Categorical Representation of Numerosity in the Pigeon Entopallium: Coding Format and Temporal Dynamics.
The 1 match
- [1] § 3. Results › 3.4. Numerosity Discriminability in QMI and QMD Neuron Populations ↔ DA_sAUROC_3D_UDs_lin_log_CV.m, lines 85–200 · score 0.56 · linear scale, logarithmic scale, sAUROC, CV, DA, bars
Paper
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The authors' code
MATLAB · 516 lines · 11 KB · no license · 1 match
- clear;
- close all
- clc;
- load('UDs_data.mat')
- %%
- Inc_LOG = mean(Inc_AUROC,3);
- Inc_LIN = mean(Inc_AUROC,3);
- Inc_POW12 = mean(Inc_AUROC,3);
- Inc_POW13 = mean(Inc_AUROC,3);
- LOG=[]
- LIN=[]
- POW12=[]
- POW13=[]
- for i=1:5
- for j=1:5
- if j>i
- Inc_LOG(i,j) = Inc_LOG(i,j) / (log2(j)-log2(i));
- LOG = [LOG Inc_LOG(i,j)];
- Inc_LIN(i,j) = Inc_LIN(i,j) / (j-i);
- LIN = [LIN Inc_LIN(i,j)];
- Inc_POW12(i,j) = Inc_POW12(i,j) / (j.^(1/2)-i.^(1/2));
- POW12 = [POW12 Inc_POW12(i,j)];
- Inc_POW13(i,j) = Inc_POW13(i,j) / (j.^(1/3)-i.^(1/3));
- POW13 = [POW13 Inc_POW13(i,j)];
- end
- end
- end
- Inc_4 = [std(LIN)/mean(LIN) std(POW12)/mean(POW12) std(POW13)/mean(POW13) std(LOG)/mean(LOG) ]
- %%
- Dec_LOG = mean(-Dec_AUROC,3);
- Dec_LIN = mean(-Dec_AUROC,3);
- Dec_POW12 = mean(-Dec_AUROC,3);
- Dec_POW13 = mean(-Dec_AUROC,3);
- LOG=[]
- LIN=[]
- POW12=[]
- POW13=[]
- for i=1:5
- for j=1:5
- if j>i
- Dec_LOG(i,j) = Dec_LOG(i,j) / (log2(j)-log2(i));
- LOG = [LOG Dec_LOG(i,j)];
- Dec_LIN(i,j) = Dec_LIN(i,j) / (j-i);
- LIN = [LIN Dec_LIN(i,j)];
- Dec_POW12(i,j) = Dec_POW12(i,j) / (j.^(1/2)-i.^(1/2));
- POW12 = [POW12 Dec_POW12(i,j)];
- Dec_POW13(i,j) = Dec_POW13(i,j) / (j.^(1/3)-i.^(1/3));
- POW13 = [POW13 Dec_POW13(i,j)];
- end
- end
- end
- Dec_4 = [ std(LIN)/mean(LIN) std(POW12)/mean(POW12) std(POW13)/mean(POW13) std(LOG)/mean(LOG)]
- %%
- Inc_AAA = mean(Inc_AUROC,3)
- Dec_AAA = mean(-Dec_AUROC,3)
- Inc_Dec_AAA = Inc_AAA;
- for i=1:5
- for j=1:5
- if j>i
- Inc_Dec_AAA(i,j)= Dec_AAA(i,j);
- end
- if j==i
- Inc_Dec_AAA(i,j)= nan;
- end
- end
- end
- Inc_Dec_AAA_log2=[]
- Inc_Dec_AAA_lin=[]
- for i=1:5
- for j=1:5
- if j~=i
- Inc_Dec_AAA_log2(i,j)= Inc_Dec_AAA(i,j) / abs(log2(j)-log2(i));
- Inc_Dec_AAA_lin(i,j)= Inc_Dec_AAA(i,j) / abs(j-i);
- end
- end
- end
- A=Inc_Dec_AAA
- triBar3_signed(A, coolwarm_mpl(256), 'DA-sAUROC');
- pause(0.5)
- A=Inc_Dec_AAA_log2
- triBar3_signed(A, coolwarm_mpl(256), ['logarithmic scale ' ] );
- pause(0.5)
- A=Inc_Dec_AAA_lin
- triBar3_signed(A, coolwarm_mpl(256), [' linear scale ' ] );
- pause(0.5)
- figure('Color','w');
- hold on;plot(Inc_4,'LineWidth',1,'LineStyle',':', 'Color',[215,48,39]/255)
- hold on;plot(Inc_4, '.','MarkerSize',24,'Color',[215,48,39]/255)
- hold on;plot(Dec_4, 'LineWidth',1,'LineStyle',':','Color',[69,117,180]/255)
