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Stabilizing fractional dynamical networks suppresses epileptic seizures.

Code ↔ Paper

2 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 2 matches
  1. [1] § Methods › Model estimation ↔ fos_model_and_ctrl/functions.py, lines 83–98 · score 0.58 · Haar wavelet transform, log, variance, fractional, Model
  2. [2] § Results › Control stabilizes most seizures with failures linked to ill-conditioned optimization ↔ analysis_and_plots/control.ipynb, lines 265–352 · score 0.57 · amplitude reduction, signal amplitude, boundary, SOZ, electrodes, seizure

Paper

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The authors' code

Python · 338 lines · 13 KB · MIT · 1 match

  1. import scipy
  2. import numpy as np
  3. from scipy.special import gamma
  4. import scipy.linalg as LA
  5. import scipy.sparse as spSparse
  6. import scipy.sparse.linalg as sLA
  7. import math
  8. import time
  10. # Code from Gaurav Gupta (https://github.com/gaurav71531/UUknowns/blob/master/fracModel.py)
  11. # Gupta, G. et al. Dealing with unknown unknowns: Identification and selection of minimal sensing for fractional dynamics with unknown inputs.
  12. #
  13. class HaarWaveletTransform(object):
  14. def __init__(self, X):
  15. self._N = np.shape(X)
  16. self.X = np.array(X)
  17. # try:
  18. # if np.size(self._N)==1:
  19. # self._N = self._N[0]
  20. # elif np.size(self._N)>1:
  21. # if self._N[0] == 1 or self._N[1]==1:
  22. # self.X = np.squeeze(X)
  23. # self._N = np.size(self.X)
  24. # else:
  25. # raise Exception('dimErr')
  26. # except Exception as err:
  27. # errStatus = err.args[0]
  28. # if errStatus == 'dimErr':
  29. # print('Only single dimensional arrays are acceptable')
  30. self._N = self._N[0]
  32. def normalize(self):
  33. mean = np.mean(self.X)
  34. self.X -= mean
  36. def _dwthaar(self, Signal):
  37. NUse = int(np.floor(np.size(Signal)/2))
  38. C = (Signal[:2*NUse:2] + Signal[1:2*NUse:2])/2
  39. S = Signal[:2*NUse:2] - C
  41. C = 2 * C / np.sqrt(2)
  42. S = -2 * S / np.sqrt(2)
  43. return C, S
  45. def transform(self):
  46. Nby2 = int(np.floor(self._N/2))
  47. W = np.zeros((Nby2,Nby2))
  48. D = np.zeros((Nby2,Nby2))
  49. j = self._N
  50. Signal = self.X
  51. for i in range(int(np.floor(np.log2(self._N)))):
  52. j = int(np.floor(j/2))
  53. w, d = self._dwthaar(Signal) # w = C, d = S
  54. W[i,:j] = w
  55. D[i,:j] = d
  56. Signal = w
  57. return W, D
  60. class fracOrdUU(object):
  61. def __init__(self, numInp=[], numFract = 20, niter = 1, B = [], lambdaUse=0.5, verbose=0):
  62. self.verbose=verbose
  63. self._order = []
  64. self._numCh = []
  65. self._K = []
  66. self._numInp = numInp
  67. self._numFract = numFract
  68. self._lambdaUse = lambdaUse
  69. self._niter = niter
  70. self._BMat = B
  71. self._zVec = []
  72. self._AMat = []
  73. self._u = []
  74. self._performSparseComputation = False
  75. self._preComputedVars = []
  77. # if np.size(B)>0:
  78. # if numInp > 0:
  79. # if numInp != np.shape(B)[1] :
  80. # print('size of B should be consistent with the number of unknown inputs')
