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Modeling the influences of non-local connectomic projections on geometrically constrained cortical dynamics.

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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.

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  1. [1] § Materials and methods › Model implementation ↔ Model/run_absorbing.m, lines 1–48 · score 0.53 · delta impulse, connectivity strength, coupling, traveling, widths, stimulus
  2. [2] § Materials and methods › Model implementation ↔ Model/run_bold_absorbing.m, the whole file · a weak match · score 0.53 · delta impulse, connectivity strength, coupling, traveling, widths, stimulus
  3. [3] § Results › Influence of a complex network of FNPs on cortical dynamics ↔ Experiments/fig7_connectome_nonrandom.m, lines 861–944 · score 0.52 · nearest hub, sampled stimulus positions, rich club, random connectomes, fits, Scatter

Paper

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The authors' code

MATLAB · 190 lines · 6.6 KB · GPL-3.0 · 1 match

  1. function ts = run_absorbing(topology,homparam,hetparam,stim)
  2. % RUN with ZERO TRIVIAL CONDITIONS: phi(r,0) = phi_t(r,0) = 0;
  3. % Absorbing boundary conditions - by adding absorbing layer over Omega
  4. % Layer has width L/2, and has effective gain ranging from nu0 to 0
  6. % Takes in input of model parameters, timesteps and lengthsteps.
  7. % Returns timeseries at each point.
  8. % List of step-size inputs (topology)
  9. % T: time domain [0, T]
  10. % L: space domain [0, L] x [0, L]
  11. % Nt: number of timesteps
  12. % Nx: number of grid points
  13. % List of homogeneous model parameters inputs (homparam)
  14. % gamma: timescale/decay - check that gamma > 0
  15. % r: characteristic axonal length
  16. % check r > 0 && r*gamma < dx/dt (stability)
  17. % nu0: dissipative rate
  18. % check that 0 <= nu0 < 1
  19. % List of heterogeneous model parameters (hetparam)
  20. % G: global coupling parameter
  21. % check G > 0
  22. % m: number of unidirectional pipe
  23. % check m > 0
  24. % cj = c1,..,cm: connectivity strength of jth pipe
  25. % check cj > 0
  26. % tauj = tau1,...,taum: travel time of jth current (as multiples of dt)
  27. % check tauj < |Rji-Rjf|/(r*gamma)
  28. % Rji = R1i,...,Rmi: regions at which pipe starts
  29. % check Rjis are in 1:N1x1:N2
  30. % Rjf = R1f,...,Rmf: regions at which pipe ends
  31. % check Rjfs are in 1:N1x1:N2
  32. % check mutually exclusive: does not exist any j1,j2 with
  33. % overlapping Rji and overlapping Rjf
  34. % List of stimulation inputs (stim)
  35. % stimnum: number of times of stimulation
  36. % stimtk = stimt1,...,stimtn = times of stimulation - check less than Nt
  37. % stimIk = stimI1,...,stimIn = stimulation intensity
  38. % stimRk = stimR1,...,stimRn = stimulation positions
  39. % sigma = [sigma_x, sigma_t] = Gaussian approximation of delta impulse
  40. % Outputs
  41. % ts: Nx x Ny x Nt timeseries array
  43. dx = topology.L / topology.Nx;
  44. dt = topology.T / topology.Nt;
  46. if (homparam.r * homparam.gamma * sqrt(2) > dx / dt)
  47. error('Error, Unstable choice of dx and dt')
  48. end
  50. % Find dimensions of outer square
  51. % Find least number of grid points needed to create of
  52. Nxabs = round(topology.L/2 / dx);
  53. Nxtot = topology.Nx + 2*Nxabs;
  55. % Initiate output timeseries array
  56. ts = zeros(topology.Nx, topology.Nx, topology.Nt);
  57. % Initiate temporary recursive timeseries array
  58. % Need at least tauj previous timesteps for convolution
  59. % and at least 1 previous timestep for wave equation
  60. % Therefore we track 1 + max(tau, 1) timesteps for each iteration
  61. if hetparam.m > 0
  62. phi = zeros(Nxtot, Nxtot, 1 + max([ceil(hetparam.tau/dt), 1]));
  63. else
  64. phi = zeros(Nxtot, Nxtot, 2);
  65. end
  67. if hetparam.m > 0
  69. % Change hetparam.Ri and hetparam.Rf to 3D array if they are 2D
  71. Ra = zeros(topology.Nx, topology.Nx, hetparam.m);
