (ER coming from layer j+1) , step k
  212. PSI(j+1,j,k,:)=CortConv( squeeze(ER(j+1,k-1,:)) ,squeeze(TC(j,:)), del(j+1,j),x,NL);
  213. ER(j,k,:)=squeeze(PSI(j-1,j,k,:))+GainFB.*squeeze(PSI(j+1,j,k,:));
  214. else
  215. % PostSynaptic Integration (PSI) of layer j (Time constant j) of FB input (ER coming from layer j+1) , step k
  216. PSI(j+1,j,k,:)=CortConv( squeeze(ER(j+1,k-1,:)) ,squeeze(TC(j,:)), del(j+1,j),x,NL);
  217. ER(j,k,:)=squeeze(ER(j,k-2,:))+GainFB.*squeeze(PSI(j+1,j,k,:));
  218. end
  219. end
  224. %% ------------------------------------------ SUPPL FIG
  225. % Not in the paper, but shows all the cycles (columns)
  226. % iterations across all hierarchical levels (color-coded, row),
  227. % to calculate HWx, estimation of phase in each steps
  228. % feedforward is dotted, feedback dashed
  230. figure(24)
  231. clf, set(gcf,'PaperPosition',[0.25 0.25 40 25]);
  233. tab=[1 1; 2 2; 1 3; 3 3; 2 4; 4 4; 1 5 ;3 5 ; 2 6 ; 4 6 ; 1 7 ; 3 7 ; 2 8 ; 4 8 ; 3 9 ; 4 10 ]; % receiving layer / time step
  236. for z=1:size(tab,1) % ---------- times steps
  237. j=tab(z,1); k=tab(z,2);
  239. subplot('Position',[k/11-0.02 j/5-0.1 0.1 0.2])
  241. plot(x,squeeze(ER(j,k,:)),'color',colcol(j,:),'linewidth',4);
  242. hold on
  243. if j>1
  244. plot(x,squeeze(PSI(j-1,j,k,:)),'color',colcol(j-1,:),'linestyle',':','linewidth',2);
  245. plot(x,GainFB.*squeeze(PSI(j+1,j,k,:)),'color',colcol(j+1,:),'linestyle','--','linewidth',2);
  246. else
  247. if k>2, plot(x,squeeze(ER(j,k-2,:)),'k:','linewidth',2); end
  248. plot(x,GainFB.*squeeze(PSI(j+1,j,k,:)),'k--','linewidth',2);
  249. end
  251. % GENERATING FF (dotted) and FB (dashed) arrows
  252. gcap=get(gca,'Position');
  253. if j<4
  254. arh=annotation('arrow', [gcap(1)+gcap(3)/2 gcap(1)+gcap(3)/2+0.03 ],[gcap(2)+gcap(4)/1.5 gcap(2)+gcap(4)/1.5+0.05] );
  255. arh.LineWidth = 2; arh.LineStyle = ':';
  257. end
  258. if j>1
  259. arh=annotation('arrow', [gcap(1)+gcap(3)/4 gcap(1)+gcap(3)/4+0.03 ],[gcap(2)-0.02 gcap(2)-0.05] );
  260. arh.LineWidth = 2; arh.LineStyle = '--';
  261. end
  263. [HWx(j,k)]=find(ER(j,k,:)>=max(squeeze(ER(j,k,:)))/2,1); % extract phase as half-width
  264. plot(x(HWx(j,k)),squeeze(ER(j,k,HWx(j,k))),'o','color',colcol(j,:),'linewidth',2,'MarkerSize',15,'MarkerFaceColor','w');
  266. line([ (del(1,2))*(j-1) (del(1,2))*(j-1)],[0 0.005],'color',colcol(j,:),'linewidth',2)
  268. xlim([-0.005 0.25])
  269. ylim([-0.001 0.025])
  270. grid;
  271. Figure_appearance
  273. end
  276. %% ------------------------------------------ FIG 2C
  277. % Figure compiling inter-cortical interactions across hierarchy
  278. % (color-coded) and cycle steps (rows)
  280. figure(23)
  281. clf,set(gcf,'PaperPosition',[0.25 0.25 50 10]);
  283. mxk=4 ;
  284. tab=[1 1; 2 2; 3 3; 4 4];
  286. for k=1:mxk
  287. subplot(1,mxk+1,k)
  288. hold on
  289. for z=1:4 % ---------- times steps