- hold on;plot(Dec_4, '.','MarkerSize',24,'Color',[69,117,180]/255)
- xticks([1 2 3 4]);
- xticklabels({'linear', 'power(1/2)', 'power(1/3)', 'log'})
- ylabel('CV');
- % Inc = Inc_4;
- % Dec = Dec_4;
- % scales = {'lin','Power(1/2)','Power(1/3)','log2'};
- %
- %
- % cA = [59 76 192]/255; % Inc
- % cB = [180 4 38]/255; % Dec
- %
- %
- % x1 = 1:4;
- % gap = 1;
- % x2 = (x1(end)+gap) + (1:4);
- %
- %
- % figure('Color','w','Position',[100 100 800 420]); hold on
- % b1 = bar(x1, Inc, 0.8, 'FaceColor','flat','EdgeColor','none'); b1.CData = repmat(cA,4,1);
- % b2 = bar(x2, Dec, 0.8, 'FaceColor','flat','EdgeColor','none'); b2.CData = repmat(cB,4,1);
- %
- % ax = gca;
- % ax.Box = 'off';
- % ax.YGrid = 'on'; ax.GridAlpha = 0.25; ax.LineWidth = 1;
- % ax.XTick = [x1 x2];
- % ax.XTickLabel = [scales scales];
- % xlabel('scale'); ylabel('CV');
- % legend([b1 b2], {'Inc','Dec'}, 'Location','northwest');
- %
- %
- %
- % for h = [b1 b2]
- % x = h.XEndPoints; y = h.YEndPoints;
- % text(x, y, compose('%.3f', y), 'HorizontalAlignment','center', ...
- % 'VerticalAlignment','bottom', 'FontSize',9);
- % end
- %
- %
- % yTop = max([Inc Dec]) * 1.12;
- % text(mean(x1), yTop, 'Inc', 'HorizontalAlignment','center','FontWeight','bold');
- % text(mean(x2), yTop, 'Dec', 'HorizontalAlignment','center','FontWeight','bold');
- %
- % xlim([0.25 x2(end)+0.75]);
- % ylim([0 yTop*1.05]);
- %%
- % % n = 5;
- % % a = 1.2;
- % % b = 0.9;
- % % theta = linspace(0,pi,n);
- % % x = a*cos(theta);
- % % y = b*sin(theta);
- %
- %
- % n = 5;
- % a = 1.2;
- % b = 0.9;
- % theta = linspace(-pi/2, pi/2, n);
- % x = a*cos(theta);
- % y = b*sin(theta);
- %
- % x=x(end:-1:1);
- % % ------------------------------------------------------------------
- % addpath cmocean
- %
- %
- %
- % cmap = bluewhitered(256);
- %
- %
- % nCol = size(cmap,1);
- % idxFun = @(v) round(((max(-1,min(1,v))+1)/2)*(nCol-1))+1;
- %
- %
- % % ---- --------------------------------------------------------------
- % figure
- % subplot(1,2,2)
- % % clf;
- % hold on;
- % axis equal off
- % for i = 1:n
- % for j = i+1:n
- % % if dist(i,j)>0.15
- %
- % c = cmap( idxFun(-Dec_AAA(i,j)), : );
- % plot([x(i) x(j)], [y(i) y(j)], 'Color', c, 'LineWidth', 2);
- %
- % % end
- % end
- % end
- %
- % Color_sum=[[220 18 20]/255; [173 76 167]/255; [0 177 63]/255; [0 127 187]/255; [250 127 0]/255];
- % for jm=1:5
- % % scatter(x(jm), y(jm), 80, Color_sum(jm,:), 'filled', 'MarkerEdgeColor','k', 'LineWidth',1.2)
- % scatter(x(jm), y(jm), 80, Color_sum(jm,:), 'filled', 'MarkerEdgeColor',Color_sum(jm,:), 'LineWidth',1.2)
- % end
- %
- % % scatter(x, y, 80, 'b', 'filled', 'MarkerEdgeColor','k', 'LineWidth',1.2)
- %
- % % for k = 1:n
- % % text(x(k), y(k)+0.05, sprintf('%d',k), ...