  72. Rb = zeros(topology.Nx, topology.Nx, hetparam.m);
  74. for k = 1:hetparam.m
  75. a_x = hetparam.a(1, k); a_y = hetparam.a(2, k);
  77. for i = 1:topology.Nx
  78. for j = 1:topology.Nx
  79. distx = abs(i*dx - a_x);
  80. disty = abs(j*dx - a_y);
  81. Ra(i, j, k) = exp(-0.5*(distx^2 + disty^2) / (hetparam.sigmaeps)^2);
  82. end
  83. end
  84. end
  86. for k = 1:hetparam.m
  87. b_x = hetparam.b(1, k); b_y = hetparam.b(2, k);
  89. for i = 1:topology.Nx
  90. for j = 1:topology.Nx
  91. distx = abs(i*dx - b_x);
  92. disty = abs(j*dx - b_y);
  93. Rb(i, j, k) = exp(-0.5*(distx^2 + disty^2) / (hetparam.sigmaeps)^2);
  94. end
  95. end
  96. end
  98. for k = 1:hetparam.m
  99. Ra(:, :, k) = Ra(:, :, k)/sum(Ra(:, :, k),'all');
  100. Rb(:, :, k) = Rb(:, :, k)/sum(Rb(:, :, k),'all');
  101. end
  103. hetparam.Ra = Ra;
  104. hetparam.Rb = Rb;
  106. % Turn hetparam.c into c / dx^2, so I dont have to keep multiplying
  107. hetparam.c = hetparam.c / dx^2;
  109. end
  111. % Create array of stimulation inputs by space
  113. stimulationinputspace = zeros(topology.Nx, topology.Nx, stim.stimnum);
  114. for n = 1:stim.stimnum
  115. i0 = stim.stimR(1, n) / dx; j0 = stim.stimR(2, n) / dx;
  116. for i = 1:topology.Nx
  117. for j = 1:topology.Nx
  118. distx = abs(i - i0);
  119. disty = abs(j - j0);
  120. stimulationinputspace(i, j, n) = exp(-0.5*(distx^2 + disty^2) * (dx^2) / (stim.sigma(1)^2));
  121. end
  122. end
  123. end
  125. stimulationinputspace = stimulationinputspace * 1/(2*pi * stim.sigma(1)^2);
  127. % Create array of stimulation inputs by time
  129. stimulationinputtime = zeros(topology.Nt, stim.stimnum);
  130. for k = 1:stim.stimnum
  131. t0 = stim.stimt(k) / dt;
  132. for n = 1:topology.Nt
  133. distt = abs((n - 1) - t0);
  134. stimulationinputtime(n, k) = exp(-0.5 *(distt^2) * (dt^2) / (stim.sigma(2)^2));
  135. end
  136. end
  138. stimulationinputtime = stimulationinputtime * 1/(sqrt(2*pi) * stim.sigma(2));
  140. % Normalise stimulationinputspace and stimulationinputtime so that weights
  141. % add to 1/dx^2 and 1/dt respectively
  143. for k = 1:stim.stimnum
  144. stimulationinputspace(:, :, k) = (1/dx^2) * ...
  145. stimulationinputspace(:, :, k) / sum(stimulationinputspace(:, :, k), "all");
  146. stimulationinputtime(:, k) = (1/dt) * ...
  147. stimulationinputtime(:, k) / sum(stimulationinputtime(:, k), 'all');
  148. end
  150. % Add absorbing layer
  152. nu0_array = zeros(Nxtot, Nxtot);
  153. for i = 1:Nxabs
  154. nu0_array(i : (Nxtot + 1 - i), i : (Nxtot + 1 - i)) = (i - 1) * homparam.nu0 / Nxabs;
  155. end
  156. nu0_array(Nxabs + (1 : topology.Nx), Nxabs + (1 : topology.Nx)) = homparam.nu0;
  159. for count = 1:topology.Nt
  161. % Calculate input for wave equation: nu0*phi + r^2*nabla^2(phi) + C(phi) + P
  162. recurrentinput = nu0_array .* phi(:, :, end);
  163. laplacianinput = (homparam.r / dx)^2 * Laplacian_2D(phi(:, :, end));
  164. if hetparam.m > 0
  165. convolutioninput = Convolution(hetparam, phi(Nxabs + (1:topology.Nx), Nxabs + (1:topology.Nx), :), dt);
  166. else
  167. convolutioninput = 0;
  168. end
  169. stimulationinput = zeros(topology.Nx, topology.Nx);
  170. for k = 1:stim.stimnum
  171. stimulationinput = stimulationinput + ...
  172. stim.stimI(k) * stimulationinputspace(:, :, k) * stimulationinputtime(count, k);
  173. end
  174. input = zeros(Nxtot, Nxtot);
  175. input(Nxabs + (1:topology.Nx), Nxabs + (1:topology.Nx)) = convolutioninput + stimulationinput;
  176. input = input + recurrentinput + laplacianinput;
  177. if count == 1
  178. % Initial velocity conditions imply that phi_1 = phi_{-1}, hence...
  179. phinew = 0.5 * input * (homparam.gamma * dt)^2;
  180. else
  181. phinew = wave_eq_2D(phi, input, homparam.gamma * dt);
  182. end
  183. phi(:, :, 1:end-1) = phi(:, :, 2:end);
  184. phi(:, :, end) = phinew;
  185. ts(:, :, count) = phinew(Nxabs + (1:topology.Nx), Nxabs + (1:topology.Nx));;
  186. end
  189. end

