Adaptation modulates effective connectivity and network stability.

Code ↔ Paper

8 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 8 matches · 1 of them tie a paragraph to a whole file, not to given lines: a weak match, whose lines are not tinted

[1] § Stability of networks without adaptation ↔ RandomMatrixTheory/RMT.m, lines 1–61 · score 0.76 · low rank structure, diagonal shifts, Random matrix theory, inhibitory neurons, outlier eigenvalue, sparse
[2] § Stability of networks without adaptation ↔ RandomMatrixTheory/RMT.m, lines 1–61 · score 0.73 · inhibitory populations, random matrix theory, low rank, outlier eigenvalues, computations, weights
[3] § Stability of networks without adaptation ↔ StabilityAnalysis/src/RMTMatrix.m, lines 1–50 · score 0.72 · inhibitory populations, random matrix theory, low rank, outlier eigenvalues, weights, excitatory
[4] § Stability of networks without adaptation ↔ StabilityAnalysis/src/RMTMatrix.m, lines 1–50 · score 0.70 · low rank structure, Random matrix theory, inhibitory neurons, outlier eigenvalue, diagonal, sparse
[5] § Adaptation modulates effective connectivity ↔ StabilityAnalysis/scripts/Fig_2_single_vs_dual_adaptation_example.m, lines 48–137 · score 0.64 · spike frequency adaptation, short term synaptic, abscissa, amplitude, rescaling, Benettin
[6] § Adaptation modulates effective connectivity ↔ StabilityAnalysis/src/algorithms/Jacobian/compute_J_eff.m, the whole file · a weak match · score 0.59 · activation function derivative, synaptic depression, connectivity matrix, effective connectivity, Jacobian, network
[7] § Adaptation modulates effective connectivity ↔ StabilityAnalysis/scripts/Fig_2_fraction_excitatory_load_and_plot.m, lines 82–227 · score 0.54 · Wilcoxon signed rank, median, stim, transient, simulated, excitatory
[8] § Adaptation modulates effective connectivity ↔ StabilityAnalysis/scripts/Fig_2_single_vs_dual_adaptation_example.m, lines 48–137 · score 0.53 · spike frequency adaptation, short term synaptic, depression, SFA, modeling, STD