  83. def _getFractionalOrder(self, x):
  84. numScales = int(np.floor(np.log2(self._K)))
  85. log_wavelet_scales = np.zeros((numScales,))
  86. scale = np.arange(1,numScales+1)
  88. Wt = HaarWaveletTransform(x)
  89. Wt.normalize()
  90. _, W = Wt.transform()
  91. j = int(np.floor(self._K/2))
  92. for i in range(numScales-1):
  93. y = W[i,:j]
  94. variance = np.var(y, ddof=1) # for unbiased estimate
  95. log_wavelet_scales[i] = np.log2(variance + 1e-10)
  96. j = int(np.floor(j/2))
  97. p = np.polyfit(scale[:numScales-1], log_wavelet_scales[:numScales-1], 1)
  98. return p[0]/2
  100. def _estimateOrder(self, X):
  101. self._order = np.empty((self._numCh,))
  103. for i in range(self._numCh):
  104. self._order[i] = self._getFractionalOrder(X[i,:])
  106. def _updateZVec(self, X):
  107. self._zVec = np.empty((self._numCh, self._K))
  108. j = np.arange(0,self._numFract+1)
  109. for i in range(self._numCh):
  110. preFactVec = gamma(-self._order[i]+j)/gamma(-self._order[i]) / gamma(j+1)
  111. y = np.convolve(X[i,:], preFactVec)
  112. self._zVec[i,:] = y[:self._K]
  114. def _setHeuristicBMat(self, A):
  115. B = np.zeros((self._numCh, self._numCh))
  116. B[np.abs(A)>0.01] = A[np.abs(A)>0.01]
  117. _, r = LA.qr(B)
  118. colInd = np.where(np.abs(np.diag(r))>1e-7)
  119. if np.size(colInd[0])<self._numInp:
  120. self._BMat = np.vstack((np.eye(self._numInp),
  121. np.zeros((self._numCh-self._numInp, self._numInp))))
  122. else:
  123. colInd = colInd[0][:self._numInp]
  124. self._BMat = B[:,colInd]
  125. print(self._BMat)
  126. if np.linalg.matrix_rank(B) < self._numInp:
  127. raise Exception('rank deficient B')
  129. def _performLeastSq(self, Y, X):
  130. # X and Y are shape of (K,numCh)
  131. # A = [a1, a2,...,an]
  132. # Y = X*A.T + E
  133. # ai = Sigma_X^-1 * E[Xyi.T]
  134. XUse = np.vstack((np.zeros((1,self._numCh)), X[:-1,:]))
  135. A = np.matmul(np.matmul(Y.T, XUse), LA.inv(np.matmul(XUse.T, XUse)))
  136. mse = LA.norm(Y - np.matmul(XUse, A.T),axis=0)**2 / self._K
  137. return A, np.mean(mse)
  139. def _factor(self, A, rho):
  140. m, n = np.shape(A)
  141. if self._performSparseComputation:
  142. if m >= n:
  143. L = LA.cholesky(np.matmul(A.T, A) + rho*spSparse.eye(n), lower=True)
  144. else:
  145. L = LA.cholesky(spSparse.eye(m) + 1/rho * np.matmul(A, A.T), lower=True)
  147. L = spSparse.csc_matrix(L)
  148. U = spSparse.csc_matrix(L.T)
  149. else:
  150. if m >= n:
  151. L = LA.cholesky(np.matmul(A.T, A) + rho*np.eye(n), lower=True)
  152. else:
  153. L = LA.cholesky(np.eye(m) + 1/rho * np.matmul(A, A.T), lower=True)
  154. U = L.T
  155. return L, U
  157. def _shrinkage(self, x, kappa):
  158. return np.maximum(0, x-kappa) - np.maximum(0, -x - kappa)
  160. def _objective(self, A, b, lambdaUse, x, z):
  161. return 0.5 * np.sum((np.matmul(A, x)-b)**2) + lambdaUse*LA.norm(z,ord=1)
  163. class _history(object):
  164. def __init__(self, N):
  165. self._objval = np.empty((N,))
  166. self._r_norm = np.empty((N,))
  167. self._s_norm = np.empty((N,))
  168. self._eps_pri = np.empty((N,))
  169. self._eps_dual = np.empty((N,))
