Figures and data
Schematic illustration of synchronization principles in visual cortex and stimulus design.
a, Four scenarios showing two texture elements (Gabor annuli) falling within receptive fields of neural assemblies (purple) in early visual cortex. Contrast determines oscillation frequency (orange), with higher contrasts leading to higher frequencies. Coupling strength (line thickness of connecting arrow) depends on cortical distance, reflecting the distance between texture elements in the visual field. b, Arnold tongue: triangular region shows combinations of detuning and coupling strength that allow synchrony (light grey). Open circles indicate scenarios: (I) Strong coupling due to close proximity, moderate detuning due to similar contrast inputs. (II) Weaker coupling due to increased distance, same detuning as (I). Closed circles indicate scenarios: (III) Weak coupling due to large distance, same detuning as (I, II). (IV) Distance and coupling as in (II), large detuning due to heterogeneous contrast inputs. Scenarios I and II are conducive to synchrony, scenarios III and IV are not. c, Example full texture stimulus comprised of nonoverlapping Gabor annuli on irregular grid. The lower right quadrant contains a vertical figure (magenta outline, not shown to participants). Blue dot: fixation point. Axes separating quadrants shown for illustration only, not visible to participants. On a given trial, the figure may be vertical or horizontal and participants indicated the figure’s orientation. d, Figure region cut-outs illustrating experimental conditions. Grid coarseness (five steps) manipulates coupling strength for both figure and background. Contrast heterogeneity (five steps) manipulates detuning within figure. Background always at maximum heterogeneity (equivalent to rightmost column). The 25 cut-outs show all combinations of grid coarseness and contrast heterogeneity used in experiments.
Behavioral and simulated Arnold tongues.
a, Average discrimination accuracy for each of the 25 experimental conditions revealed a behavioral Arnold tongue in the space defined by contrast heterogeneity and grid coarseness. Contrast heterogeneity translates into the variance of frequencies (detuning) whereas grid coarseness translates into cortical distance (coupling strength). b, Fitted behavioral Arnold tongue after fitting a two-dimensional psychometric curve to the results in (a). The dashed line indicates the combination of contrast heterogeneity and grid coarseness corresponding to 75% accuracy. c, Zero-lag synchrony among model oscillators showing an Arnold tongue in the same parameter space as (a). Simulation conditions matched the 25 experimental conditions. d, High-resolution visualization of zero-lag synchrony, using 900 conditions (30 levels each of contrast heterogeneity and grid coarseness) to provide a more detailed representation of the Arnold tongue.
Comparison of behavioral and simulated Arnold tongues across coupling parameter space.
a, Pearson correlation between the behavioral Arnold tongue and simulated Arnold tongues obtained from models with coupling weights determined by different combinations of maximum coupling strength and coupling decay factor. The point labelled by the black circle shows the combination of parameters that were obtained from independent (macaque) data. b, Weighted Jaccard similarity between the behavioral Arnold tongue and simulated Arnold tongues. This metric is displayed across the same parameter space as in (a).
Learning effects on Arnold tongues.
a, Group average behavioral Arnold tongues for the 25 experimental conditions for each session. The vertical black line separates transfer session 9 from training sessions 1 to 8. b, Two-dimensional psychometric curves fitted to session-specific group average behavioral Arnold tongues. The dashed line again indicates the combination of contrast heterogeneity and grid coarseness at which participants achieve 75% accuracy. c, Simulated Arnold tongues for each of the eight training sessions including session-by-session learning in the model. We did not include a simulation of the ninth session because the location-specificity of the model learning rule would render it identical to the first session. Note that for visualization purposes we simulated the model for 30 levels of contrast heterogeneity and 30 levels of grid coarseness, in both cases including the 5 levels investigated experimentally.
Effects of contrast heterogeneity on discrimination accuracy across sessions.
CI = Confidence Interval. Log-odds and Odds Ratios represent the effect of a one-unit increase in contrast heterogeneity on the odds of correct discrimination. P-values are for the simple effect of contrast heterogeneity in each session.
Model predictions of learning effects.
a, Pearson correlations between simulated and behavioral Arnold tongues for each training session. Error bars indicate 95% confidence intervals. Grey regions indicate a noise ceiling that was obtained by computing the fit between average behavioral Arnold tongues in a fold and the behavioral Arnold tongue of the left-out participant. The grey regions reflect the 25th to the 75th percentile of fit values obtained using this procedure. b, Weighted Jaccard similarity values between simulated and behavioral Arnold tongues for each training session. Error bars and grey regions as in (a). c, Sizes of simulated (blue circles) and behavioral (orange squares) Arnold tongues across sessions. Arnold tongue sizes were averaged across participants and subsequently min-max normalized. This normalization highlights the growth patterns while accounting for the different value ranges of simulated and behavioral Arnold tongues. d, Sizes of behavioral Arnold tongues as a function of sizes of simulated Arnold tongues. The best fitting regression (black line) was obtained from a mixed effects model fitted to data from sessions 3-8 (blue circles). Red circles reflect data from the first two sessions that was not included in the mixed effect model. The black line was extended to include these points. Error bars indicate 95% confidence intervals.
Results of logistic regression analysis for each participant.
Individual behavioral Arnold tongues.
Average discrimination accuracy for each of the 25 discrete experimental conditions. Contrast heterogeneity translates into the variance of intrinsic frequencies (detuning) whereas grid coarseness translates into cortical distance (coupling strength). Panels a through h display results of participants 1 through 8, respectively.
Main effects of participant-specific logistic regression analyses of learning effects.