Paper

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The authors' code

MATLAB · 478 lines · 18 KB · MIT · 2 matches

classdef RMT < handle
% RMT - Random Matrix Theory class following Harris et al. (2023)
% Variable names match the paper's notation for equations 15-18, 24-25, 30-31
properties
N % System size
alpha % Sparsity/connection probability (0 < alpha <= 1)
f % Fraction of excitatory neurons
% Normalized population statistics (tilde notation from Harris 2023)
% These are the pre-sparsity parameters: mu_tilde = mu/sqrt(N), sigma_tilde = sigma/sqrt(N)
mu_tilde_e % Normalized mean of excitatory population
mu_tilde_i % Normalized mean of inhibitory population
sigma_tilde_e % Normalized std dev of excitatory population
sigma_tilde_i % Normalized std dev of inhibitory population
% Internal matrices
A % Base random matrix (Gaussian, mean 0, var 1)
S % Sparsity mask (logical)
% Control flags
zrs_mode % 'none', 'ZRS', 'SZRS', 'Partial_SZRS'
shift % Scalar shift for eigenvalues (diagonal shift)
% Visualization
description
outlier_threshold % Multiplier for R to determine outlier eigenvalues (default 1.03)
end
properties (Dependent)
% Population indices (computed from f and N)
E % Logical index for Excitatory neurons
I % Logical index for Inhibitory neurons
% Low-rank structure M = u * v' (Eq 12)
u % Left vector: ones(N,1)
v % Right vector: [mu_tilde_e repeated Nf times, mu_tilde_i repeated N(1-f) times]
% Variance structure (Eq 11)
D % Diagonal variance matrix: diag(sigma_tilde_e repeated Nf, sigma_tilde_i repeated N(1-f))
% Weight/Jacobian matrix
W % Jacobian matrix (computed on access)
% Sparse statistics (Eq 15, 16)
mu_se % Sparse excitatory mean: alpha * mu_tilde_e
mu_si % Sparse inhibitory mean: alpha * mu_tilde_i
sigma_se_sq % Sparse excitatory variance (Eq 16)
sigma_si_sq % Sparse inhibitory variance (Eq 16)
% Theoretical predictions (Eq 17, 18)
lambda_O % Outlier eigenvalue
R % Spectral radius
end
properties (Access = private)
eigenvalues_cache % Cached eigenvalue computation
eigenvalues_valid % Flag indicating if cache is valid
end
methods
function obj = RMT(N)
% RMT Constructor
obj.N = N;
% Defaults
obj.alpha = 1.0;
obj.f = 0.5;
obj.mu_tilde_e = 0;
obj.mu_tilde_i = 0;
obj.sigma_tilde_e = 1/sqrt(N); % Default: unit variance when scaled by sqrt(N)
obj.sigma_tilde_i = 1/sqrt(N);
obj.zrs_mode = 'none';
obj.shift = 0;
obj.description = '';
obj.outlier_threshold = 1.04;
% Initialize random matrices
obj.A = randn(N, N); % Mean 0, Var 1
obj.update_sparsity();
% Initialize eigenvalue cache
obj.eigenvalues_cache = [];
obj.eigenvalues_valid = false;
end
%% Dependent Property Getters
function val = get.E(obj)
val = false(obj.N, 1);
val(1:round(obj.f * obj.N)) = true;
end
function val = get.I(obj)
val = ~obj.E;
end
function val = get.u(obj)
val = ones(obj.N, 1);
end
function val = get.v(obj)
val = zeros(obj.N, 1);
E_idx = obj.E;
val(E_idx) = obj.mu_tilde_e;
val(~E_idx) = obj.mu_tilde_i;
end
function val = get.D(obj)
% Eq 11: D = diag(sigma_tilde_e repeated Nf times, sigma_tilde_i repeated N(1-f) times)
D_vec = zeros(obj.N, 1);
E_idx = obj.E;
D_vec(E_idx) = obj.sigma_tilde_e;
D_vec(~E_idx) = obj.sigma_tilde_i;
val = diag(D_vec);
end
function val = get.W(obj)
% Construct weight matrix W based on Harris 2023 equations
% Get diagonal variance matrix D (Eq 11) and low-rank structure M (Eq 12)