  290. j=z+(k-1)*2;
  291. plot(x, squeeze(ER(z,j,:)) ,'color',colcol(z,:),'linewidth',3)
  292. plot(x(HWx(z,j)),squeeze(ER(z,j,HWx(z,j))),'o','color',colcol(z,:),'linewidth',2,'MarkerSize',10,'MarkerFaceColor','w');
  293. line([ (del(1,2))*(z-1) (del(1,2))*(z-1)],[0 0.005],'color',colcol(z,:),'linewidth',2)
  295. xlim([0 0.2])
  296. ylim([0 0.025])
  297. grid; Figure_appearance
  298. end
  299. end
  301. subplot(1,mxk+1,mxk+1) % ---------- last plot recapitulating all phase (HWx)
  303. hold on
  304. line([0 7],1000*x(HWx(1,1))+[0 7],'color','k','linewidth',3,'linestyle',':')
  305. line([0 7],1000*x(HWx(1,1))+[0 14],'color','k','linewidth',2,'linestyle',':')
  306. line([0 7],1000*x(HWx(1,1))+[0 28],'color','k','linewidth',1,'linestyle',':')
  307. line([0 7],1000*x(HWx(1,1))+[0 56],'color','k','linewidth',0.5,'linestyle',':')
  308. line([0 7],1000*x(HWx(1,1))+[0 112],'color','k','linewidth',0.25,'linestyle',':')
  310. sz=size(HWx);
  311. for k=1:mxk
  313. zz=1:4;
  314. jj=zz+(k-1)*2;
  315. plot(1000*(zz-1)*del(1,2),1000*x(HWx(sub2ind(sz,zz,jj))),'-','color','k','linewidth',k/2);
  317. for z=1:4 % times steps
  318. j=z+(k-1)*2;
  319. plot(1000*(z-1)*del(1,2),1000*x(HWx(z,j)),'o','color',colcol(z,:),'linewidth',2,'MarkerSize',10,'MarkerFaceColor','w');
  320. end
  322. end
  323. xlim([0 6.5])
  324. ylim([0 90])
  326. grid; Figure_appearance
  328. footer(['NL =' num2str(NL) ' | GainFB =' num2str(GainFB) ' | DEL12 =' num2str(del(1,2)) ' | DEL21 =' num2str(del(2,1)) ' | TC1 =' num2str(a1(1))])
  333. %% Convolution of the output of a structure (G) with a recipient structure with time constant (g), after a propagation delay d - time is x
  335. function Gt = CortConv(G,g,dd,x,NL)
  336. % G : input integrated by a recipient structure with time constant (g)
  337. % a power law exponent NL, and after a propagation delay d - time is x
  339. if sum(G)~=0,
  340. Gs=G.^NL./sum(G.^NL); % Nonlinearity to go from Voltage to Spike (Chen et al 2012)
  341. else
  342. Gs=G;
  343. end
  345. if sum(g)~=0,
  346. Gsg=conv(Gs,g,'full'); % convolution between the output of structure 1 and the postsynaptic integration time constant g
  347. else
  348. Gsg=Gs;
  349. end
  351. if sum(Gsg)~=0,
  352. Gsg=Gsg./sum(Gsg); % normalizing
  353. end
  355. d=find(x>=dd,1);
  356. Gt=[zeros(1,d) Gsg(1:length(x)-d)]; % adding delay d
  359. end
  363. %% Figure appearance
  365. function [] = Figure_appearance()
  366. box off
  367. set(gca,'TickDir','out')
  368. set(gca,'XScale', 'linear')
  369. set(gca,'fontangle','oblique')
  370. set(gca,'fontsize',16)
  371. set(gca,'ticklength',[0.01 0.025])
  372. axis square
  373. set(gcf,'Color','w')
  374. unis = get(gcf,'units');
  375. ppos = get(gcf,'paperposition');
  376. set(gcf,'units',get(gcf,'paperunits'));
  377. pos = get(gcf,'position');
  378. pos(3:4) = ppos(3:4);
  379. set(gcf,'position',pos);
  380. end

