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Cortical representation of multidimensional handwriting movement and implications for neuroprostheses.

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4 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 4 matches
  1. [1] § Results › Neural encoding of multidimensional handwriting movements ↔ full model-Fig4F-S8.py, lines 136–213 · score 0.60 · axis velocity, full model, firing rates, Vz, LNP, EMG
  2. [2] § Methods › Neural encoding: model-based encoding and evaluation ↔ bits_per_spike-Fig4.py, lines 35–66 · score 0.60 · mutual information, bits, firing rate, MI, metric, spike
  3. [3] § Results › Neural encoding of multidimensional handwriting movements ↔ encoding model-Fig4d-S7.py, lines 67–129 · score 0.56 · encoding model, grip force, firing rates, S7, Vxy, EMG
  4. [4] § Methods › Neural encoding: model-based encoding and evaluation ↔ full model-Fig4F-S8.py, lines 136–213 · score 0.54 · full model, axis velocity, EMG, pressure, variables, encoding

Paper

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The authors' code

Python · 213 lines · 11 KB · GPL-3.0 · 2 matches

  1. import time
  2. from scipy.io import loadmat
  3. import numpy as np
  4. from torch.utils.data import DataLoader, TensorDataset
  5. import math
  6. import scipy.io as io
  7. from scipy.interpolate import interp1d
  8. import torch
  9. from sklearn import preprocessing
  11. def find_samesegments(arr):
  12. segments = []
  13. n = len(arr)
  14. if n == 0:
  15. return segments
  16. start_idx = 0
  17. for i in range(1, n):
  18. if arr[i] != arr[start_idx]:
  19. segments.append((start_idx, i - 1))
  20. start_idx = i
  21. segments.append((start_idx, n - 1))
  23. return segments
  25. def cal_spike_counts(predict):
  26. lambdas = predict.detach().cpu().numpy()
  27. spike_count = np.empty_like(lambdas)
  28. for i, lmbda_val in enumerate(lambdas):
  29. if np.isnan(lmbda_val):
  30. spike_count[i] = np.nan
  31. else:
  32. spike_count[i] = np.random.poisson(lmbda_val)
  33. spike_count = torch.tensor(spike_count, dtype=torch.float).to('cuda')
  35. return spike_count
  37. def fit_lnp(variables, spikes,num_epochs):
  38. dataset = TensorDataset(variables, spikes)
  39. batch_size = 256
  40. dataloader = DataLoader(dataset, batch_size=batch_size, shuffle=True)
  41. # Use a random vector of weights to start (mean 0, sd .1)
  42. w = torch.normal(0, 0.1, (1,14)).to('cuda').requires_grad_(True)
  43. optimizer = torch.optim.SGD([w], lr=1e-3)
  44. scheduler = torch.optim.lr_scheduler.StepLR(optimizer, step_size=30, gamma=0.1)
  45. for epoch in range(num_epochs):
  46. start = time.time()
  47. total_log_lik = 0
  48. for X, y in dataloader:
  49. rate = torch.exp(torch.sum(X * w[0,0:13],dim=1) + w[0,-1]).float()
  50. # Compute the Poisson log likelihood
  51. log_lik = -(torch.unsqueeze(y, 0) @ torch.log(rate) - rate.sum())
  52. optimizer.zero_grad()
  53. log_lik.backward()
  54. optimizer.step()
  55. total_log_lik += log_lik.item()
  56. scheduler.step()
  58. avg_loss = total_log_lik / len(dataloader)
  59. end = time.time()
  60. print(f"Epoch {epoch + 1}/{num_epochs}, log_lik: {avg_loss:.4f}, time:{end - start:.4f}s")
  61. return w
  63. def predict_fr_lnp(variables, theta=None):
  64. yhat = torch.exp(torch.sum(variables * theta[0,0:13],dim=1) + theta[0,-1])
  65. return yhat
  68. # encoding of an example session
  69. data = loadmat('data0623.mat')
  70. bined_spk = data['bined_spk'] # neural data
  71. break_ind = data['break_ind']
  72. trial_mask = data['trial_mask']
  73. trial_target = data['trial_target']
  74. velocity_xy = data['velocity'][:2,:] # average handwriting data
  75. velocity_z = data['velocity'][2,:]
  76. Fgrip = data['Fgrip']/1000*9.8 # g -> N
  77. Fpres = data['Fpres']/1000*9.8
  79. data = loadmat('0623_s1.mat')
  80. emg = data['emg_data']
  81. # neurons with spike rate<1Hz were removed
  82. firing_rates = bined_spk / 0.2
  83. neuron_ind = np.where(np.mean(firing_rates,1) >= 1)[0]
  84. bined_spk = bined_spk[neuron_ind,:]
  86. num_epochs = 70
  88. stroke_ind = np.where(break_ind[0]>0)
  89. velocity_z[stroke_ind[0]] = 0
  90. # velocity normalization
  91. v_max = np.nanmax(velocity_xy)
  92. v_min = np.nanmin(velocity_xy)