D = obj.D;
M = obj.u * obj.v';
switch obj.zrs_mode
case 'none'
% Standard construction: W = S .* (A*D + M) (Eq 6)
W_dense = (obj.A * D) + M;
val = obj.S .* W_dense;
case 'ZRS'
% Dense ZRS using Projection Operator P (Eq 24, 25)
% Eq 24: P = I_N - (u*u')/N
% Eq 25: W = A*D*P + u*v'
if obj.alpha < 1
warning('RMT:SparsityWarning', 'Using ''ZRS'' (projection) with sparse matrix. This will destroy sparsity. Consider ''SZRS''.');
end
% Eq 24: Projection operator
P = eye(obj.N) - (obj.u * obj.u') / obj.N;
% Eq 25: W = A*D*P + M
val = (obj.A * D * P) + M;
if obj.alpha < 1
val = obj.S .* val;
end
case 'SZRS'
% Sparse Zero Row Sum (Eq 30, 31)
% Eq 30: W = S .* (A*D + u*v') - B
% Eq 31: W_bar_i = sum_j W_ij / sum_j S_ij
% Base sparse matrix
W_base = obj.S .* ((obj.A * D) + M);
% Eq 31: Row averages of non-zero elements
row_sums = sum(W_base, 2);
row_counts = sum(obj.S, 2);
row_counts(row_counts == 0) = 1; % Avoid division by zero
W_bar_i = row_sums ./ row_counts;
% Correction matrix B: B_ij = S_ij * W_bar_i
B = obj.S .* W_bar_i;
% Eq 30: Final matrix
val = W_base - B;
case 'Partial_SZRS'
% Partial SZRS (Eq 32)
% Apply correction ONLY to random component J = S .* (A*D)
% Keep M component (S .* M) intact to preserve imbalance
% Random component
J_base = obj.S .* (obj.A * D);
% Mean structure component
M_base = obj.S .* M;
% Eq 32: Row averages of random component J only
J_row_sums = sum(J_base, 2);
row_counts = sum(obj.S, 2);
row_counts(row_counts == 0) = 1;
J_bar_i = J_row_sums ./ row_counts;
% Partial correction B
B_partial = obj.S .* J_bar_i;
% W = (J_base - B_partial) + M_base
val = (J_base - B_partial) + M_base;
end
% Apply diagonal shift
val = val + obj.shift * eye(obj.N);
end
function val = get.mu_se(obj)
% Eq 15: mu_se = alpha * mu_tilde_e
val = obj.alpha * obj.mu_tilde_e;
end
function val = get.mu_si(obj)
% Eq 15: mu_si = alpha * mu_tilde_i
val = obj.alpha * obj.mu_tilde_i;
end
function val = get.sigma_se_sq(obj)
% Eq 16: sigma_se^2 = alpha*(1-alpha)*mu_tilde_e^2 + alpha*sigma_tilde_e^2
val = obj.alpha * (1 - obj.alpha) * obj.mu_tilde_e^2 + obj.alpha * obj.sigma_tilde_e^2;
end
function val = get.sigma_si_sq(obj)
% Eq 16: sigma_si^2 = alpha*(1-alpha)*mu_tilde_i^2 + alpha*sigma_tilde_i^2
val = obj.alpha * (1 - obj.alpha) * obj.mu_tilde_i^2 + obj.alpha * obj.sigma_tilde_i^2;
end
function val = get.lambda_O(obj)
% Eq 17: lambda_O = N * [f * mu_se + (1-f) * mu_si]
val = obj.N * (obj.f * obj.mu_se + (1 - obj.f) * obj.mu_si);
end
function val = get.R(obj)
% Eq 18: R = sqrt(N * [f * sigma_se^2 + (1-f) * sigma_si^2])
val = sqrt(obj.N * (obj.f * obj.sigma_se_sq + (1 - obj.f) * obj.sigma_si_sq));
end
%% Property Setters with cache invalidation
function set.alpha(obj, val)
obj.alpha = val;
if ~isempty(obj.A)
obj.update_sparsity();
end
obj.invalidate_eigenvalues();
end
function set.f(obj, val)
obj.f = val;
obj.invalidate_eigenvalues();
end
function set.mu_tilde_e(obj, val)
obj.mu_tilde_e = val;
obj.invalidate_eigenvalues();
end
function set.mu_tilde_i(obj, val)
obj.mu_tilde_i = val;
obj.invalidate_eigenvalues();
end
function set.sigma_tilde_e(obj, val)
obj.sigma_tilde_e = val;
obj.invalidate_eigenvalues();
end
function set.sigma_tilde_i(obj, val)
obj.sigma_tilde_i = val;
obj.invalidate_eigenvalues();
end
function set.zrs_mode(obj, val)
obj.zrs_mode = val;
