A cortical semantic map integrates fractions and integers in the human brain.
The 9 matches · 1 of them tie a paragraph to a whole file without given lines: a weak match, whose lines are not tinted
- [1] § Methods › Voxel tuning ↔ fMRI/Gaussian_fit/gaussianfit_averagegroups_aggruns_figure7CD.ipynb, lines 162 to 273 · score 0.79 · 0.1–2, amplitude, bounded, 0–5, Gaussian, Glasser · Report a mismatch
- [2] § Methods › Voxel tuning ↔ fMRI/Gaussian_fit/correlation_between_fractions_integers_figureS7.ipynb, the whole file · a weak match · score 0.68 · smoothed noise, FWHM, IP2, PF, volumes, Glasser · Report a mismatch
- [3] § Methods › Voxel tuning ↔ fMRI/Gaussian_fit/correlation-relation_between_fractions_integers_figures8.ipynb, lines 21 to 165 · score 0.64 · smoothed noise, FWHM, IP2, PF, volumes, match · Report a mismatch
- [4] § Methods › Representational similarity analysis (RSA) ↔ fMRI/Multiple_regression/searchlight_analysis_allsubs_multipleregression_figure6.py, lines 184 to 273 · score 0.59 · multiple regression, sphere, searchlight, radius, RSA, mask · Report a mismatch
- [5] § Methods › Representational similarity analysis (RSA) ↔ fMRI/Multiple_regression/secondlevel_analyses_searchlight_figure6_tableS1.ipynb, lines 104 to 225 · score 0.58 · multiple regression, radius, searchlight, RSA, mask, FDR · Report a mismatch
- [6] § Methods › Voxel tuning ↔ fMRI/Gaussian_fit/relation_between_runs_integ_figure7A.ipynb, lines 136 to 192 · score 0.58 · diagonal elements, normalized activation, shuffled, permutation, rows, voxels · Report a mismatch
- [7] § Methods › Voxel tuning ↔ fMRI/Gaussian_fit/relation_between_runs_fractions_figure7B.ipynb, lines 142 to 192 · score 0.56 · diagonal elements, normalized activation, shuffled, permutation, voxels, matrix · Report a mismatch
- [8] § Methods › Anatomical and functional preprocessing ↔ fMRI/Gaussian_fit/gaussianfit_averagegroups_aggruns_figure7CD.ipynb, lines 162 to 273 · score 0.54 · residual, affine, variance, volume, threshold, square · Report a mismatch
- [9] § Results › Individual voxel tuning and numerotopic map ↔ fMRI/Gaussian_fit/relation_between_fractions_integers_figureS7.ipynb, lines 102 to 182 · score 0.51 · preferred integer, normalized activation, Gaussian, S7, preferences, fitted · Report a mismatch
Paper
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The authors' code
Jupyter notebook · 273 lines · 11 KB · no license · 2 matches
- # %%
- import numpy as np
- import matplotlib.pyplot as plt
- import time
- from scipy import linalg # Using scipy.linalg.lstsq might offer more options later if needed, but numpy is fine
- from scipy.optimize import curve_fit
- import os
- import sys
- import numpy as np
- import pandas as pd
- import json
- import pickle
- import nibabel as nib
- import time
- from nilearn.image import load_img
- from nilearn.glm.first_level import FirstLevelModel
- from nilearn.glm.first_level import make_first_level_design_matrix
- from nilearn.plotting import plot_design_matrix
- from nilearn.image import resample_to_img
- from nilearn.image import new_img_like
- from nilearn import surface
- from nilearn import plotting
- from nilearn.image import smooth_img
- from matplotlib.colors import ListedColormap, BoundaryNorm
- from nilearn import plotting
- import glob
- import os.path as op
- from nilearn.image import smooth_img
- from scipy.stats import sem # standard error of the mean
- import matplotlib.pyplot as plt
- from nilearn.maskers import NiftiMasker
- from matplotlib import cm
