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Dorsoventral gradient of theta sweeps in the medial entorhinal cortex.

Code ↔ Paper

9 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 9 matches
  1. [1] § MATERIALS AND METHODS › Computational modeling ↔ ComputationalModellingFig4/network_models.py, lines 248–268 · score 0.63 · offset length, phase offset, firing rate, conjunctive, GC, connectivity
  2. [2] § MATERIALS AND METHODS › Computational modeling ↔ ComputationalModellingFig4/Fig4_thetasweeps.ipynb, lines 510–623 · score 0.61 · phase offset, theta modulation, internal direction, theta phases, sensory, GC
  3. [3] § RESULTS › Efficient learning of hippocampal spatial maps via theta sweeps with varied angles ↔ ComputationalModellingFig4/network_models.py, lines 21–139 · score 0.60 · synaptic connectivity, bump center, Place cells, square, network, distance
  4. [4] § MATERIALS AND METHODS › Analyzing directional sweeps and locational sweeps across theta phase bins ↔ EmpiricalDataAnalysis/SI3_SweepAngle_across_phase_bins_forward_and_backward.ipynb, lines 601–722 · score 0.60 · phase bins, left sweeps, right sweep, theta phase, backward, locational
  5. [5] § MATERIALS AND METHODS › Statistical analysis ↔ EmpiricalDataAnalysis/Fig1_Bar_GridsweepAngle.ipynb, lines 14–60 · score 0.58 · likelihood ratio, full model, MixedLM, LMMs, fitted, sweep angle
  6. [6] § MATERIALS AND METHODS › Statistical analysis ↔ EmpiricalDataAnalysis/Fig3_Bar_IDmvl.ipynb, lines 8–51 · score 0.57 · likelihood ratio, full model, MixedLM, LMMs, fitted, animals
  7. [7] § MATERIALS AND METHODS › Decoding directional theta sweeps in tmDCs ↔ ComputationalModellingFig4/Fig4_tmDC_skipping.ipynb, lines 337–390 · score 0.54 · head direction bin, tuning curves, smoothed, circular, Gaussian, cell
  8. [8] § MATERIALS AND METHODS › Computational modeling ↔ ComputationalModellingFig4/Fig4_thetasweeps.ipynb, lines 168–237 · score 0.51 · angular speed, Theta modulation, oscillation, linearly, Computational
  9. [9] § MATERIALS AND METHODS › Computational modeling ↔ ComputationalModellingFig4/Fig4_tmDC_skipping.ipynb, lines 168–237 · score 0.51 · angular speed, Theta modulation, oscillation, linearly, Computational