  172. class _preComputedVars_(object):
  173. def __init__(self):
  174. self._lasso_L = []
  175. self._lasso_U = []
  176. self._lasso_LInv = []
  177. self._lasso_UInv = []
  179. def _updateLassoLUMat(self, A, rho):
  180. self._lasso_L, self._lasso_U = fracOrdUU()._factor(A, rho)
  181. self._lasso_LInv = LA.inv(self._lasso_L)
  182. self._lasso_UInv = LA.inv(self._lasso_U)
  185. def _getLassoSoln(self, b, lambdaUse):
  187. # code borrowed from
  188. # https://web.stanford.edu/~boyd/papers/admm/lasso/lasso.html
  189. A = self._BMat
  190. b = np.reshape(b, (np.size(b),1))
  191. MAX_ITER = 100
  192. ABSTOL = 1e-4
  193. RELTOL = 1e-2
  195. m, n = np.shape(A)
  196. Atb = np.matmul(A.T, b)
  197. rho = 1/lambdaUse
  198. alpha = 1
  200. z = np.zeros((n,1))
  201. u = np.zeros((n,1))
  202. L, U = self._factor(A, rho)
  203. LInv = self._preComputedVars._lasso_LInv
  204. UInv = self._preComputedVars._lasso_UInv
  206. history = self._history(MAX_ITER)
  207. for k in range(MAX_ITER):
  208. # x-update
  209. q = Atb + rho * (z-u)
  210. if self._performSparseComputation:
  211. if m >= n: # is skinny
  212. x = sLA.inv(U) * (sLA.inv(L) * q)
  213. else: # if fat
  214. x = q/rho - np.matmul(A.T, sLA.inv(U) *
  215. (sLA.inv(L) * np.matmul(A, q)))/rho**2
  216. else:
  217. if m >= n: # is skinny
  218. x = np.matmul(UInv, np.matmul(LInv, q))
  219. # x = LA.solve(U, LA.solve(L, q))
  220. else: # if fat
  221. x = q/rho - np.matmul(A.T, np.matmul(LA.inv(U),
  222. np.matmul(LA.inv(L), np.matmul(A, q))))/rho**2
  224. zold = np.array(z)
  225. x_hat = alpha*x + (1-alpha)*zold
  226. z = self._shrinkage(x_hat + u, lambdaUse/rho)
  228. # u-update
  229. u += x_hat - z
  231. history._objval[k] = self._objective(A, b, lambdaUse, x, z)
  232. history._r_norm[k] = LA.norm(x-z)
  233. history._s_norm[k] = LA.norm(-rho*(z-zold))
  234. history._eps_pri[k] = (np.sqrt(n)*ABSTOL
  235. + RELTOL*np.max((LA.norm(x), LA.norm(-z))))
  236. history._eps_dual[k] = np.sqrt(n)*ABSTOL + RELTOL*LA.norm(rho*u)
  238. if (history._r_norm[k] < history._eps_pri[k] and
  239. history._s_norm[k] < history._eps_dual[k]):
  240. break
  241. return np.squeeze(z)
  243. def fit(self, X):
  244. # X must be data in the shape of (sensors, time)
  245. X = np.array(X,dtype='float')
  246. self._numCh, self._K = np.shape(X)
  247. if np.size(self._numInp) == 0:
  248. self._numInp = int(np.floor(self._numCh/2))
  249. self._AMat = np.empty((self._niter+1, self._numCh, self._numCh))
  250. self._u = np.zeros((self._numInp,self._K))
  251. # try:
  252. # if self._numCh == 1:
  253. # raise Exception('oneSensor')
  254. # if self._K < self._numCh:
  255. # raise Exception('lessData')
  256. # if np.size(self._BMat)>0:
  257. # if np.shape(self._BMat) != (self._numCh, self._numInp):
  258. # raise Exception('BMatDim')
  260. self._estimateOrder(X)
  261. self._updateZVec(X)
  262. self._AMat[0,:,:], mse = self._performLeastSq(self._zVec.T, X.T)
  264. if np.size(self._BMat) == 0:
  265. self._setHeuristicBMat(self._AMat[0,:,:])
  267. # initiate precomputed variables process,
  268. # compute all variable need to be computed exactly, again and again.
