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Endogenous precision of the number sense.

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The 2 matches
  1. [1] § Results › Estimation task ↔ Data Analysis Estimation Task.ipynb, lines 163–244 · score 0.64 · Absolute error, relative error, Standard deviation, coefficients, variations, prior width
  2. [2] § Results › Estimation task ↔ Data Analysis Estimation Task.ipynb, lines 163–244 · score 0.59 · absolute error, relative error, standard deviation, prior width, square

Paper

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The authors' code

Jupyter notebook · 325 lines · 12 KB · no license · 2 matches

  1. # %%
  2. # %matplotlib inline
  3. from matplotlib.pyplot import *
  4. import numpy as np
  5. import pandas as pd
  6. from scipy import stats, optimize
  7. import itertools, tabulate
  8. from datetime import datetime
  10. # %%
  11. from scipy import __version__ as scipy_version
  12. print(np.__version__)
  13. print(scipy_version)
  14. print(pd.__version__)
  16. # %%
  17. import library_estimation as le
  18. #import apc_utils as apc
  19. #import statsmodels.api as sm
  21. # %%
  22. np.set_printoptions(linewidth=160)
  24. # %%
  25. # number spaces for each width
  26. XS_DELTA = {}
  27. for delta in le.DELTAS:
  28. lo, hi = le.RANGES_DELTA[delta]
  29. xxx = np.arange( int(lo), int(hi) + 1 )
  30. XS_DELTA[delta] = xxx
  31. XS_DELTA
  33. # %%
  34. def mean_variance_from_pmf(xhats, p_xhats):
  35. m = (xhats*p_xhats).sum()
  36. v = (p_xhats*(xhats-m)**2).sum()
  37. return m,v
  39. # %% [markdown]
  40. # # Data
  42. # %%
  43. META = pd.read_csv('data_estimation/subjects_info.csv', index_col=0)
  44. META
  46. # %%
  47. DATA = pd.read_csv('data_estimation/data.csv')
  48. DATA
  50. # %%
  51. len(META), DATA.ID.unique().shape
  53. # %%
  54. META.Gender.value_counts()
  56. # %%
  57. META.Age.mean(), META.Age.std()
  59. # %%
  60. META.Laterality.value_counts()
  62. # %%
  63. META.Reward.mean(), META.Reward.std()
  65. # %%
  67. # def estimate_mean_responses_ols(data):
  68. # A = np.vstack([data.Number, np.ones(len(data.Number))]).T
  69. # m, c = np.linalg.lstsq(A, data.Response, rcond=None)[0]
  70. # xs = np.arange( data.Number.min(), data.Number.max()+1 )
  71. # return { x : m*x + c for x in xs}
  73. # def estimate_mean_responses_gaussian_kernel(data, conv_w, xs=None):
  74. # if xs is None:
  75. # xs = np.arange(int(data.Number.min()), int(data.Number.max())+1)
  76. # return dict( zip( *apc.smooth_ys(conv_w, data.Number, data.Response, xs) ) )
  78. # %% [markdown]
  79. # ## Figure 1
  81. # %%
  82. def get_mean_responses(data):
  83. xs = np.arange( data.Number.min(), data.Number.max()+1 )
  84. return {x:data.Response[data.Number==x].mean() for x in xs}
  86. # %%
  87. fig = figure(layout="constrained", figsize=(12,9))
  88. axd = fig.subplot_mosaic(
  89. """
  90. ..BCC
  91. AAACC
  92. AAADE
  93. """, height_ratios=[3,1.8,4.2], width_ratios=[.5,.4,1.3,1,1],
  94. )
  95. axPrior = axd['B']
  96. axSTD = axd['A']
  97. axLIN = axd['C']
  98. axCV = axd['D']
  99. axERR = axd['E']
  100. axERRT = axERR.twinx()
  101. all_axs = list( axd.values() )
  103. # priors
  104. for delta in le.DELTAS:
  105. data = DATA[DATA.Delta==delta]
  106. lo, hi = le.RANGES_DELTA[delta]
  107. c = le.COLORS_DELTA[delta]
  108. xxx = np.array([lo, hi])
  109. yyy = stats.uniform(loc=lo, scale=delta).pdf(xxx)