obj.invalidate_eigenvalues();
end
function set.shift(obj, val)
obj.shift = val;
obj.invalidate_eigenvalues();
end
%% Parameter Setters
function set_params(obj, mu_tilde_e, mu_tilde_i, sigma_tilde_e, sigma_tilde_i, f, alpha)
% Set all parameters in Harris 2023 notation
% Arguments: mu_tilde_e, mu_tilde_i, sigma_tilde_e, sigma_tilde_i, f, alpha
if nargin > 1, obj.mu_tilde_e = mu_tilde_e; end
if nargin > 2, obj.mu_tilde_i = mu_tilde_i; end
if nargin > 3, obj.sigma_tilde_e = sigma_tilde_e; end
if nargin > 4, obj.sigma_tilde_i = sigma_tilde_i; end
if nargin > 5, obj.f = f; end
if nargin > 6, obj.alpha = alpha; end
end
function set_alpha(obj, alpha)
% Set alpha (sparsity) independently
obj.alpha = alpha;
end
function set_zrs_mode(obj, mode)
% Set the zero row-sum mode
valid_modes = {'none', 'ZRS', 'SZRS', 'Partial_SZRS'};
if ~ismember(mode, valid_modes)
error('Invalid ZRS mode. Valid choices: %s', strjoin(valid_modes, ', '));
end
obj.zrs_mode = mode;
end
function sigma_tilde_i = compute_sigma_tilde_i_for_target_variance(obj, target_variance)
% Compute sigma_tilde_i to achieve a target expected variance Var(W)
% Check that alpha = 1 (dense case only)
if obj.alpha < 1
error('RMT:SparseCaseNotSupported', ...
'compute_sigma_tilde_i_for_target_variance only supports dense matrices (alpha=1). For alpha<1, a more complex solver is needed.');
end
% For dense case (alpha=1), sigma_se^2 = sigma_tilde_e^2
sigma_se_sq = obj.sigma_tilde_e^2;
sigma_si_sq = (target_variance - obj.f * sigma_se_sq) / (1 - obj.f);
% Check that the result is valid (non-negative)
if sigma_si_sq < 0
error('RMT:InvalidTargetVariance', ...
'Target variance %.4f is too small. Minimum achievable is %.4f (when sigma_tilde_i=0).', ...
target_variance, obj.f * sigma_se_sq);
end
sigma_tilde_i = sqrt(sigma_si_sq);
end
%% Internal Updates
function update_sparsity(obj)
obj.S = rand(obj.N, obj.N) < obj.alpha;
obj.invalidate_eigenvalues();
end
%% Display and Diagnostics
function display_parameters(obj)
% Display measured statistics from W and compare to theoretical predictions
W_mat = obj.W;
% Remove diagonal for statistics since they may contain shift
W_no_diag = W_mat;
W_no_diag(1:obj.N+1:end) = NaN;
% Extract E and I columns
E_idx = obj.E;
W_E = W_no_diag(:, E_idx);
W_I = W_no_diag(:, ~E_idx);
% For sparse matrices, only consider non-zero entries
W_E_vals = W_E(~isnan(W_E) & (W_E ~= 0));
W_I_vals = W_I(~isnan(W_I) & (W_I ~= 0));
% Measured statistics (of non-zero entries)
measured_mu_E = mean(W_E_vals);
measured_mu_I = mean(W_I_vals);
measured_sigma_E = std(W_E_vals, 1);
measured_sigma_I = std(W_I_vals, 1);
% Theoretical predictions (use dependent properties directly)
mu_se = obj.mu_se;
mu_si = obj.mu_si;
sigma_se_sq = obj.sigma_se_sq;
sigma_si_sq = obj.sigma_si_sq;
lambda_O = obj.lambda_O;
R = obj.R;
fprintf('\n========== RMT Parameter Summary ==========\n');
if ~isempty(obj.description)
fprintf('Description: %s\n', obj.description);
end
fprintf('Mode: %s\n', obj.zrs_mode);
fprintf('N: %d\n', obj.N);
fprintf('alpha: %.4f\n', obj.alpha);
fprintf('f: %.4f\n', obj.f);
fprintf('\n--- Harris 2023 Notation ---\n');
fprintf(' Set Value Sparse Eff. Measured(NZ)\n');
fprintf('--------------------------------------------------------------\n');
fprintf('mu_tilde_e %10.4f mu_se=%.4f %.4f\n', obj.mu_tilde_e, mu_se, measured_mu_E);