- from matplotlib.colors import Normalize
- from nilearn.image.image import mean_img
- from nilearn.plotting import plot_roi, plot_epi, show
- # %%
- # Define a Gaussian function
- def gaussian(x, a, x0, sigma):
- return a * np.exp(-(x - x0)**2 / (2 * sigma**2))
- # %% [markdown]
- # # Integers
- #
- # aggregate runs, loop through rois
- # %%
- r_threshold = 0.5
- rois = ["locp005_math", "glasser_bilateral_frontal", "glasser_bilateral_ips", "glasser_bilateral_temporal", "hippocampus", "parahippocampal", "bilateral_PF_IP2"]
- for roi in rois:
- print(f"\n--- ROI: {roi} ---")
- file_path = f"/home_local/Daniela_fmri_analyses/Results/gaussian_fit/group_analysis_aggregate_runs/{roi}/grouplevel_matrix_targetsXvoxels_coords_tmap_mni-space_{roi}_ordercateg_smooth4.npz"
- data = np.load(file_path)
- # Assuming the first key contains the matrix, print the first row
- first_key = data.files[0]
- matrix = data[first_key]
- tuning_curves = np.zeros((matrix.shape[0], 3))
- fitted_gaussians = np.zeros((matrix.shape[0], 6)) #to collect the fitted gaussian model for each voxel
- target_tmap_all = np.zeros((matrix.shape[0], 6))
- for i_voxel in range(matrix.shape[0]):
- #print("Voxel", i_voxel)
- target_tmap = matrix[i_voxel, -6:] # all voxels for the integers
- target_tmap = (target_tmap - np.min(target_tmap)) /(np.max(target_tmap) - np.min(target_tmap)) # Normalize target_betas between 0 and 1
- target_tmap = np.nan_to_num(target_tmap)
- target_tmap_all[i_voxel] = target_tmap # to store
- x = [0, 1, 2, 3, 4, 5]
- high_res_x = np.linspace(0, len(target_tmap) - 1, len(target_tmap))
- amplitude, center, size = np.nan, np.nan, np.nan # Initialize outputs
- try:
- # Attempt to fit the curve
- # Fit the Gaussian to target_betas with constrained parameters
- # Bounds: amplitude (0 to 1), center (0 to 5), sigma (0.1 to 2)
- popt, pcov = curve_fit(
- gaussian,
- x,
- target_tmap,
- p0=[1, np.argmax(target_tmap), 1],
- bounds=([0, 0, 0.1], [1, 5, 2]) # Lower and upper bounds
- )
- except RuntimeError as e:
- print(f"Curve fitting failed: {e}")
- # Outputs remain as NaN or can be set to zero
- amplitude, center, size = 0, 0, 0
- # Extract the fitted parameters
- amplitude, center, size = popt
- # Generate the Gaussian fit at the original resolution
- # It has 6 datapoints to the 6 conditions
- fitted_gaussian = gaussian(x, amplitude, center, size)
- fitted_gaussians[i_voxel] = fitted_gaussian # to store
- # Generate the high-resolution Gaussian
- high_res_gaussian = gaussian(high_res_x, amplitude, center, size)
- # Calculate the variance explained (R²)
- ss_total = np.sum((target_tmap - np.mean(target_tmap))**2)
- ss_residual = np.sum((target_tmap - fitted_gaussian)**2)
- r_squared = 1 - (ss_residual / ss_total)
- # Ensure R² is non-negative
- modified_r_squared = max(0, r_squared)
- tuning_curves[i_voxel, 0] = center
- tuning_curves[i_voxel, 1] = size
- tuning_curves[i_voxel, 2] = modified_r_squared
- # Assign values from numTune to the corresponding voxel indices in voxel_ijk
- numTune = tuning_curves[:,0] #center
- numTune [tuning_curves[:, 2] <= r_threshold] = np.nan # only to have r2 > 0.5
- # Load the mask used to extract the matrix (same space & dimensions as reference image)
- mask_img = nib.load(f"/home_local/Daniela_fmri_analyses/Results/gaussian_fit/ROIs/{roi}.nii")
- mask_data = mask_img.get_fdata()
- volume_shape = mask_img.shape
- affine = mask_img.affine
- # Initialize an empty volume (full brain size)
- volume = np.zeros(volume_shape)