  110. lbl = le.LABELS_DELTA[delta]
  111. axPrior.plot(xxx, yyy, c=c, label=lbl)
  112. axPrior.vlines(xxx, 0, yyy, color=c, ls=':')
  113. axPrior.text(x=60, y=1/delta-0.004, s=f'$w={delta}$', ha='center', color=c)
  114. leg = axPrior.legend(loc=(0.725,.6), facecolor='white', framealpha=1, edgecolor='none')
  115. leg.set_in_layout(False)
  116. axPrior.set_ylim(0,None)
  117. axPrior.set_xticks([30,40,50,60,70,80,90])
  118. axPrior.set_yticks([])
  119. axPrior.set_xlabel('Number $x$')
  120. axPrior.set_ylabel('pdf')
  121. axPrior.set_title('Priors')
  122. cc1 = 'purple'
  123. cc2 = '#606060'
  124. for binned in [False, True]:
  125. vars_per_delta = {}
  126. excursions_per_delta = {}
  127. xs_per_delta = {}
  128. vars_per_delta = {}
  129. errors_per_delta = {}
  130. for delta in reversed(le.DELTAS):
  131. data = DATA[DATA.Delta==delta]
  132. lo, hi = le.RANGES_DELTA[delta]
  133. c = le.COLORS_DELTA[delta]
  134. bin_edges = le.BINS_EDGES_DELTA[delta] if binned else np.linspace(*le.RANGES_DELTA[delta], delta+2)
  135. binned_data = le.split_in_bins(data, bin_edges)
  136. mean_resps = get_mean_responses(data) # { x : mean_xhat }
  137. excursions = data.apply(lambda row: row.Response - mean_resps[row.Number], axis='columns') # xhat - mean_xhat
  138. excursions_per_delta[delta] = excursions
  139. binned_excursions = le.split_in_bins(excursions, bin_edges, xcol=None, xs=data.Number)
  140. mean_xhats = np.array([da.Response.mean() for da in binned_data])
  141. vars = np.array( [ (excs**2).mean() for excs in binned_excursions] ); vars_per_delta[delta] = vars
  142. stds = np.sqrt(vars)
  143. sesds = np.array( [ le.sesd(excs) for excs in binned_excursions] )
  144. sevs = np.array( [ le.sev(excs) for excs in binned_excursions] )
  145. xs = np.array([da.Number.mean() for da in binned_data])
  146. xs_per_delta[delta] = xs
  147. cvs = np.array([ stds[i]/m_xhat for i,m_xhat in enumerate(mean_xhats) ])
  148. vars_per_delta[delta] = vars
  149. errors_per_delta[delta] = data.Error
  150. if not binned:
  151. axSTD.plot(xs, stds, c=c, alpha=.2, clip_on=False)
  152. axCV.plot(xs, cvs, c=c, alpha=.2, clip_on=False)
  153. print( delta, stds[xs==60] )
  154. else:
  155. axSTD.errorbar(xs, stds, sesds, c=c, label=f'{le.LABELS_DELTA[delta]} prior $(w={delta})$')
  156. axCV.errorbar(xs, cvs, sesds/xs, c=c)
  157. ##### MODEL
  158. ν_1, σ = 1.22553588, 3.62413533
  159. β = 1/2
  160. ν = ν_1*delta**(β-1)
  161. ps = le.probs_xhats_given_x_for_all_xs_MP(lo, delta, ν=ν, σ=σ)
  162. xs = le.discrete_xs(lo, delta)
  163. xhats_means = []
  164. xhats_vars = []
  165. for x,p_xhats in zip(xs,ps):
  166. m,v = mean_variance_from_pmf(xs, p_xhats)
  167. xhats_means.append(m)
  168. xhats_vars.append(v)
  169. axSTD.plot(xs, np.sqrt(xhats_vars), c=c, ls=':', zorder=-1000)
  170. if binned:
  171. ys = np.array( [ (excursions_per_delta[delta]**2).mean() for delta in le.DELTAS ] )
  172. yerrs = np.array( [ le.sev(excursions_per_delta[delta]) for delta in le.DELTAS ] )
  173. line, caps, bars = axLIN.errorbar(le.DELTAS, ys, 2*yerrs, c=cc1, ecolor=[le.COLORS_DELTA[d] for d in le.DELTAS])
  174. for bar in bars: bar.set_zorder(2000)
  175. axT = axLIN.twiny()
  176. line, caps, bars = axT.errorbar(np.array(le.DELTAS)**2, ys, 2*yerrs, c=cc2, ecolor=[le.COLORS_DELTA[d] for d in le.DELTAS])
  177. for bar in bars: bar.set_zorder(2000)
  178. pred_vars = vars_per_delta[20] + (vars_per_delta[40]-vars_per_delta[20])*(60**2-20**2)/(40**2-20**2)