  269. self._preComputedVars = self._preComputedVars_()
  270. self._preComputedVars._updateLassoLUMat(self._BMat, 1/self._lambdaUse)
  272. #t0 = time.time()
  273. mseIter = np.empty((self._niter+1,))
  274. mseIter[0] = mse
  275. for iterInd in range(self._niter):
  276. for kInd in range(1,self._K):
  277. yUse = self._zVec[:,kInd] - np.matmul(self._AMat[iterInd,:,:], X[:,kInd-1])
  278. self._u[:,kInd] = self._getLassoSoln(yUse, self._lambdaUse)
  279. # clf = linear_model.Lasso(alpha=self._lambdaUse)
  280. # clf.fit(self._BMat * np.sqrt(self._numCh), yUse* np.sqrt(self._numCh))
  281. # self._u[:,kInd] = clf.coef_
  283. self._AMat[iterInd+1,:,:],mseIter[iterInd+1] = self._performLeastSq(
  284. (self._zVec - np.matmul(self._BMat, self._u)).T, X.T)
  285. return mseIter
  286. #print('time taken = %f'%(time.time()-t0))
  288. # except Exception as err:
  289. # errStatus = err.args[0]
  290. # if errStatus == 'oneSensor': #problemo
  291. # print('The number of sensors must be > 1, retry...')
  292. # elif errStatus == 'lessData':
  293. # print('The number of data points are less than number of sensors, retry...')
  294. # elif errStatus == 'BMatDim':
  295. # print('size of B should be consistent with the number of channels and number of inputs')
  296. # else:
  297. # print('some different error')
  299. def adjust_fontsize(num_subplots, max_fontsize=12):
  300. """Adjust fontsize based on the number of subplots."""
  301. # Determine base fontsize based on the total number of subplots
  302. return max(6, max_fontsize - (num_subplots // 10))
  304. def reconstruct_FOS(alpha, A, X, num_chns, sampling_rate, window_length):
  306. infit = 5 # the maximum number of states in the past should be considered
  307. numStep = 1 # number of steps ahead
  308. p = 1 # number of past states
  309. TSteps = sampling_rate*window_length
  311. xPred = np.zeros((num_chns, TSteps*numStep))
  312. xPred[:, 0:numStep] = X[:, 0:numStep]
  315. for i in range(1,TSteps):
  316. XTemp = np.zeros((num_chns, TSteps*numStep))
  317. XTemp[:, 0:i*numStep] = X[:, 0:i*numStep]
  319. for stepInd in range(numStep):
  320. for chInd in range(num_chns):
  321. alpha_inst = alpha[chInd]
  322. #check whether alpha is fractional
  323. if math.ceil(alpha_inst) != alpha_inst:
  324. trailLen = np.min(np.array([infit, i*numStep + stepInd - 1]))
  325. j = np.arange(1, trailLen + 1)
  326. preFact = scipy.special.gamma(-alpha_inst + j) / (scipy.special.gamma(-alpha_inst) * scipy.special.gamma(j + 1))
  327. XTemp[chInd, i* numStep + stepInd] = XTemp[chInd, i*numStep + stepInd] - np.sum(XTemp[chInd, i*numStep + stepInd - j] * preFact)
  328. XUse = np.zeros((num_chns,p))
  329. for pInd in range(p):
  330. if i*numStep + stepInd - pInd < 1:
  331. break
  332. XUse[:, pInd] = XTemp[:, i*numStep + stepInd - pInd]
  334. XTemp[:, i*numStep + stepInd] = XTemp[:, i*numStep + stepInd] + np.dot(np.squeeze(A), XUse[:, pInd])
  335. # if (i == 512 or i == 720):
  336. # print("second:", XTemp)
  337. xPred[:, (i)*numStep:(i+1)*numStep] = XTemp[:, (i)*numStep:(i+1)*numStep]
  338. return xPred