- # Get the (i, j, k) indices of nonzero voxels (i.e., selected voxels in the mask)
- voxel_ijk = np.array(np.nonzero(mask_data)).T # shape: (els,n_vox 3)
- # Assume voxel_ijk is already available and numTune contains values to fill
- for idx, (i, j, k) in enumerate(voxel_ijk):
- volume[i, j, k] = numTune[idx]
- voxel_mni = nib.affines.apply_affine(affine, voxel_ijk)
- # Save NIfTI
- output_img = nib.Nifti1Image(volume, affine=affine)
- numTune_path = f"/home_local/Daniela_fmri_analyses/Results/gaussian_fit/group_analysis_aggregate_runs/{roi}/grouplevel_numTuning_integers_{roi}_r{r_threshold}_smooth4_norm.nii.gz"
- nib.save(output_img, numTune_path)
- save_path = f"/home_local/Daniela_fmri_analyses/Results/gaussian_fit/group_analysis_aggregate_runs/{roi}/grouplevel_integers_{roi}_fit_outputs_smooth4_norm.npz"
- np.savez(
- save_path,
- target_tmap_all=target_tmap_all, #save t values after being normalized
- fitted_gaussians=fitted_gaussians, #predicted values
- tuning_curves=tuning_curves, #preferred centers
- voxel_coords=voxel_mni #voxel coordinates
- )
- # %% [markdown]
- # # Fractions
- #
- # aggregate runs
- # %%
- r_threshold = 0.5
- rois = ["locp005_math", "glasser_bilateral_frontal", "glasser_bilateral_ips", "glasser_bilateral_temporal", "hippocampus", "parahippocampal", "bilateral_PF_IP2"]
- for roi in rois:
- print(f"\n--- ROI: {roi} ---")
- file_path = f"/home_local/Daniela_fmri_analyses/Results/gaussian_fit/group_analysis_aggregate_runs/{roi}/grouplevel_matrix_targetsXvoxels_coords_tmap_mni-space_{roi}_ordercateg_smooth4.npz"
- data = np.load(file_path)
- # Assuming the first key contains the matrix, print the first row
- first_key = data.files[0]
- matrix = data[first_key]
- tuning_curves = np.zeros((matrix.shape[0], 3))
- fitted_gaussians = np.zeros((matrix.shape[0], 6)) #to collect the fitted gaussian model for each voxel
- target_tmap_all = np.zeros((matrix.shape[0], 6))
- for i_voxel in range(matrix.shape[0]):
- #print("Voxel", i_voxel)
- target_tmap = matrix[i_voxel, 4:10] # all voxels for the fractions
- target_tmap = (target_tmap - np.min(target_tmap)) /(np.max(target_tmap) - np.min(target_tmap)) # Normalize target_betas between 0 and 1
- target_tmap = np.nan_to_num(target_tmap)
- target_tmap_all[i_voxel] = target_tmap # to store
- x = [1/4, 1/3, 1/2, 2/3, 3/2, 5/2]
- high_res_x = np.linspace(0, len(target_tmap) - 1, len(target_tmap))
- amplitude, center, size = np.nan, np.nan, np.nan # Initialize outputs
- try:
- # Attempt to fit the curve
- # Fit the Gaussian to target_betas with constrained parameters
- # Bounds: amplitude (0 to 1), center (0 to 5), sigma (0.1 to 2)
- popt, pcov = curve_fit(
- gaussian,
- x,
- target_tmap,
- p0=[1, np.clip(np.argmax(target_tmap), 0.25, 2.5), 1],
- bounds=([0, 0.25, 0.1], [1, 2.5, 2]) # Lower and upper bounds
- )
- except RuntimeError as e:
- print(f"Curve fitting failed: {e}")
- # Outputs remain as NaN or can be set to zero
- amplitude, center, size = 0, 0, 0
- # Extract the fitted parameters
- amplitude, center, size = popt
- # Generate the Gaussian fit at the original resolution
- # It has 6 datapoints to the 6 conditions
- fitted_gaussian = gaussian(x, amplitude, center, size)
- fitted_gaussians[i_voxel] = fitted_gaussian # to store
- # Generate the high-resolution Gaussian
- high_res_gaussian = gaussian(high_res_x, amplitude, center, size)
- # Calculate the variance explained (R²)
- ss_total = np.sum((target_tmap - np.mean(target_tmap))**2)
- ss_residual = np.sum((target_tmap - fitted_gaussian)**2)
- r_squared = 1 - (ss_residual / ss_total)