- % % 'HorizontalAlignment','center','FontSize',11);
- % % end
- % colormap(cmap); caxis([-1 1])
- % cb = colorbar('southoutside');
- % cb.Label.String = '2(ROC_{area}-0.5)';
- % title('Category distinction coded by 2(AUC-0.5)');
- %
- %
- %
- % subplot(1,2,1)
- % % clf;
- % hold on;
- % axis equal off
- % for i = 1:n
- % for j = i+1:n
- % % if dist(i,j)>0.15
- %
- % c = cmap( idxFun(Inc_AAA(i,j)), : );
- % plot([x(i) x(j)], [y(i) y(j)], 'Color', c, 'LineWidth', 2);
- %
- % % end
- % end
- % end
- %
- % Color_sum=[[220 18 20]/255; [173 76 167]/255; [0 177 63]/255; [0 127 187]/255; [250 127 0]/255];
- % for jm=1:5
- % % scatter(x(jm), y(jm), 80, Color_sum(jm,:), 'filled', 'MarkerEdgeColor','k', 'LineWidth',1.2)
- % scatter(x(jm), y(jm), 80, Color_sum(jm,:), 'filled', 'MarkerEdgeColor',Color_sum(jm,:), 'LineWidth',1.2)
- % end
- %
- % % scatter(x, y, 80, 'b', 'filled', 'MarkerEdgeColor','k', 'LineWidth',1.2)
- %
- % % for k = 1:n
- % % text(x(k), y(k)+0.05, sprintf('%d',k), ...
- % % 'HorizontalAlignment','center','FontSize',11);
- % % end
- % colormap(cmap); caxis([-1 1])
- % cb = colorbar('southoutside');
- % cb.Label.String = '2(ROC_{area}-0.5)';
- % title('Category distinction coded by 2(AUC-0.5)');
- %
- %
- %%
- n = 5;
- a = 0.9;
- b = 0.83;
- ccm=20;
- theta = linspace(-pi/2 + pi/ccm, pi/2 - pi/ccm, n);
- x = a*cos(theta);
- y = b*sin(theta);
- x=x(end:-1:1);
- % -----------------------------------------------------------------
- addpath cmocean
- cmap = bluewhitered(256);
- nCol = size(cmap,1);
- idxFun = @(v) round(((max(-1,min(1,v))+1)/2)*(nCol-1))+1;
- % ------------------------------------------------------------------
- figure('Color','w');
- % subplot(1,2,2)
- % clf;
- hold on;
- axis equal off
- % axis equal
- % axis off
- for i = 1:n
- for j = i+1:n
- c = cmap( idxFun(-Dec_AAA(i,j)), : );
- plot([x(i) x(j)], [y(i) y(j)], 'Color', c, 'LineWidth', 2);
- pause(0.1)
- end
- end
- Color_sum=[[220 18 20]/255; [173 76 167]/255; [0 177 63]/255; [0 127 187]/255; [250 127 0]/255];
- for jm=1:5
- % scatter(x(jm), y(jm), 80, Color_sum(jm,:), 'filled', 'MarkerEdgeColor','k', 'LineWidth',1.2)
- scatter(x(jm), y(jm), 80, Color_sum(jm,:), 'filled', 'MarkerEdgeColor',Color_sum(jm,:), 'LineWidth',1.2)
- pause(0.1)
- end
- % scatter(x, y, 80, 'b', 'filled', 'MarkerEdgeColor','k', 'LineWidth',1.2)
- % for k = 1:n
- % text(x(k), y(k)+0.05, sprintf('%d',k), ...