fprintf('mu_tilde_i %10.4f mu_si=%.4f %.4f\n', obj.mu_tilde_i, mu_si, measured_mu_I);
fprintf('sigma_tilde_e %10.4f sigma_se=%.4f %.4f\n', obj.sigma_tilde_e, sqrt(sigma_se_sq), measured_sigma_E);
fprintf('sigma_tilde_i %10.4f sigma_si=%.4f %.4f\n', obj.sigma_tilde_i, sqrt(sigma_si_sq), measured_sigma_I);
fprintf('\n--- Theoretical Predictions (Eq 17, 18) ---\n');
fprintf('lambda_O (outlier): %.4f\n', lambda_O);
fprintf('R (radius): %.4f\n', R);
fprintf('==============================================\n\n');
end
%% Eigenvalue Computation (with caching)
function eigs = get_eigenvalues(obj)
% Get eigenvalues, computing only if cache is invalid
if ~obj.eigenvalues_valid || isempty(obj.eigenvalues_cache)
obj.eigenvalues_cache = eig(obj.W);
obj.eigenvalues_valid = true;
end
eigs = obj.eigenvalues_cache;
end
function compute_eigenvalues(obj)
% Force recomputation and cache update
obj.eigenvalues_cache = eig(obj.W);
obj.eigenvalues_valid = true;
end
function eigs = eigenvalues(obj)
% Property-like access for eigenvalues
eigs = obj.get_eigenvalues();
end
%% Plotting
function plot_spectrum(obj, ax)
if nargin < 2
figure; ax = gca;
end
eigs = obj.get_eigenvalues();
% Get theoretical radius and center
R = obj.R;
xc = obj.shift;
yc = 0;
% Compute distances from center for all eigenvalues
distances = abs(eigs - xc - 1i*yc);
% Plot interior eigenvalues (within R) as black circles
mSize = 4;
interior_mask = distances <= R;
interior_eigs = eigs(interior_mask);
plot(ax, real(interior_eigs), imag(interior_eigs), 'ko', 'MarkerSize', mSize, 'MarkerFaceColor', 'none', 'LineWidth', 0.5);
hold(ax, 'on');
% Plot theoretical radius (Eq 18)
theta = linspace(0, 2*pi, 100);
plot(ax, xc + R*cos(theta), yc + R*sin(theta), 'k-', 'LineWidth', 2);
% Plot near outlier eigenvalues (between R and outlier_threshold*R) as black Xs
near_outlier_mask = (distances > R) & (distances <= obj.outlier_threshold * R);
near_outlier_eigs = eigs(near_outlier_mask);
if ~isempty(near_outlier_eigs)
plot(ax, real(near_outlier_eigs), imag(near_outlier_eigs), 'kx', 'MarkerSize', mSize, 'LineWidth', 0.5);
end
% Plot far outlier eigenvalues (beyond outlier_threshold*R) as green filled circles
far_outlier_mask = distances > obj.outlier_threshold * R;
far_outlier_eigs = eigs(far_outlier_mask);
if ~isempty(far_outlier_eigs)
plot(ax, real(far_outlier_eigs), imag(far_outlier_eigs), 'o', 'MarkerSize', mSize, 'MarkerFaceColor', [0 .7 0], 'MarkerEdgeColor', [0 .7 0]);
end
xlabel(ax, 'Re(\lambda)');
ylabel(ax, 'Im(\lambda)');
grid(ax, 'on');
axis(ax, 'equal');
hold(ax, 'off');
end
%% Deep Copy
function new_obj = copy(obj)
% Create new object with same N
new_obj = RMT(obj.N);
% Copy stored (non-dependent) properties
new_obj.alpha = obj.alpha;
new_obj.f = obj.f;
new_obj.mu_tilde_e = obj.mu_tilde_e;
new_obj.mu_tilde_i = obj.mu_tilde_i;
new_obj.sigma_tilde_e = obj.sigma_tilde_e;
new_obj.sigma_tilde_i = obj.sigma_tilde_i;
new_obj.A = obj.A;
new_obj.S = obj.S;
new_obj.zrs_mode = obj.zrs_mode;
new_obj.shift = obj.shift;
new_obj.description = obj.description;
new_obj.outlier_threshold = obj.outlier_threshold;
new_obj.eigenvalues_cache = obj.eigenvalues_cache;
new_obj.eigenvalues_valid = obj.eigenvalues_valid;
end
end
methods (Access = private)
function invalidate_eigenvalues(obj)
obj.eigenvalues_valid = false;
end
end
end