- # Ensure R² is non-negative
- modified_r_squared = max(0, r_squared)
- tuning_curves[i_voxel, 0] = center
- tuning_curves[i_voxel, 1] = size
- tuning_curves[i_voxel, 2] = modified_r_squared
- # Assign values from numTune to the corresponding voxel indices in voxel_ijk
- numTune = tuning_curves[:,0] #center
- numTune [tuning_curves[:, 2] <= r_threshold] = np.nan # only to have r2 in 0.5
- #print("Number tuning", numTune.shape)
- # Load the mask used to extract the matrix (same space & dimensions as reference image)
- mask_img = nib.load(f"/home_local/Daniela_fmri_analyses/Results/gaussian_fit/ROIs/{roi}.nii")
- mask_data = mask_img.get_fdata()
- volume_shape = mask_img.shape
- affine = mask_img.affine
- # Initialize an empty volume (full brain size)
- volume = np.zeros(volume_shape)
- # Get the (i, j, k) indices of nonzero voxels (i.e., selected voxels in the mask)
- voxel_ijk = np.array(np.nonzero(mask_data)).T # shape: (n_voxels, 3)
- # Assume voxel_ijk is already available and numTune contains values to fill
- for idx, (i, j, k) in enumerate(voxel_ijk):
- volume[i, j, k] = numTune[idx]
- voxel_mni = nib.affines.apply_affine(affine, voxel_ijk)
- # Save NIfTI
- output_img = nib.Nifti1Image(volume, affine=affine)
- numTune_path = f"/home_local/Daniela_fmri_analyses/Results/gaussian_fit/group_analysis_aggregate_runs/{roi}/grouplevel_numTuning_fractions_{roi}_r{r_threshold}_smooth4_norm.nii.gz"
- nib.save(output_img, numTune_path)
- save_path = f"/home_local/Daniela_fmri_analyses/Results/gaussian_fit/group_analysis_aggregate_runs/{roi}/grouplevel_fractions_{roi}_fit_outputs_smooth4_norm.npz"
- np.savez(
- save_path,
- target_tmap_all=target_tmap_all,
- fitted_gaussians=fitted_gaussians,
- tuning_curves=tuning_curves,
- voxel_coords=voxel_mni #voxel coordinates
- )
gaussianfit_averagegroups_aggruns_figure7CD.ipynb, no license · at the source
Overview
- Université Paris Saclay, INSERM, CEA, Cognitive Neuroimaging Unit, NeuroSpin Center, Gif-sur-Yvette, France
- Collège de France, PSL University, Paris, France
Abstract
How does the human brain represent the meaning of abstract symbols? Some theories postulate the existence of semantic spaces where concepts occupy positions that reflect their conceptual relationships. In the number domain, psychological evidence suggests that integers are represented along a mental number line which, with education, integrates higher-level number concepts such as fractions. To test this hypothesis, we recorded whole-brain 7T fMRI responses to integer and fraction symbols during an active magnitude comparison task designed to engage magnitude processing. Consistent with predictions, we found both behavioral and neural numerical distance effects. Activation vectors in intraparietal, inferior temporal, prefrontal, hippocampal, and parahippocampal cortices formed a two-dimensional semantic space organized by numerical magnitude and domain (fractions versus integers). Gaussian fits revealed a topographic map of numerical preferences in the anterior inferior parietal cortex, common to both domains. Our results suggest that, when educated adults engage in an explicit magnitude comparison task, their brain can construct an ordered representation that integrates fractions and integers, with a topographic organization in the anterior IPS/
Reproduced under the paper's license (CC BY), from the paper cited above.
Repositories
Its files are read in the Code ↔ Paper reader above, with 9 matches between paragraphs and lines of code.