  179. axSTD.plot(xs_per_delta[60], np.sqrt(pred_vars), 'x', c=le.COLORS_DELTA[60])
  180. pred_vars = vars_per_delta[20] + (vars_per_delta[40]-vars_per_delta[20])*(60-20)/(40-20)
  181. axSTD.plot(xs_per_delta[60], np.sqrt(pred_vars), 'o', c=le.COLORS_DELTA[60], mfc='none')
  182. #
  183. ### Relative error
  184. if axERR is not None:
  185. ys = np.array( [ np.abs(errors_per_delta[delta]).mean() for delta in le.DELTAS ] )
  186. yerrs = np.array( [ stats.sem(np.abs(errors_per_delta[delta])) for delta in le.DELTAS ] )
  187. line, caps, bars = axERR.errorbar(le.DELTAS, ys, 2*yerrs, color='grey', ecolor=[le.COLORS_DELTA[d] for d in le.DELTAS])
  188. for bar in bars: bar.set_zorder(2000)
  189. ys = np.array( [ np.abs(errors_per_delta[delta]).mean()/delta for delta in le.DELTAS ] )
  190. yerrs = np.array( [ stats.sem(np.abs(errors_per_delta[delta]/delta)) for delta in le.DELTAS ] )
  191. line, caps, bars = axERRT.errorbar(le.DELTAS, ys, 2*yerrs, color='grey', ecolor=[le.COLORS_DELTA[d] for d in le.DELTAS], ls='--')
  192. for bar in bars: bar.set_zorder(2000)
  193. axSTD.set_ylim(0,10.5)
  194. axSTD.set_xlim(30,90)
  195. axCV.set_ylim(0,.18)
  196. axCV.set_xlim(30,90)
  197. axCV.set_yticks([0,.05,.1,.15])
  198. for ax in all_axs:
  199. ax.spines['top'].set_visible(False)
  200. ax.spines['right'].set_visible(False)
  201. axSTD.set_xlabel('Presented number $x$')
  202. axSTD.set_ylabel('$\\operatorname{StdDev}[\\hat x]$')
  203. axSTD.set_title('Standard deviation of responses')
  204. axCV.set_xlabel('Presented number $x$')
  205. axCV.set_ylabel('$CV = \\operatorname{StdDev}[\\hat x]/\\operatorname{Mean}[\\hat x]$')
  206. axCV.set_title('Coefficient of Variation')
  207. #
  208. leg = axSTD.legend(frameon=False)
  209. axSTD.legend([Line2D([],[],c='grey',alpha=.2), Line2D([],[],c='grey'), Line2D([],[],c='grey', ls=':'), ],
  210. ['Subjects', 'Subjects (binned $x$)', 'Model'],
  211. frameon=False, loc='lower right')
  212. axSTD.add_artist(leg)
  213. #
  214. some_ticks = np.array([4,5,6,7,8])
  215. axLIN.set_yticks( some_ticks**2, labels=[f'${x}^2$' for x in some_ticks] )
  216. axLIN.set_xticks(le.DELTAS)
  217. axT_ticks = np.array(le.DELTAS)
  218. axT.set_xticks( axT_ticks**2, labels=[f'${x}^2$' for x in axT_ticks] )
  219. xlabel_ax = axLIN.set_xlabel('Prior width $w$', color=cc1)
  220. axT.set_xlabel('Squared prior width $w^2$', color=cc2)
  221. axT.xaxis.set_label_coords(.5, .15)
  222. axT.spines['bottom'].set_position(('outward', -30))
  223. axT.xaxis.set_ticks_position('bottom')
  224. axT.xaxis.set_label_position('bottom')
  225. axLIN.tick_params(axis='x', colors=cc1)
  226. axT.tick_params(axis='x', colors=cc2)
  227. axLIN.spines['bottom'].set_color(cc1)
  228. axT.spines['bottom'].set_color(cc2)
  229. axT.spines['top'].set_visible(False)
  230. axT.spines['right'].set_visible(False)
  231. axLIN.set_ylabel('$\\operatorname{Var}[\\hat x]$')
  232. axLIN.set_ylim(0,8**2)
  233. axLIN.set_title('Variance vs. $w$ and $w^2$')
  234. ##
  235. if axERR is not None:
  236. axERRT.spines['top'].set_visible(False)
  237. axERR.spines['right'].set_ls((0,(8,5))); axERRT.spines['right'].set_ls((0,(8,5)))
  238. axERR.set_xticks(le.DELTAS)
  239. xlabel_ax = axERR.set_xlabel('Prior width $w$')
  240. axERR.set_ylabel('Absolute error $|\\hat x - x|$'); axERRT.set_ylabel('Relative error $|\\hat x - x| / w$')
  241. axERR.set_title('Absolute and relative error')