RMT.m at commit ac4d3b9, under MIT · at the source

Overview

Authors: Thomas J. Richner¹, Martynas Dervinis¹, Brian Nils Lundstrom¹

Department of Neurology, Mayo Clinic, Rochester, MN, United States

Institutions: Mayo Clinic (United States)

Journal: Frontiers in computational neuroscience, volume 20, article 1761735

Dates: received 5 December 2025; accepted 14 February 2026; published online 10 April 2026

Type: Brief report · Language: English

License: CC BY

Identifiers: DOI 10.3389/fncom.2026.1761735 · PMID 42038529 · PMCID PMC13106433 · OpenAlex W7153018175

Open access: gold, a free copy (OpenAlex)

Status: code verified

Methods: Statistics, Machine learning, Single-unit activity, calcium imaging

Keywords: adaptation, edge of chaos, recurrent neural networks, spike frequency adaptation, short-term synaptic depression, effective connectivity, random matrix theory, excitation-inhibition balance

Topic: Neural dynamics and brain function (Cognitive Neuroscience, Neuroscience), according to OpenAlex

Funding: HHS | NIH | National Institute of Neurological Disorders and Stroke (NINDS) (R01NS129622, K23NS112339)

Citations: cited by 1 paper (Europe PMC); 70 references in the paper

Abstract

The brain is a highly recurrent, nonlinear network hypothesized to remain near the edge of chaos for optimal performance. Excitation and inhibition must be balanced precisely within every neuron to ensure a consistent level of dynamical stability and rich dynamics during transition to chaos. However, analysis of biologically realistic synaptic weight matrices suggests that sparsity and low-dimensional structure interact such that there is no known synaptic balancing rule that constrains the stability (i.e., eigenvalues) of the network while also preserving computationally useful, low-dimensional structure. Further, even if a network were well-balanced, external stimuli interact with the nonlinear activation functions to unbalance the network in real time. Therefore, the brain must utilize dynamic, rather than static, mechanisms to actively regulate its level of stability. We propose that two specific adaptation mechanisms, spike frequency adaptation (SFA) and short-term synaptic depression (STD), continuously modulate the effective connectivity, keeping the brain near the edge of chaos and reducing dynamical fluctuations caused by stimuli. This theoretical framework links intrinsic and synaptic negative feedback mechanisms to network-level dynamics. This offers an explanation of why data-driven modeling of human brain signals, an exciting and useful method in epilepsy and anesthesiology research, seems to require linear time-varying (LTV) models which are refit every half second: difficult to observe adaptation processes interact with nonlinearities to make connectivity effectively dynamic at the macroelectrode scale. We suggest that compromised adaptation may underlie neurological conditions characterized by altered excitability, and that targeted brain stimulation could be used to probe the regulatory action of adaptation.

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 8 matches between paragraphs and lines of code.

TomRichner/ConnectivityAdaptation

License: MIT

State: the link answers, verified on 29 September 2026

Evidence: files inventoried

Commit: ac4d3b92aa678686afd3e734248c743ed2a3614f, 7 May 2026

Languages: MATLAB (56), Shell (2)

Size: 188 files, 58 scripts

Software Heritage: not archived

Found in: “Data availability statement”

Holds: README, license file, documentation

Not found: CITATION.cff, environment file, tests, continuous integration

Tools: Statistics and Machine Learning Toolbox (3 files), Signal Processing Toolbox (1 file)