run_absorbing.m at commit 2c6fde1, under GPL-3.0 · at the source

Overview

Authors: Rishikesan Maran1,2, Eli J Müller1,2,3, Ben D Fulcher1,2
ORCID iDs: Ben D Fulcher
  1. School of Physics, The University of Sydney, Sydney, New South Wales, Australia
  2. Centre for Complex Systems, The University of Sydney, Sydney, New South Wales, Australia
  3. School of Medical Sciences, The University of Sydney, Sydney, New South Wales, Australia
Institutions: The University of Sydney (Australia)
Journal: PLoS computational biology, volume 22, issue 8, article e1014673
Dates: received 20 March 2026; accepted 5 August 2026; published online 26 August 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.1371/journal.pcbi.1014673 · PMID 42647573 · PMCID PMC13552967 · OpenAlex W4414684716
Open access: gold, a free copy (OpenAlex)
Preprint: arxiv:2506.19800
Status: code verified
Categories: human (organism), computational (subfield)
Methods: Machine learning
MeSH: Cerebral Cortex*, Connectome*, Models, Neurological*, Nerve Net*, Animals, Computational Biology, Computer Simulation, Humans (* major topic)
Topic: Functional Brain Connectivity Studies (Cognitive Neuroscience, Neuroscience), according to OpenAlex
Funding: Australian Research Council (FT240100418, DP240101295, DE250100540); Australian Government Research Training Program; Australian Government Research Training Program (RTP) scholarship
Citations: not cited yet (Europe PMC); 109 references in the paper