  242. axERR.set_ylim(0,None); axERRT.set_ylim(0,None)
  243. axERRT.yaxis.set_major_formatter(matplotlib.ticker.PercentFormatter(1., decimals=0))
  244. axERR.legend([Line2D([],[],c='grey'),Line2D([],[],c='grey',ls='--')], ['Absolute error', 'Relative error'], frameon=False)
  246. #fig.subplots_adjust(hspace=.25)
  247. fig.savefig('figures/result_estimation_task.pdf', bbox_inches='tight')
  249. # %%
  252. # %% [markdown]
  253. # ## Tests of equality of variances
  255. # %% [markdown]
  256. # ### across bins
  258. # %%
  259. for delta in le.DELTAS:
  260. data = DATA[DATA.Delta==delta]
  261. nbbins = 5
  262. bin_edges = le.BINS_EDGES_DELTA[delta]
  263. binned_data = le.split_in_bins(data, bin_edges)
  264. mean_resps = get_mean_responses(data) # { x : mean_xhat }
  265. excursions = data.apply(lambda row: row.Response - mean_resps[row.Number], axis='columns')
  266. binned_excursions = le.split_in_bins(excursions, bin_edges, xs=data.Number, xcol=None)
  267. print(f'w={delta}')
  268. print('Bins 3,4', stats.levene(*[binned_excursions[i] for i in [2,3]]).pvalue)
  269. print( [binned_excursions[i].std() for i in [2,3]] )
  270. print('Bins 3,5', stats.levene(*[binned_excursions[i] for i in [2,4]]).pvalue)
  271. print( [binned_excursions[i].std() for i in [2,4]] )
  272. print()
  274. # %% [markdown]
  275. # ### across conditions
  276. # Narrow-Medium, Narrow-Wide, Medium-Narrow
  278. # %% [markdown]
  279. # The Levene's test of equality of variances in the three conditions rejects the null hypothesis.
  281. # %%
  282. #### With each number in the narrowest range
  283. excs_per_x_per_delta = {}
  284. xs = np.arange(50,71)
  285. pvs = []
  286. for x in xs:
  287. excs_per_x_per_delta[x] = {}
  288. for delta in reversed(le.DELTAS):
  289. data = DATA[(DATA.Delta==delta) & (DATA.Number==x)]
  290. excursions = data.Response - data.Response.mean()
  291. excs_per_x_per_delta[x][delta] = excursions
  292. pvs.append(stats.levene(*excs_per_x_per_delta[x].values()).pvalue)
  293. print(x, pvs[-1] )
  294. np.max(pvs), np.median(pvs)
  296. # %% [markdown]
  297. # # Model
  299. # %% [markdown]
  300. # $x \in [a, a+w]$, where $a = 60 - w/2$.
  301. # $p(r|x) = N(r; \frac{x-a}{w}, \nu_w^2)$, with $\nu_w = \nu_1 w^{\beta-1}$. Note that this is slightly different than in the paper (but it is equivalent).
  302. # The Fisher information is $I(x) = \left( \frac{1}{w\nu_w} \right)^2 = \left( \frac{1}{\nu_1 w^{\beta} } \right)^2 = \frac{1}{\nu_1^2 w^{2\beta} }.$
  303. # The Bayesian estimate, given $r$, is
  304. # $$x_B(r) = a + wr + w\nu\frac{\varphi(\frac{r}{\nu}) - \varphi(\frac{r-1}{\nu})}{\Phi(\frac{r}{\nu}) - \Phi(\frac{r-1}{\nu})}.$$
  305. # With truncated motor noise:
  306. # $y = [x_B(r) + \sigma \varepsilon]_{[a,a+w]}$, where $\varepsilon \sim N(0,1)$.
  307. # Responses are integers. We round:
  308. # $\hat x = round(y)$.
  309. #
  310. # This model has 2 or 3 parameters: $\nu_1$, $\sigma$, and $\beta$ which can be fixed or allowed to take any value.
  312. # %%
  313. # This function computes the log-likelihood of `data` for delta, ν_1, σ, and β defined as above.
  314. le.LL_data_w_params(data=DATA, delta=20, ν_1=.3, σ=3, β=1)
  316. # %%
  317. def make_x0s(bounds, n=2):
  318. spaces = [ [x,] if np.isscalar(x) else np.linspace(x[0],x[1],n) for x in bounds ]
  319. return list( itertools.product(*spaces) )
  321. # %%
  322. # TO BE COMPLETED
  324. # %%