Availability: 1 check, the latest on 29 September 2026: the link answers

29 September 2026: the link answers

60 files

Final_figures/convert_table_and_caption_to_pdf.sh, Shell, 35 lines
RandomMatrixTheory/AddLetters2Plots.m, MATLAB, 236 lines
RandomMatrixTheory/Fig_1_RMT_examples.m, MATLAB, 200 lines
RandomMatrixTheory/RMT.m, MATLAB, 478 lines, 2 matches
RandomMatrixTheory/save_some_figs_to_folder_2.m, MATLAB, 59 lines
StabilityAnalysis/scripts/Fig_2_fraction_excitatory_analysis.m, MATLAB, 198 lines
StabilityAnalysis/scripts/Fig_2_fraction_excitatory_load_and_plot.m, MATLAB, 265 lines, 1 match
StabilityAnalysis/scripts/Fig_2_single_vs_dual_adaptation_example.m, MATLAB, 586 lines, 2 matches
StabilityAnalysis/scripts/Simple_network_with_dual_adaptation.m, MATLAB, 35 lines
StabilityAnalysis/scripts/Sompolinsky_N_1000_g_1p8.m, MATLAB, 203 lines
StabilityAnalysis/scripts/Sompolinsky_N_200_g_1p8.m, MATLAB, 203 lines
StabilityAnalysis/scripts/Sompolinsky_N_200_g_2p1.m, MATLAB, 203 lines
StabilityAnalysis/scripts/setup_paths.m, MATLAB, 19 lines
StabilityAnalysis/src/ParamSpaceAnalysis.m, MATLAB, 974 lines
StabilityAnalysis/src/RMTMatrix.m, MATLAB, 195 lines, 2 matches
StabilityAnalysis/src/SRNNModel.m, MATLAB, 1,272 lines
StabilityAnalysis/src/algorithms/Jacobian/compute_J_eff.m, MATLAB, 140 lines, 1 match
StabilityAnalysis/src/algorithms/Jacobian/compute_Jacobian.m, MATLAB, 468 lines
StabilityAnalysis/src/algorithms/Jacobian/compute_Jacobian_at_indices.m, MATLAB, 48 lines
StabilityAnalysis/src/algorithms/Jacobian/compute_Jacobian_fast.m, MATLAB, 235 lines
StabilityAnalysis/src/algorithms/Jacobian/get_minMaxRange.m, MATLAB, 31 lines
StabilityAnalysis/src/algorithms/Lyapunov/benettin_algorithm.m, MATLAB, 115 lines
StabilityAnalysis/src/algorithms/Lyapunov/compute_lyapunov_exponents.m, MATLAB, 131 lines
StabilityAnalysis/src/algorithms/Lyapunov/lyapunov_spectrum_qr.m, MATLAB, 176 lines
StabilityAnalysis/src/generate_stimulus/generate_external_input.m, MATLAB, 148 lines
StabilityAnalysis/src/nonlinearities/logisticSigmoid.m, MATLAB, 27 lines
StabilityAnalysis/src/nonlinearities/logisticSigmoidDerivative.m, MATLAB, 29 lines
StabilityAnalysis/src/nonlinearities/piecewiseSigmoid.m, MATLAB, 83 lines
StabilityAnalysis/src/nonlinearities/piecewiseSigmoidDerivative.m, MATLAB, 76 lines
StabilityAnalysis/src/nonlinearities/tanhActivation.m, MATLAB, 25 lines
StabilityAnalysis/src/nonlinearities/tanhActivationDerivative.m, MATLAB, 27 lines
StabilityAnalysis/src/plotting/AddLetters2Plots.m, MATLAB, 207 lines
StabilityAnalysis/src/plotting/beeswarm.m, MATLAB, 243 lines
StabilityAnalysis/src/plotting/blue_gray_red_colormap.m, MATLAB, 50 lines
StabilityAnalysis/src/plotting/concatenate_figs.m, MATLAB, 153 lines
StabilityAnalysis/src/plotting/excitatory_colormap.m, MATLAB, 69 lines
StabilityAnalysis/src/plotting/inhibitory_colormap.m, MATLAB, 70 lines
StabilityAnalysis/src/plotting/paired_beeswarm.m, MATLAB, 186 lines
StabilityAnalysis/src/plotting/param_space_plots/load_and_make_unit_histograms.m, MATLAB, 285 lines
StabilityAnalysis/src/plotting/param_space_plots/load_and_plot_lle_by_stim_period.m, MATLAB, 488 lines
StabilityAnalysis/src/plotting/param_space_plots/load_and_plot_param_space_analysis.m, MATLAB, 93 lines
StabilityAnalysis/src/plotting/plot_SRNN_combined_tseries.m, MATLAB, 244 lines
StabilityAnalysis/src/plotting/plot_SRNN_tseries.m, MATLAB, 161 lines
StabilityAnalysis/src/plotting/plot_adaptation.m, MATLAB, 67 lines
StabilityAnalysis/src/plotting/plot_dendritic_state.m, MATLAB, 48 lines
StabilityAnalysis/src/plotting/plot_eigenvalues.m, MATLAB, 139 lines
StabilityAnalysis/src/plotting/plot_external_input.m, MATLAB, 41 lines
StabilityAnalysis/src/plotting/plot_firing_rate.m, MATLAB, 38 lines
StabilityAnalysis/src/plotting/plot_lines_with_colormap.m, MATLAB, 48 lines
StabilityAnalysis/src/plotting/plot_lyapunov.m, MATLAB, 147 lines
StabilityAnalysis/src/plotting/plot_std_variable.m, MATLAB, 64 lines
StabilityAnalysis/src/plotting/plot_synaptic_output.m, MATLAB, 38 lines
StabilityAnalysis/src/plotting/redwhiteblue_colormap.m, MATLAB, 55 lines
StabilityAnalysis/src/plotting/save_some_figs_to_folder_2.m, MATLAB, 59 lines
StabilityAnalysis/src/plotting/unit_histogram_patch.m, MATLAB, 154 lines
docs/EquationsParametersDocs/plot_piecewiseSigmoid_example.m, MATLAB, 25 lines
docs/convert_md_docs_to_pdf.sh, Shell, 48 lines
run_all_figures.m, MATLAB, 120 lines
LICENSE, License, 21 lines
README.md, Text, 52 lines