  93. for i in range(velocity_xy.shape[0]):
  94. for j in range(velocity_xy.shape[1]):
  95. velocity_xy[i][j] = (2*(velocity_xy[i][j]-v_min)/(v_max-v_min))-1 #[-1,1]
  97. z_scale = max(np.abs(np.nanmin(velocity_z)),np.abs(np.nanmax(velocity_z)))
  98. velocity_z = velocity_z/z_scale
  99. velocity = torch.tensor(np.vstack([velocity_xy, velocity_z])).to('cuda')
  100. bined_spk = torch.tensor(bined_spk,dtype=torch.float).to('cuda')
  101. # grip force and pressure normalization
  102. min_max_scaler = preprocessing.MinMaxScaler(feature_range=(0, 1))
  103. Fgrip = (min_max_scaler.fit_transform(Fgrip.T)).T
  104. Fpres = (min_max_scaler.fit_transform(Fpres.T)).T
  105. # emg normalization
  106. emg_max = np.max(emg)
  107. emg_min = np.min(emg)
  108. for i in range(emg.shape[0]):
  109. for j in range(emg.shape[1]):
  110. emg[i][j] = (emg[i][j]-emg_min)/(emg_max-emg_min)
  112. handwriting_data = torch.cat((velocity,torch.tensor(Fgrip).to('cuda'),torch.tensor(Fpres).to('cuda'),torch.tensor(emg).to('cuda')),dim=0)
  114. for i_stroke in range(2):
  115. if i_stroke == 0:
  116. ind = np.where(break_ind[0] < 0) # cohesion ind
  117. print('cohesion')
  118. else:
  119. ind = np.where(break_ind[0] > 0) # stroke ind
  120. print('stroke')
  122. lamda_pre = torch.zeros((bined_spk.shape[0], bined_spk.shape[1]), dtype=torch.double).to('cuda')# initialize the predicted firing rates
  123. lamda_pre_delV = torch.zeros((bined_spk.shape[0], bined_spk.shape[1]), dtype=torch.double).to('cuda') # full moodel-Vel
  124. lamda_pre_delVz = torch.zeros((bined_spk.shape[0], bined_spk.shape[1]), dtype=torch.double).to('cuda')# full moodel-Vz
  125. lamda_pre_delg = torch.zeros((bined_spk.shape[0], bined_spk.shape[1]), dtype=torch.double).to('cuda') # full moodel-grip
  126. lamda_pre_delp = torch.zeros((bined_spk.shape[0], bined_spk.shape[1]), dtype=torch.double).to('cuda') # full moodel-pres
  127. lamda_pre_delemg = torch.zeros((bined_spk.shape[0], bined_spk.shape[1]), dtype=torch.double).to('cuda') # full moodel-emg
  129. spk_predict = torch.zeros((bined_spk.shape[0], bined_spk.shape[1]), dtype=torch.float).to('cuda')# initialize the predicted spike
  130. spk_predict_delV = torch.zeros((bined_spk.shape[0], bined_spk.shape[1]), dtype=torch.float).to('cuda') # full moodel-Vel
  131. spk_predict_delVz = torch.zeros((bined_spk.shape[0], bined_spk.shape[1]), dtype=torch.float).to('cuda')# full moodel-Vz
  132. spk_predict_delg = torch.zeros((bined_spk.shape[0], bined_spk.shape[1]), dtype=torch.float).to('cuda') # full moodel-grip
  133. spk_predict_delp = torch.zeros((bined_spk.shape[0], bined_spk.shape[1]), dtype=torch.float).to('cuda') # full moodel-pres
  134. spk_predict_delemg = torch.zeros((bined_spk.shape[0], bined_spk.shape[1]), dtype=torch.float).to('cuda') # full moodel-emg
  136. # encode each neuron in turn
  137. for channel_num in range(bined_spk.shape[0]):
  138. bined_spk_channelnum = bined_spk[channel_num, :] # each neuron
  140. numbers = list(range(1, 31)) # 30 characters in this session
  141. for count in range(10): # 10 fold
  142. print(f'neuron:{channel_num + 1},fold:{count + 1}')
  143. test_numbers = np.array(numbers[:3])
  144. del numbers[:3]
  145. character_ind = np.where(trial_target == test_numbers)[0]
  146. test_indices = np.where(trial_mask[0].reshape(-1, 1) == (character_ind + 1))[0] # character index for test
  147. tr_target_indices = np.setdiff1d(np.arange(len(trial_mask[0])), test_indices) # character index for training
  149. test_indices = np.intersect1d(ind, test_indices) # stroke/cohesion index for test
  150. tr_target_indices = np.intersect1d(ind, tr_target_indices) # stroke/cohesion index for training
  152. tr_idx = []
  153. seg_tr = find_samesegments(break_ind[0, tr_target_indices])
  154. for i_seg in range(len(seg_tr)):
  155. seg_s = bined_spk_channelnum.T[tr_target_indices[seg_tr[i_seg][0]]:tr_target_indices[seg_tr[i_seg][1]] + 1]
  156. if torch.any(seg_s.ne(0)):
  157. tr_idx.append(tr_target_indices[seg_tr[i_seg][0]:seg_tr[i_seg][1] + 1])
  158. tr_idx = np.concatenate(tr_idx)
  160. X_test, y_test = handwriting_data.T[test_indices], bined_spk_channelnum[test_indices] # test data
  161. X_train, y_train = handwriting_data.T[tr_idx], bined_spk_channelnum[tr_idx] # training data