Data Analysis Estimation Task.ipynb, no license · at the source

Overview

Authors: Arthur Prat-Carrabin1, Michael Woodford1
ORCID iDs: Arthur Prat-Carrabin, Michael Woodford
  1. Department of Economics, Columbia University, New York, United States
Institutions: Columbia University (United States)
Journal: eLife, volume 13, article RP101277
Dates: published online 15 April 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.7554/elife.101277 · PMID 41983455 · PMCID PMC13082791 · OpenAlex W4402685021
Open access: gold, a free copy (OpenAlex)
Status: code verified
Categories: human (organism), cognitive (subfield)
Methods: Statistics
Keywords: Human
MeSH: Brain*, Mathematical Concepts*, Humans (* major topic)
Topic: Cognitive and developmental aspects of mathematical skills (Statistics and Probability, Mathematics), according to OpenAlex
Funding: National Science Foundation (SES DRMS 1949418)
Citations: cited by 4 papers (Europe PMC); 62 references in the paper

Abstract

The behavioral variability in psychophysical experiments and the stochasticity of sensory neurons have revealed the inherent imprecision in the brain’s representations of environmental variables. Numerosity studies yield similar results, pointing to an imprecise ‘number sense’ in the brain. If the imprecision in representations reflects an optimal allocation of limited cognitive resources, as suggested by efficient-coding models, then it should depend on the context in which representations are elicited. Through an estimation task and a discrimination task, both involving numerosities, we show that the scale of subjects’ imprecision increases, but sublinearly, with the width of the prior distribution from which numbers are sampled. This sublinear relation is notably different in the two tasks. The double dependence of the imprecision — both on the prior and on the task — is consistent with the optimization of a tradeoff between the expected reward, different for each task, and a resource cost of the encoding neurons’ activity. Comparing the two tasks allows us to clarify the form of the resource constraint. Our results suggest that perceptual noise is endogenously determined, and that the precision of percepts varies both with the context in which they are elicited and with the observer’s objective.

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 2 matches between paragraphs and lines of code.

OSF d6k3m

License: none: the authors keep all their rights
State: the link answers, verified on 29 September 2026
Evidence: files inventoried
Languages: Jupyter (2), Python (2)
Size: 13 files, 4 scripts
Software Heritage: not checked
Found in: “Data availability”
Holds: 2 notebooks
Not found: README, license file, CITATION.cff, environment file, tests, continuous integration, documentation
Tools: NumPy (4 files), SciPy (4 files), Matplotlib (2 files), pandas (2 files), statsmodels (1 file)
Availability: 1 check, the latest on 29 September 2026: the link answers (HTTP 200)
  • 29 September 2026: the link answers (HTTP 200)
4 files
At the source: osf.io/d6k3m

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.

What the map holds:

  • 1 repository of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
  • 4 scripts, each with its path and the digest of its content;
  • 2 matches between paragraphs of the paper and lines of the code (method lexical-v1);
  • neither the text of the paper nor the code itself.

Its JSON (tracing-map.json) is deposited on Zenodo with its DOI once the map is validated.

Data

Datasets cited

Data availability

The data and the code are available at https://osf.io/d6k3m.

The following dataset was generated:

Prat-Carrabin A, Woodford M. 2024. Endogenous Precision of the Number Sense: Data & Code. Open Science Framework. d6k3m

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

Versions

The history of this record: each version stored by the harvester or made by a correction of its authors or of the maintainers of its code, and what changed in its facts. The texts of the paper (its abstract, its availability statements) are not part of it; versions that changed only those are not listed.