functions.py at commit 73cfda0, under MIT · at the source

Overview

Authors: Yaoyue Wang1, Arian Ashourvan2, Guilherme Ramos3, Emily A Pereira4
ORCID iDs: Guilherme Ramos, Emily A Pereira
  1. Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA USA
  2. Department of Psychology, University of Kansas, Lawrence, KS USA
  3. Department of Computer Science and Engineering, Instituto Superior Técnico, University of Lisbon and Instituto de Telecomunicações, Lisbon, Portugal
  4. Department of Electrical and Computer Engineering, Texas Tech University, Lubbock, TX 79409 USA
Institutions: University of Southern California (United States); University of Kansas (United States); University of Lisbon (Portugal); Instituto de Telecomunicações (Portugal); Instituto Superior Técnico (Portugal); Texas Tech University (United States)
Journal: Scientific reports, volume 16, issue 1, article 16037
Dates: received 16 December 2025; accepted 2 March 2026; published online 25 May 2026
Type: Research article · Language: English
License: CC BY-NC-ND
Identifiers: DOI 10.1038/s41598-026-43151-1 · PMID 42178319 · PMCID PMC13199506 · OpenAlex W4417272888
Open access: gold, a free copy (OpenAlex)
Preprint: arxiv:2511.20950
Status: code verified
Categories: EEG (modality), intracranial EEG (iEEG / ECoG / SEEG) (modality), human (organism), epilepsy (population)
Methods: Statistics, Connectivity, Spectral & time-frequency
Keywords: Epilepsy, Fractional-order systems, Seizure control, Intracranial EEG, Network dynamics, Diseases, Neurology, Neuroscience
MeSH: Epilepsy*, Seizures*, Brain, Electroencephalography, Humans, Nerve Net (* major topic)
Topic: Functional Brain Connectivity Studies (Cognitive Neuroscience, Neuroscience), according to OpenAlex
Funding: Texas Tech University
Citations: cited by 1 paper (Europe PMC); 76 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 2 matches between paragraphs and lines of code.

Yaoyuewang/fractional-control-epilepsy

License: MIT
State: the link answers, verified on 28 September 2026
Evidence: files inventoried
Commit: 73cfda05a74adbc81fd468418fc46ca2aa64bb82, 4 April 2026
Languages: Python (6), Jupyter (5)
Size: 15 files, 11 scripts
Software Heritage: not archived
Found in: “Code availability”
Holds: README, license file, 5 notebooks
Not found: CITATION.cff, environment file, tests, continuous integration, documentation
Tools: NumPy (11 files), SciPy (10 files), Matplotlib (7 files), pandas (5 files), scikit-learn (2 files), seaborn (2 files), statsmodels (1 file)
Availability: 1 check, the latest on 28 September 2026: the link answers
  • 28 September 2026: the link answers
13 files
At the source: github.com/Yaoyuewang/fractional-control-epilepsy

Code availability statement

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

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  • 11 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);
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Its JSON (tracing-map.json) is deposited on Zenodo with its DOI once the map is validated.

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Version 1, 28 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 4 authors, 8 keywords, 6 MeSH terms, 1 funder, 33 references.

Cite

This paper

Wang, Y., Ashourvan, A., Ramos, G., & Pereira, E. A. (2026). Stabilizing fractional dynamical networks suppresses epileptic seizures. Scientific reports, 16(1), 16037. https://doi.org/10.1038/s41598-026-43151-1

BibTeX

@article{wang2026stabilizing,
author = {Wang, Yaoyue and Ashourvan, Arian and Ramos, Guilherme and Pereira, Emily A},
title = {{Stabilizing fractional dynamical networks suppresses epileptic seizures}},
journal = {Scientific reports},
year = {2026},
month = may,
volume = {16},
number = {1},
pages = {16037},
publisher = {Nature Publishing Group},
issn = {2045-2322},
doi = {10.1038/s41598-026-43151-1},
url = {https://doi.org/10.1038/s41598-026-43151-1},
pmid = {42178319},
pmcid = {PMC13199506}
}

RIS

TY - JOUR
AU - Wang, Yaoyue
AU - Ashourvan, Arian
AU - Ramos, Guilherme
AU - Pereira, Emily A
TI - Stabilizing fractional dynamical networks suppresses epileptic seizures
T2 - Scientific reports
J2 - Sci Rep
PY - 2026
DA - 2026/05/25
VL - 16
IS - 1
SP - 16037
SN - 2045-2322
PB - Nature Publishing Group
DO - 10.1038/s41598-026-43151-1
UR - https://doi.org/10.1038/s41598-026-43151-1
LA - en
ER -

CSL-JSON

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"title": "Stabilizing fractional dynamical networks suppresses epileptic seizures",
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}
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