At the source: github.com/TomRichner/ConnectivityAdaptation

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

Tracing map

Proposed by the machine: these links were found in the paper and verified at the source, without human review. The map will receive a Zenodo DOI once one of the paper's authors has validated it with their ORCID.

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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;
58 scripts, each with its path and the digest of its content;
8 matches between paragraphs of the paper and lines of the code (method lexical-v1);
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Data

No dataset and no data link were found in the paper.

Data availability statement

The datasets presented in this study can be found in an online repository. Additional documentation, and all code to reproduce the data and figures, is available in the following repository: https://github.com/TomRichner/ConnectivityAdaptation.

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

Versions

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Version 1, 29 September 2026: the first record

Recorded: type, language, journal, volume, pages, dates, 3 authors, 8 keywords, 1 funder, 68 references.

Cite

This paper

Richner, T. J., Dervinis, M., & Lundstrom, B. N. (2026). Adaptation modulates effective connectivity and network stability. Frontiers in computational neuroscience, 20, 1761735. https://doi.org/10.3389/fncom.2026.1761735

BibTeX

@article{richner2026adaptation, author = {Richner, Thomas J. and Dervinis, Martynas and Lundstrom, Brian Nils}, title = {{Adaptation modulates effective connectivity and network stability}}, journal = {Frontiers in computational neuroscience}, year = {2026}, month = apr, volume = {20}, pages = {1761735}, publisher = {Frontiers Media SA}, issn = {1662-5188}, doi = {10.3389/fncom.2026.1761735}, url = {https://doi.org/10.3389/fncom.2026.1761735}, pmid = {42038529}, pmcid = {PMC13106433} }

RIS

TY - JOUR AU - Richner, Thomas J. AU - Dervinis, Martynas AU - Lundstrom, Brian Nils TI - Adaptation modulates effective connectivity and network stability T2 - Frontiers in computational neuroscience J2 - Front Comput Neurosci PY - 2026 DA - 2026/04/10 VL - 20 SP - 1761735 SN - 1662-5188 PB - Frontiers Media SA DO - 10.3389/fncom.2026.1761735 UR - https://doi.org/10.3389/fncom.2026.1761735 LA - en ER -

CSL-JSON

{ "id": "10.3389/fncom.2026.1761735", "type": "article-journal", "title": "Adaptation modulates effective connectivity and network stability", "container-title": "Frontiers in computational neuroscience", "author": [ { "family": "Richner", "given": "Thomas J." }, { "family": "Dervinis", "given": "Martynas" }, { "family": "Lundstrom", "given": "Brian Nils" } ], "container-title-short": "Front Comput Neurosci", "volume": "20", "page": "1761735", "DOI": "10.3389/fncom.2026.1761735", "PMID": "42038529", "PMCID": "PMC13106433", "ISSN": "1662-5188", "publisher": "Frontiers Media SA", "URL": "https://doi.org/10.3389/fncom.2026.1761735", "language": "en", "issued": { "date-parts": [ [ 2026, 4, 10 ] ] } }

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