Abstract

The function and dynamics of the cortex are fundamentally shaped by the specific wiring configurations of its constituent axonal fibers, also known as the connectome. However, many dynamical properties of macroscale cortical activity are well captured by instead describing the activity as propagating waves across the cortical surface, constrained only by the surface’s two-dimensional geometry. It thus remains an open question why the local geometry of the cortex can successfully capture macroscale cortical dynamics, despite neglecting the specificity of Fast-conducting, Non-local Projections (FNPs) which are known to mediate the rapid and non-local propagation of activity between remote neural populations. Here we address this question by conducting a range of investigations using a mathematical model of macroscale cortical activity, in which cortical populations interact both by a continuous sheet and by an additional set of FNPs wired independently of the sheet’s geometry. By simulating the model across a range of external inputs, timescales, and idealized connectome topologies, we demonstrate that the addition of FNPs strongly shape the model dynamics of rapid, stimulus-evoked responses on fine millisecond timescales, but contribute relatively little to slower, spontaneous fluctuations over longer order-of-seconds timescales, which increasingly resemble geometrically constrained dynamics without FNPs. Our results suggest that the discrepant views regarding the relative contributions of local (geometric) and non-local (connectomic) cortico-cortical interactions are context-dependent: While FNPs specified by the connectome are needed to capture rapid communication between specific distant populations (as per the rapid processing of sensory inputs), they play a relatively minor role in shaping slower spontaneous fluctuations (as per resting-state functional magnetic resonance imaging).

Reproduced under the paper's license (CC BY), from the paper cited above.

Repository

Its files are read in the Code ↔ Paper reader above, with 3 matches between paragraphs and lines of code.

DynamicsAndNeuralSystems/geometricFNPmodel

License: GPL-3.0
State: the link answers, verified on 27 September 2026
Evidence: files inventoried
Commit: 2c6fde160b2e28e9e4e3ae0283e96940cc39d4f7, 7 June 2026
Languages: MATLAB (26)
Size: 40 files, 26 scripts
Software Heritage: not archived
Found in: “Data Availability”
Holds: README, license file
Not found: CITATION.cff, environment file, tests, continuous integration, documentation
Tools: Statistics and Machine Learning Toolbox (11 files)
Availability: 1 check, the latest on 27 September 2026: the link answers
  • 27 September 2026: the link answers
28 files
At the source: github.com/DynamicsAndNeuralSystems/geometricFNPmodel

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

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  • 1 repository of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
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Data

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Data Availability

Code to reproduce results reported here is available at https://github.com/DynamicsAndNeuralSystems/geometricFNPmodel.

Reproduced under the paper's license (CC BY), from the paper cited above.

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Version 1, 27 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 3 authors, 8 MeSH terms, 3 funders, 101 references.

Cite

This paper

Maran, R., Müller, E. J., & Fulcher, B. D. (2026). Modeling the influences of non-local connectomic projections on geometrically constrained cortical dynamics. PLoS computational biology, 22(8), e1014673. https://doi.org/10.1371/journal.pcbi.1014673

BibTeX

@article{maran2026modeling,
author = {Maran, Rishikesan and Müller, Eli J and Fulcher, Ben D},
title = {{Modeling the influences of non-local connectomic projections on geometrically constrained cortical dynamics}},
journal = {PLoS computational biology},
year = {2026},
month = aug,
volume = {22},
number = {8},
pages = {e1014673},
publisher = {PLOS},
issn = {1553-734X},
doi = {10.1371/journal.pcbi.1014673},
url = {https://doi.org/10.1371/journal.pcbi.1014673},
pmid = {42647573},
pmcid = {PMC13552967}
}

RIS

TY - JOUR
AU - Maran, Rishikesan
AU - Müller, Eli J
AU - Fulcher, Ben D
TI - Modeling the influences of non-local connectomic projections on geometrically constrained cortical dynamics
T2 - PLoS computational biology
J2 - PLoS Comput Biol
PY - 2026
DA - 2026/08/26
VL - 22
IS - 8
SP - e1014673
SN - 1553-734X
PB - PLOS
DO - 10.1371/journal.pcbi.1014673
UR - https://doi.org/10.1371/journal.pcbi.1014673
LA - en
ER -

CSL-JSON

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