Model-TW-Fig2.m at commit f720be0, no license · at the source

Overview

Authors: Laura Dugué1,2, Frédéric Chavane3
ORCID iDs: Laura Dugué, Frédéric Chavane
  1. Université Paris Cité, CNRS, Integrative Neuroscience and Cognition Center, Paris, France
  2. Institut Universitaire de France (IUF), Paris, France
  3. Aix-Marseille Université, CNRS, Institut de Neurosciences de la Timone, UMR7289, Marseille, France
Institutions: Centre National de la Recherche Scientifique (France); Institut Universitaire de France (France); Université Paris Cité (France); Centre Neurosciences intégratives et Cognition (France); Aix-Marseille Université (France); Institut de Neurosciences de la Timone (France)
Journal: n/a, volume 14, article e106753
Dates: received 12 March 2025; accepted 5 November 2025; published online 19 November 2025
Type: Review · Language: English
License: none stated
Identifiers: DOI 10.7554/elife.106753 · PMCID PMC12629594 · OpenAlex W4416538761
Open access: gold, a free copy (OpenAlex)
Status: code verified
Categories: human (organism), computational (subfield)
Methods: Connectivity, Evoked potentials, fMRI & imaging, Physiology & signal measures, Spectral & time-frequency
Keywords: Cortex, Neuroscience, Traveling Waves, Spatial Scales, Generative Mechanisms
MeSH: Brain*, Cerebral Cortex*, Models, Neurological*, Neurons*, Animals, Humans (* major topic)
Topic: Neural dynamics and brain function (Cognitive Neuroscience, Neuroscience), according to OpenAlex
Funding: European Research Council (852139); Agence Nationale de la Recherche (ANR-23-CE37-0019, ANR-20-CE37-0018, ANR-23-CE37-0024)
Citations: cited by 10 papers (Europe PMC); 98 references in the paper

Abstract

The abstract is not reproduced here: the paper's license (none stated) does not allow it. Read it in the paper, at the publisher or on Europe PMC.

Repository

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fchavane/Model_TW

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State: the link answers, verified on 26 September 2026
Evidence: files inventoried
Commit: f720be0d17610942057fbb2f07ff05453e7f096f, 14 November 2025
Languages: MATLAB (1)
Size: 2 files, 1 script
Software Heritage: not archived
Found in: “Data availability”
Holds: README
Not found: license file, CITATION.cff, environment file, tests, continuous integration, documentation
Availability: 1 check, the latest on 26 September 2026: the link answers
  • 26 September 2026: the link answers
2 files
At the source: github.com/fchavane/Model_TW

The paper's code and data availability statement is in the Data section.

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Read it in the paper: doi.org/10.7554/elife.106753.

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Recorded: type, language, journal, volume, pages, dates, 2 authors, 5 keywords, 6 MeSH terms, 2 funders, 95 references.

Cite

This paper

Dugué, L., & Chavane, F. (2025). Traveling waves across scales: Different mechanisms but same canonical computation? eLife, 14, e106753. https://doi.org/10.7554/elife.106753

BibTeX

@article{dugue2025traveling,
author = {Dugué, Laura and Chavane, Frédéric},
title = {{Traveling waves across scales: Different mechanisms but same canonical computation?}},
journal = {eLife},
year = {2025},
volume = {14},
pages = {e106753},
publisher = {eLife Sciences Publications, Ltd},
issn = {2050-084X},
doi = {10.7554/elife.106753},
url = {https://doi.org/10.7554/elife.106753},
pmcid = {PMC12629594}
}

RIS

TY - JOUR
AU - Dugué, Laura
AU - Chavane, Frédéric
TI - Traveling waves across scales: Different mechanisms but same canonical computation?
T2 - eLife
J2 - Elife
PY - 2025
DA - 2025
VL - 14
SP - e106753
SN - 2050-084X
PB - eLife Sciences Publications, Ltd
DO - 10.7554/elife.106753
UR - https://doi.org/10.7554/elife.106753
LA - en
ER -

CSL-JSON

{
"id": "10.7554/elife.106753",
"type": "article-journal",
"title": "Traveling waves across scales: Different mechanisms but same canonical computation?",
"container-title": "eLife",
"author": [
{
"family": "Dugué",
"given": "Laura"
},
{
"family": "Chavane",
"given": "Frédéric"
}
],
"container-title-short": "Elife",
"volume": "14",
"page": "e106753",
"DOI": "10.7554/elife.106753",
"PMCID": "PMC12629594",
"ISSN": "2050-084X",
"publisher": "eLife Sciences Publications, Ltd",
"URL": "https://doi.org/10.7554/elife.106753",
"language": "en",
"issued": {
"date-parts": [
[
2025
]
]
}
}

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