- % 'HorizontalAlignment','center','FontSize',11);
- % end
- ax = subplot(1,1,1);
- colormap(ax,cmap); caxis(ax,[-1 1])
- cb = colorbar(ax,'southoutside');
- cb.Label.String = '2(ROC_{area}-0.5)';
- % title('Category distinction coded by 2(AUC-0.5)');
- %%
- theta = linspace(-pi/2 + pi/ccm, pi/2 - pi/ccm, n); % cos(theta) >= 0
- x = -a*cos(theta);
- y = -b*sin(theta);
- % subplot(1,2,1)
- % clf;
- hold on;
- % axis equal off
- % axis equal
- % axis off
- for i = 1:n
- for j = i+1:n
- % if dist(i,j)>0.15
- c = cmap( idxFun(Inc_AAA(i,j)), : );
- plot([x(i) x(j)], [y(i) y(j)], 'Color', c, 'LineWidth', 2);
- pause(0.1)
- % end
- end
- end
- Color_sum=[[220 18 20]/255; [173 76 167]/255; [0 177 63]/255; [0 127 187]/255; [250 127 0]/255];
- for jm=1:5
- % scatter(x(jm), y(jm), 80, Color_sum(jm,:), 'filled', 'MarkerEdgeColor','k', 'LineWidth',1.2)
- scatter(x(jm), y(jm), 80, Color_sum(jm,:), 'filled', 'MarkerEdgeColor',Color_sum(jm,:), 'LineWidth',1.2)
- pause(0.1)
- end
- % scatter(x, y, 80, 'b', 'filled', 'MarkerEdgeColor','k', 'LineWidth',1.2)
- % for k = 1:n
- % text(x(k), y(k)+0.05, sprintf('%d',k), ...
- % 'HorizontalAlignment','center','FontSize',11);
- % end
- % colormap(cmap); caxis([-1 1])
- % cb = colorbar('southoutside');
- colormap(ax,cmap); caxis(ax,[-1 1])
- cb = colorbar(ax,'southoutside');
- cb.Label.String = '2(ROC_{area}-0.5)';
- % title('Category distinction coded by 2(AUC-0.5)');
- % if ispc
- % fontCN = 'Microsoft YaHei';
- % elseif ismac
- % fontCN = 'PingFang SC';
- % else
- % fontCN = 'SimHei';
- % end
- %
- %
- % load('cmapL.mat')
- %
- %
- % Reds = cmapL(6:end,:)
- %
- % Blues = cmapL(4:-1:1,:)
- % % Reds = [254 229 217;
- % % 252 174 145;
- % % 251 106 74;
- % % 203 24 29] / 255;
- % % Blues = [222 235 247;
- % % 158 202 225;
- % % 66 146 198;
- % % 8 81 156] / 255;
- %
- % figure('Color','w','Units','centimeters','Position',[2 2 14 8]);
- %
- % % ax = axes('Position',[0.06 0.12 0.90 0.80]);
- % ax = subplot(1,1,1);
- % hold(ax,'on');
- % xlim([0 5]); ylim([0 3]);
- % axis ij;
- % axis equal;
- % % axis off;
- %
- % % for r = 0:2
- % % for c = 0:4
- % % rectangle('Position',[c r 1 1], 'EdgeColor',[0 0 0], ...