  162. # remove each variable from the full model
  163. X_test_delV = X_test[:, 3:]
  164. X_test_delVz = torch.cat((X_test[:, :2], X_test[:, 3:]), dim=1)
  165. X_test_delg = torch.cat((X_test[:, :3], X_test[:, 4:]), dim=1)
  166. X_test_delp = torch.cat((X_test[:, :4], X_test[:, 5:]), dim=1)
  167. X_test_delemg = X_test[:, :5]
  169. # Fit LNP model
  170. theta_lnp = fit_lnp(X_train, y_train, num_epochs) # full model
  171. theta_lnp_delV = theta_lnp[:, 3:] # remove weights for velocity
  172. theta_lnp_delVz = torch.cat((theta_lnp[:, :2], theta_lnp[:, 3:]), dim=1) # remove weights for z-axis velocity
  173. theta_lnp_delg = torch.cat((theta_lnp[:, :3], theta_lnp[:, 4:]), dim=1) # remove weights for grip
  174. theta_lnp_delp = torch.cat((theta_lnp[:, :4], theta_lnp[:, 5:]), dim=1) # remove weights for pressure
  175. theta_lnp_delemg = torch.cat((theta_lnp[:, :5], theta_lnp[:, 13:]), dim=1) # remove weights for emg
  177. # test
  178. predict = predict_fr_lnp(X_test, theta_lnp) # predicted firing rate
  179. predict_delV = torch.exp(torch.sum(X_test_delV * theta_lnp_delV[0, :-1], dim=1) + theta_lnp_delV[0, -1])
  180. predict_delVz = torch.exp(torch.sum(X_test_delVz * theta_lnp_delVz[0, :-1], dim=1) + theta_lnp_delVz[0, -1])
  181. predict_delg = torch.exp(torch.sum(X_test_delg * theta_lnp_delg[0, :-1], dim=1) + theta_lnp_delg[0, -1])
  182. predict_delp = torch.exp(torch.sum(X_test_delp * theta_lnp_delp[0, :-1], dim=1) + theta_lnp_delp[0, -1])
  183. predict_delemg = torch.exp(torch.sum(X_test_delemg * theta_lnp_delemg[0, :-1], dim=1) + theta_lnp_delemg[0, -1])
  185. lamda_pre[channel_num, test_indices] = predict
  186. lamda_pre_delV[channel_num, test_indices] = predict_delV
  187. lamda_pre_delVz[channel_num, test_indices] = predict_delVz
  188. lamda_pre_delg[channel_num, test_indices] = predict_delg
  189. lamda_pre_delp[channel_num, test_indices] = predict_delp
  190. lamda_pre_delemg[channel_num, test_indices] = predict_delemg
  192. # predicted spike counts
  193. spk_predict[channel_num, test_indices] = cal_spike_counts(predict)
  194. spk_predict_delV[channel_num, test_indices] = cal_spike_counts(predict_delV)
  195. spk_predict_delVz[channel_num, test_indices] = cal_spike_counts(predict_delVz)
  196. spk_predict_delg[channel_num, test_indices] = cal_spike_counts(predict_delg)
  197. spk_predict_delp[channel_num, test_indices] = cal_spike_counts(predict_delp)
  198. spk_predict_delemg[channel_num, test_indices] = cal_spike_counts(predict_delemg)
  199. # save results
  200. if i_stroke == 0:
  201. io.savemat('cohesion/full.mat',{'spk_predict': spk_predict.detach().cpu().numpy(), 'lamda_pre': lamda_pre.detach().cpu().numpy()})
  202. io.savemat('cohesion/delV.mat', {'spk_predict': spk_predict_delV.detach().cpu().numpy(),'lamda_pre': lamda_pre_delV.detach().cpu().numpy()})
  203. io.savemat('cohesion/delVz.mat', {'spk_predict': spk_predict_delVz.detach().cpu().numpy(),'lamda_pre': lamda_pre_delVz.detach().cpu().numpy()})
  204. io.savemat('cohesion/delg.mat', {'spk_predict': spk_predict_delg.detach().cpu().numpy(),'lamda_pre': lamda_pre_delg.detach().cpu().numpy()})
  205. io.savemat('cohesion/delp.mat', {'spk_predict': spk_predict_delp.detach().cpu().numpy(),'lamda_pre': lamda_pre_delp.detach().cpu().numpy()})
  206. io.savemat('cohesion/delemg.mat', {'spk_predict': spk_predict_delemg.detach().cpu().numpy(),'lamda_pre': lamda_pre_delemg.detach().cpu().numpy()})
  207. else:
  208. io.savemat('stroke/full.mat',{'spk_predict': spk_predict.detach().cpu().numpy(), 'lamda_pre': lamda_pre.detach().cpu().numpy()})
  209. io.savemat('stroke/delV.mat', {'spk_predict': spk_predict_delV.detach().cpu().numpy(),'lamda_pre': lamda_pre_delV.detach().cpu().numpy()})
  210. io.savemat('stroke/delVz.mat', {'spk_predict': spk_predict_delVz.detach().cpu().numpy(),'lamda_pre': lamda_pre_delVz.detach().cpu().numpy()})
  211. io.savemat('stroke/delg.mat', {'spk_predict': spk_predict_delg.detach().cpu().numpy(),'lamda_pre': lamda_pre_delg.detach().cpu().numpy()})
  212. io.savemat('stroke/delp.mat', {'spk_predict': spk_predict_delp.detach().cpu().numpy(),'lamda_pre': lamda_pre_delp.detach().cpu().numpy()})
  213. io.savemat('stroke/delemg.mat', {'spk_predict': spk_predict_delemg.detach().cpu().numpy(),'lamda_pre': lamda_pre_delemg.detach().cpu().numpy()})