OSF jqcna
Availability: 1 check, the latest on 25 October 2026: the link answers (HTTP 200)
- 25 October 2026: the link answers (HTTP 200)
23 files
- Behavioral/
BIS_R_data_figure1.R , R, 387 lines - Behavioral/
Group_analyses_RTs-error , Jupyter, 440 liness_efficiencyscore_figure 1.ipynb - Behavioral/
distance_effect_final_v2 , Jupyter, 662 lines_figure1BC.ipynb - Behavioral/
efficiency_score_indscal , R, 112 lines_mds_figure_s1.R - fMRI/
Gaussian_fit/ , Jupyter, 248 lines, 1 matchcorrelation-relation_bet ween_fractions_integers_ figures8.ipynb - fMRI/
Gaussian_fit/ , Jupyter, 159 lines, 1 matchcorrelation_between_frac tions_integers_figureS7. ipynb - fMRI/
Gaussian_fit/ , Jupyter, 273 lines, 2 matchesgaussianfit_averagegroup s_aggruns_figure7CD.ipyn b - fMRI/
Gaussian_fit/ , Jupyter, 232 linesgeodist_nativespace_figu reS10.ipynb - fMRI/
Gaussian_fit/ , Jupyter, 84 linesmatrix_creation_aggruns_ averagesubs.ipynb - fMRI/
Gaussian_fit/ , Jupyter, 182 lines, 1 matchrelation_between_fractio ns_integers_figureS7.ipy nb - fMRI/
Gaussian_fit/ , Jupyter, 238 lines, 1 matchrelation_between_runs_fr actions_figure7B.ipynb - fMRI/
Gaussian_fit/ , Jupyter, 235 lines, 1 matchrelation_between_runs_in teg_figure7A.ipynb - fMRI/
Multiple_regression/ , Python, 273 lines, 1 matchsearchlight_analysis_all subs_multipleregression_ figure6.py - fMRI/
Multiple_regression/ , Jupyter, 225 lines, 1 matchsecondlevel_analyses_sea rchlight_figure6_tableS1 .ipynb - fMRI/
PCA/ , Jupyter, 167 linespca_allsubs _figureS3.ipynb - fMRI/
PCA/ , Jupyter, 182 linespca_allsubs_figure3.ipyn b - fMRI/
RSA/ , R, 114 linesmds_inscal_6rois_figures 4_5.R - fMRI/
RSA/ , Jupyter, 401 linesrsa_analyses_hipp_parah_ final_figure5.ipynb - fMRI/
RSA/ , Jupyter, 201 linesrsa_analyses_loc_rois_fi nal_figure4.ipynb - fMRI/
RSA/ , Jupyter, 395 linesrsa_analyses_loc_rois_se paratedomains_figure_S5. ipynb - fMRI/
RSA/ , Jupyter, 526 linesrsa_analyses_locrois_ips _final_figure4.ipynb - fMRI/
RSA/ , Jupyter, 518 linesrsa_analyses_locrois_itg _final_figure4.ipynb - fMRI/
RSA/ , Jupyter, 512 linesrsa_analyses_locrois_mfg _final_figure4.ipynb
OSF 267s5
Availability: 1 check, the latest on 30 September 2026: the link answers (HTTP 200)
- 30 September 2026: the link answers (HTTP 200)
3 files
- paper_analysis.Rmd, R, 1,122 lines
- paper_analysis_exp_2.Rmd
, R, 800 lines - supplementary_analyses.R
md , R, 605 lines
The paper's code and data availability statement is in the Data section.
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All data, code, and outputs to reproduce the main results are publicly available on the Open Science Foundation (OSF): https://
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Version 1, 25 October 2026: the first record
Recorded: type, language, journal, volume, issue, pages, dates, 6 authors, 9 MeSH terms, 1 funder, 114 references, 2 RRIDs.
Cite
This paper
Valério, D., Debray, S., Karami, A., Cauté, M., Gravel, N., & Dehaene, S. (2026). A cortical semantic map integrates fractions and integers in the human brain. PLoS biology, 24(10), e3003820. https://
BibTeX
@article{valerio2026cort
author = {Valério, Daniela and Debray, Samuel and Karami, Alireza and Cauté, Maxime and Gravel, Nicolás and Dehaene, Stanislas},
title = {{A cortical semantic map integrates fractions and integers in the human brain}},
journal = {PLoS biology},
year = {2026},
month = oct,
volume = {24},
number = {10},
pages = {e3003820},
publisher = {PLOS},
issn = {1544-9173},
doi = {10.1371/
url = {https://
pmid = {42911907},
pmcid = {PMC13690230}
}
RIS
TY - JOUR
AU - Valério, Daniela
AU - Debray, Samuel
AU - Karami, Alireza
AU - Cauté, Maxime
AU - Gravel, Nicolás
AU - Dehaene, Stanislas
TI - A cortical semantic map integrates fractions and integers in the human brain
T2 - PLoS biology
J2 - PLoS Biol
PY - 2026
DA - 2026/
VL - 24
IS - 10
SP - e3003820
SN - 1544-9173
PB - PLOS
DO - 10.1371/
UR - https://
LA - en
ER -
CSL-JSON
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"container-title": "PLoS biology",
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"family": "Valério",
"given": "Daniela"
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{
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{
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"given": "Maxime"
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"given": "Nicolás"
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"publisher": "PLOS",
"URL": "https://
"language": "en",
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}
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