- % % 'LineWidth',0.8, 'FaceColor','none');
- % % end
- % % end
- % % rectangle('Position',[0 0 5 3], 'EdgeColor','k', 'LineWidth',1.0, 'FaceColor','none');
- %
- %
- % text(0+0.08, 0+0.5, 'Large-preferring neurons', 'FontSize',12, ...
- % 'HorizontalAlignment','left','VerticalAlignment','middle');
- %
- %
- %
- %
- % text(0+0.08, 1+0.5, 'Small-preferring neurons', 'FontSize',12, ...
- % 'HorizontalAlignment','left','VerticalAlignment','middle');
- % text(0+0.08, 2+0.5, 'Numerical distance', 'FontSize',12, ...
- % 'HorizontalAlignment','left','VerticalAlignment','middle');
- %
- %
- % for k = 1:4
- % rectangle('Position',[k+0.2 0.2 0.6 0.6], 'FaceColor',Reds(k,:), ...
- % 'EdgeColor','k', 'LineWidth',0.6);
- % end
- %
- % for k = 1:4
- % rectangle('Position',[k+0.2 1+0.2 0.6 0.6], 'FaceColor',Blues(k,:), ...
- % 'EdgeColor','k', 'LineWidth',0.6);
- % end
- %
- % for k = 1:4
- %
- % text(k+0.5, 2+0.5, num2str(k), 'HorizontalAlignment','center', ...
- % 'VerticalAlignment','middle', 'FontSize',12, 'FontName','Arial');
- % end
DA_sAUROC_3D_UDs_lin_log_CV.m at commit ae87aa6, no license · at the source
Overview
- School of Electrical and Information Engineering, Zhengzhou University, Zhengzhou 450001, China; (P.W.); (Y.P.); (J.Z.); (Q.H.); (J.W.); (X.N.); (S.W.)
- Henan Key Laboratory of Brain Science and Brain-Computer Interface Technology, Zhengzhou University, Zhengzhou 450001, China
- Department of Automation, Tsinghua University, Beijing 100084, China
Abstract
Numerosity perception is an evolutionarily conserved ability observed across diverse taxa, from insects and fish to birds and primates. Unlike traditional visual categories, numerosity possesses an intrinsic metric structure, making it well suited for quantitatively investigating how categorical representations emerge along the visual hierarchy. While numerical representations are well characterized in high-level associative areas of non-human primates and avian species, neuronal processing of numerosity in upstream regions remains largely unexplored. To address this gap, we recorded single-unit activity in the pigeon entopallium during a delayed match-to-numerosity task. We found a subset of neurons that encoded numerosity independently of the non-numerical feature controlled in the corresponding recording session, exhibiting quasi-monotonic increasing (QMI) or decreasing (QMD) response profiles. Compared with QMI neurons, QMD neurons exhibited a markedly later coding window and stronger category discriminability. Moreover, in both neuronal populations, the normalized response functions and category discriminability were better described by compressed numerosity scales than by a linear scale, with the logarithmic scale showing a modest overall advantage. These findings help refine current theoretical frameworks for how numerosity information is extracted and represented along the avian visual processing hierarchy, providing a comparative basis for cross-species research.
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 1 match between paragraphs and lines of code.
BrainSystemsLab/Data_and_Code_for_ENTO
ae87aa6c9a2418260ddaa7e46872f3d909a39a8a, 11 August 2026Availability: 1 check, the latest on 27 September 2026: the link answers
- 27 September 2026: the link answers
11 files
- DA_sAUROC_3D_UDs_lin_log
_CV.m , MATLAB, 516 lines, 1 match - Discriminability_compari
son_PEV.m , MATLAB, 545 lines - QMI_QMD_normalized_respo
nse_p_value.m , MATLAB, 179 lines - Spike_density_function_a
novan_sAUROC.m , MATLAB, 250 lines - coolwarm_mpl.m, MATLAB, 10 lines
- hex2rgb.m, MATLAB, 19 lines
- lin_metrics.m, MATLAB, 26 lines
- plot_fit_linearity.m, MATLAB, 20 lines
- stdshade_W.m, MATLAB, 68 lines
- triBar3_signed.m, MATLAB, 130 lines
- README.md, Text, 9 lines
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;
- 10 scripts, each with its path and the digest of its content;
- 1 match 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
No dataset and no data link were found in the paper.