Version 1, 29 September 2026: the first record

Recorded: type, language, journal, volume, pages, dates, 2 authors, 1 keyword, 3 MeSH terms, 1 funder, 55 references.

Cite

This paper

Prat-Carrabin, A., & Woodford, M. (2026). Endogenous precision of the number sense. eLife, 13, RP101277. https://doi.org/10.7554/elife.101277

BibTeX

@article{pratcarrabin2026endogenous,
author = {Prat-Carrabin, Arthur and Woodford, Michael},
title = {{Endogenous precision of the number sense}},
journal = {eLife},
year = {2026},
month = apr,
volume = {13},
pages = {RP101277},
publisher = {eLife Sciences Publications, Ltd},
issn = {2050-084X},
doi = {10.7554/elife.101277},
url = {https://doi.org/10.7554/elife.101277},
pmid = {41983455},
pmcid = {PMC13082791}
}

RIS

TY - JOUR
AU - Prat-Carrabin, Arthur
AU - Woodford, Michael
TI - Endogenous precision of the number sense
T2 - eLife
J2 - Elife
PY - 2026
DA - 2026/04/15
VL - 13
SP - RP101277
SN - 2050-084X
PB - eLife Sciences Publications, Ltd
DO - 10.7554/elife.101277
UR - https://doi.org/10.7554/elife.101277
LA - en
ER -

CSL-JSON

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"type": "article-journal",
"title": "Endogenous precision of the number sense",
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"author": [
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"given": "Arthur"
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"family": "Woodford",
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"container-title-short": "Elife",
"volume": "13",
"page": "RP101277",
"DOI": "10.7554/elife.101277",
"PMID": "41983455",
"PMCID": "PMC13082791",
"ISSN": "2050-084X",
"publisher": "eLife Sciences Publications, Ltd",
"URL": "https://doi.org/10.7554/elife.101277",
"language": "en",
"issued": {
"date-parts": [
[
2026,
4,
15
]
]
}
}

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[2] doi:10.1371/journal.pcbi.1014251 [code]
Distilling noise characteristics and prior expectations in multisensory causal inference.
Journal: PLoS computational biology
In common: cognitive, 5 references
[3] doi:10.1162/netn.a.544 [code]
Brain network reconfiguration during reward prediction error processing.
Journal: Network neuroscience (Cambridge, Mass.)
In common: statsmodels, pandas, SciPy, 2 other tools, cognitive, 2 references
[4] doi:10.1038/s41593-026-02255-7 [code]
Neural circuits encode prior knowledge of temporal statistics.
Journal: Nature neuroscience
In common: pandas, SciPy, Matplotlib, 1 other tool, 3 references
[5] doi:10.1371/journal.pbio.3003829 [code]
Identity-specific reward expectations in orbitofrontal cortex guide goal-directed choices.
Journal: PLoS biology
In common: statsmodels, pandas, SciPy, 2 other tools, cognitive, 1 reference
[6] doi:10.1162/imag.a.1207 [code]
Investigating the temporal dynamics and modeling of mid-level feature representations in humans.
Journal: Imaging neuroscience (Cambridge, Mass.)
In common: statsmodels, pandas, SciPy, 2 other tools, cognitive, 1 reference
[7] doi:10.1111/psyp.70397 [code]
Cortical Contributions to Attentional Orienting and Response Cancellation in Action Stopping.
Journal: Psychophysiology
In common: statsmodels, pandas, SciPy, 2 other tools, cognitive, 1 reference
[8] doi:10.1038/s41467-026-71568-9 [code]
Convergent and selective representations of pain, appetitive processes, aversive processes, and cognitive control in the insula.
Journal: Nature communications
In common: statsmodels, pandas, SciPy, 2 other tools, cognitive, 1 reference
[9] doi:10.1016/j.isci.2026.117375 [code]
Motor priming is associated with widespread recruitment into neural ensembles and more rapid ensemble transitions.
Journal: iScience
In common: statsmodels, pandas, SciPy, 2 other tools, 1 reference
[10] doi:10.7554/elife.108109 [code]
Multimodal MRI marker of cognition explains the association between cognition and mental health in the UK Biobank.
Journal: eLife
In common: pandas, SciPy, Matplotlib, 1 other tool, cognitive, 1 reference

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