full model-Fig4F-S8.py at commit 97b0bc6, under GPL-3.0 · at the source

Overview

Authors: Zebin Wang1,2,3, Guangxiang Xu1,2,3, Bowen Yu1,2,3, Kedi Xu3, Junming Zhu4, Gang Pan1,5, Jianmin Zhang4, Yueming Wang2,5, Yaoyao Hao1,2,5
ORCID iDs: Zebin Wang, Gang Pan, Jianmin Zhang, Yueming Wang, Yaoyao Hao
  1. The State Key Lab of Brain-Machine Intelligence, Zhejiang University,Hangzhou, China
  2. Nanhu Brain-Computer Interface Institute, Hangzhou, China
  3. Department of Biomedical Engineering, Zhejiang University,Hangzhou, China
  4. Department of Neurosurgery, Second Affiliated Hospital of Zhejiang University School of Medicine,Hangzhou, China
  5. College of Computer Science and Technology, Zhejiang University,Hangzhou, China
Institutions: Zhejiang University (China); Second Affiliated Hospital of Zhejiang University (China)
Journal: Nature communications, volume 17, issue 1, article 3966
Dates: received 29 January 2025; accepted 24 February 2026; published online 14 March 2026
Type: Research article · Language: English
License: CC BY-NC-ND
Identifiers: DOI 10.1038/s41467-026-70536-7 · PMID 41832195 · PMCID PMC13133357 · OpenAlex W7135420386
Open access: gold, a free copy (OpenAlex)
Status: code verified
Categories: other (modality), human (organism), systems (subfield)
Methods: Spectral & time-frequency, Connectivity, Statistics, Smoothing, state filtering, decompositions, Machine learning, Preprocessing, Single-unit activity, calcium imaging, Physiology & signal measures
Keywords: Motor cortex, Brain-machine interface
MeSH: Brain-Computer Interfaces*, Handwriting*, Motor Cortex*, Neural Prostheses*, Adult, Biomechanical Phenomena, Electromyography, Hand Strength, Humans, Male, Movement (* major topic)
Topic: Writing and Handwriting Education (Education, Social Sciences), according to OpenAlex
Funding: National Natural Science Foundation of China (62336007, STI2030); Zhejiang University (SN-ZJU-SIAS-002); Fundamental Research Funds for the Central Universities (2024ZFJH01-01, 2023ZFJH01-01)
Citations: cited by 1 paper (Europe PMC); 56 references in the paper