Data Availability Statement
The data and analysis code supporting this study are available in the following GitHub repository: https://
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, 27 September 2026: the first record
Recorded: type, language, journal, volume, issue, pages, dates, 9 authors, 6 keywords, 3 funders, 64 references.
Cite
This paper
Wu, P., Peng, Y., Zhu, J., He, Q., Wang, J., Niu, X., Wang, S., Wang, Z., & Shi, L. (2026). Categorical Representation of Numerosity in the Pigeon Entopallium: Coding Format and Temporal Dynamics. Animals : an open access journal from MDPI, 16(16), 2494. https://
BibTeX
@article{wu2026categoric
author = {Wu, Peng and Peng, Yanyan and Zhu, Juncai and He, Qingzhi and Wang, Jiangtao and Niu, Xiaoke and Wang, Songwei and Wang, Zhizhong and Shi, Li},
title = {{Categorical Representation of Numerosity in the Pigeon Entopallium: Coding Format and Temporal Dynamics}},
journal = {Animals : an open access journal from MDPI},
year = {2026},
month = aug,
volume = {16},
number = {16},
pages = {2494},
publisher = {Multidisciplinary Digital Publishing Institute (MDPI)},
issn = {2076-2615},
doi = {10.3390/
url = {https://
pmid = {42651898},
pmcid = {PMC13508866}
}
RIS
TY - JOUR
AU - Wu, Peng
AU - Peng, Yanyan
AU - Zhu, Juncai
AU - He, Qingzhi
AU - Wang, Jiangtao
AU - Niu, Xiaoke
AU - Wang, Songwei
AU - Wang, Zhizhong
AU - Shi, Li
TI - Categorical Representation of Numerosity in the Pigeon Entopallium: Coding Format and Temporal Dynamics
T2 - Animals : an open access journal from MDPI
J2 - Animals (Basel)
PY - 2026
DA - 2026/
VL - 16
IS - 16
SP - 2494
SN - 2076-2615
PB - Multidisciplinary Digital Publishing Institute (MDPI)
DO - 10.3390/
UR - https://
LA - en
ER -
CSL-JSON
{
"id": "10.3390/
"type": "article-journal",
"title": "Categorical Representation of Numerosity in the Pigeon Entopallium: Coding Format and Temporal Dynamics",
"container-title": "Animals : an open access journal from MDPI",
"author": [
{
"family": "Wu",
"given": "Peng"
},
{
"family": "Peng",
"given": "Yanyan"
},
{
"family": "Zhu",
"given": "Juncai"
},
{
"family": "He",
"given": "Qingzhi"
},
{
"family": "Wang",
"given": "Jiangtao"
},
{
"family": "Niu",
"given": "Xiaoke"
},
{
"family": "Wang",
"given": "Songwei"
},
{
"family": "Wang",
"given": "Zhizhong"
},
{
"family": "Shi",
"given": "Li"
}
],
"container-title-short":
"volume": "16",
"issue": "16",
"page": "2494",
"DOI": "10.3390/
"PMID": "42651898",
"PMCID": "PMC13508866",
"ISSN": "2076-2615",
"publisher": "Multidisciplinary Digital Publishing Institute (MDPI)",
"URL": "https://
"language": "en",
"issued": {
"date-parts": [
[
2026,
8,
11
]
]
}
}
The tracing map gets a citation of its own once an author has validated it and it has a DOI.
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