Abstract

The abstract is not reproduced here: the paper's license (CC BY-NC-ND) does not allow it. Read it in the paper, at the publisher or on Europe PMC.

Repository

Its files are read in the Code ↔ Paper reader above, with 4 matches between paragraphs and lines of code.

yaoyao-hao/handwriting_codec

License: GPL-3.0
State: the link answers, verified on 30 September 2026
Evidence: files inventoried
Commit: 97b0bc6b3f4f6930986bc4684f7a4e42efd148f8, 3 December 2025
Languages: Python (5)
Size: 8 files, 5 scripts
Software Heritage: not archived
Found in: “Code availability”
Holds: README, license file, environment (requirements.txt)
Not found: CITATION.cff, tests, continuous integration, documentation
Tools: NumPy (5 files), SciPy (5 files), scikit-learn (4 files), PyTorch (3 files)
Availability: 1 check, the latest on 30 September 2026: the link answers
  • 30 September 2026: the link answers
7 files
At the source: github.com/Yaoyao-Hao/Handwriting_codec/releases/tag/release2026

Code availability statement

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Read it in the paper: doi.org/10.1038/s41467-026-70536-7.

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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;
  • 5 scripts, each with its path and the digest of its content;
  • 4 matches between paragraphs of the paper and lines of the code (method lexical-v1);
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Its JSON (tracing-map.json) is deposited on Zenodo with its DOI once the map is validated.

Data

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Data availability statement

The paper has a data availability statement. Its license (CC BY-NC-ND) does not allow reproducing it here; in short, from what the harvester recognized in it:

Read it in the paper: doi.org/10.1038/s41467-026-70536-7.

Versions

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Version 1, 30 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 9 authors, 2 keywords, 11 MeSH terms, 3 funders, 44 references.

Cite

This paper

Wang, Z., Xu, G., Yu, B., Xu, K., Zhu, J., Pan, G., Zhang, J., Wang, Y., & Hao, Y. (2026). Cortical representation of multidimensional handwriting movement and implications for neuroprostheses. Nature communications, 17(1), 3966. https://doi.org/10.1038/s41467-026-70536-7

BibTeX

@article{wang2026cortical,
author = {Wang, Zebin and Xu, Guangxiang and Yu, Bowen and Xu, Kedi and Zhu, Junming and Pan, Gang and Zhang, Jianmin and Wang, Yueming and Hao, Yaoyao},
title = {{Cortical representation of multidimensional handwriting movement and implications for neuroprostheses}},
journal = {Nature communications},
year = {2026},
month = mar,
volume = {17},
number = {1},
pages = {3966},
publisher = {Nature Publishing Group},
issn = {2041-1723},
doi = {10.1038/s41467-026-70536-7},
url = {https://doi.org/10.1038/s41467-026-70536-7},
pmid = {41832195},
pmcid = {PMC13133357}
}

RIS

TY - JOUR
AU - Wang, Zebin
AU - Xu, Guangxiang
AU - Yu, Bowen
AU - Xu, Kedi
AU - Zhu, Junming
AU - Pan, Gang
AU - Zhang, Jianmin
AU - Wang, Yueming
AU - Hao, Yaoyao
TI - Cortical representation of multidimensional handwriting movement and implications for neuroprostheses
T2 - Nature communications
J2 - Nat Commun
PY - 2026
DA - 2026/03/14
VL - 17
IS - 1
SP - 3966
SN - 2041-1723
PB - Nature Publishing Group
DO - 10.1038/s41467-026-70536-7
UR - https://doi.org/10.1038/s41467-026-70536-7
LA - en
ER -

CSL-JSON

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"family": "Wang",
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