Paper

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The authors' code

Python · 504 lines · 20 KB · no license · 2 matches

  1. from dataclasses import dataclass
  2. import brainpy as bp
  3. import brainpy.math as bm
  4. import jax
  5. import numpy as np
  6. import networkx as nx
  8. @dataclass
  9. class PCParams:
  10. tau: float = 10.0
  11. tau_v: float = 100.0
  12. noise_strength: float = 0.0
  13. k: float = 0.2
  14. adaptation_strength: float = 15.0
  15. a: float = 0.2
  16. A: float = 5.0
  17. J0: float = 1.0
  18. g: float = 1.0
  19. conn_noise: float = 0.0
  21. class PCNet(bp.DynamicalSystem):
  22. """
  23. Graph-based continuous-attractor place cell network (linearized track version).
  25. Each node in the graph corresponds to a place cell.
  26. Synaptic connectivity is defined as a Gaussian function of the
  27. geodesic distance between nodes.
  28. If it is a linear track, the geodesic distance is the same as the Euclidean distance.
  29. If it is a T maze track or other more complex track, the geodesic distance is the shortest path distance along the track.
  30. This distance measurement is important for the network behaviours
  32. Parameters
  33. ----------
  34. Graph : networkx.Graph
  35. Graph where nodes represent place cells and edge weights represent distances.
  36. Must include 'dx' in Graph.graph.
  37. params : PCParams
  38. Parameter object containing model constants such as a, J0, tau, etc.
  40. Attributes
  41. ----------
  42. cell_num : int
  43. Number of place cells (nodes).
  44. D : brainpy.math array
  45. Matrix of geodesic distances between nodes.
  46. conn_mat : brainpy.math array
  47. Synaptic weight matrix.
  48. r, u, v : bm.Variable
  49. Neural rate, internal state, and adaptation state.
  50. center : bm.Variable
  51. Estimated bump centre position.
  52. """
  53. def __init__(self, Graph, params: PCParams = PCParams()):
  54. super().__init__()
  55. self.Graph = Graph
  56. self.params = params
  58. # number of cells = number of nodes in graph
  59. self.cell_num = len(Graph.nodes)
  60. self.node_list = list(Graph.nodes)
  62. dx = self.Graph.graph.get("dx", None)
  63. if dx is None:
  64. raise ValueError("Graph.graph['dx'] must be defined (spatial step size).")
  66. self.x = bm.asarray(np.arange(self.cell_num) * dx)
  68. # --- derived parameters ---
  69. self.m = params.adaptation_strength * params.tau / params.tau_v
  71. # --- compute geodesic distance matrix (cell_num×cell_num)
  72. geodist = dict(nx.all_pairs_dijkstra_path_length(Graph, weight='weight'))
  73. D = np.zeros((self.cell_num, self.cell_num))
  74. for i, ni in enumerate(self.node_list):
  75. for j, nj in enumerate(self.node_list):
  76. D[i, j] = geodist[ni][nj]
  77. self.D = bm.asarray(D)
  79. # --- build connectivity based on geodesic distance ---
  80. base_connection = self.make_connection(self.D)
  81. noise_connection = np.random.normal(0, params.conn_noise, size=(self.cell_num, self.cell_num))
  82. self.conn_mat = base_connection + noise_connection
  84. # --- state variables ---
  85. self.r = bm.Variable(bm.zeros(self.cell_num))
  86. self.u = bm.Variable(bm.zeros(self.cell_num))
  87. self.v = bm.Variable(bm.zeros(self.cell_num))
  88. self.center = bm.Variable(bm.zeros(1))
  90. # --- integrator ---
  91. self.integral = bp.odeint(method="exp_euler", f=self.derivative)
  93. @property
  94. def derivative(self):
  95. du = lambda u, t, input: (-u + input - self.v) / self.params.tau
  96. dv = lambda v, t: (-v + self.m * self.u) / self.params.tau_v
  97. return bp.JointEq([du, dv])
  99. # ===== connectivity based on geodesic distances =====
  100. def make_connection(self, D):
  101. """
  102. Gaussian weight kernel based on graph geodesic distances.
  103. """
  104. a = self.params.a
  105. J0 = self.params.J0
  106. W = J0 * bm.exp(-0.5 * (D / a) ** 2)
  107. # normalise or scale if desired
  108. W = W / (bm.sqrt(2 * bm.pi) * a)
  109. return W
  111. def get_bump_center(self, r, x):
  112. denom = bm.sum(r) + 1e-12
  113. center = bm.sum(r * x) / denom
  114. return center.reshape(-1,)
  116. # ===== external input based on animal position =====
  117. def input_bump(self, animal_pos_node_index):
  118. """
  119. Generate Gaussian bump centred on the node corresponding to the animal's current position.
  120. node_index: integer index into self.nodes
  121. """
  122. d = self.D[animal_pos_node_index]
  123. return self.params.A * bm.exp(-0.5 * (d / self.params.a) ** 2)
  125. # ===== update loop =====
  126. def update(self, animal_pos_node_index, ThetaInput):
  127. self.center.value = self.get_bump_center(r=self.r, x=self.x)
  128. Iext = ThetaInput * self.input_bump(animal_pos_node_index)
  129. Irec = bm.matmul(self.conn_mat, self.r)
  130. noise = bm.random.randn(self.cell_num) * self.params.noise_strength
  131. input_total = Iext + Irec + noise
  133. # integrate for current step
  134. u, v = self.integral(self.u, self.v, bp.share.load("t"), input_total)
  135. self.u.value = bm.where(u > 0, u, 0)
  136. self.v.value = v
  138. u_sq = bm.square(self.u)
  139. self.r.value = self.params.g * u_sq / (1.0 + self.params.k * bm.sum(u_sq))
  142. @dataclass
  143. class DCParams:
  144. tau: float = 10.0
  145. tau_v: float = 100.0
  146. noise_strength: float = 0.0
  147. k: float = 0.2
  148. adaptation_strength: float = 15.0
  149. a: float = 0.7
  150. A: float = 3.0
  151. J0: float = 1.0
  152. g: float = 1.0
  153. z_min: float = -bm.pi
  154. z_max: float = bm.pi
  155. conn_noise: float = 0.0
  158. class DCNet(bp.DynamicalSystem):
  159. """
  160. 1D continuous-attractor direction cell network
  161. """
  162. def __init__(self, cell_num: int, params: DCParams = DCParams()):
  163. super().__init__()
  164. self.cell_num = cell_num
  165. self.params = params
  167. # --- derived parameters ---
  168. self.m = params.adaptation_strength * params.tau / params.tau_v
  170. # --- feature space ---
  171. self.z_min = params.z_min
  172. self.z_max = params.z_max
  173. self.z_range = self.z_max - self.z_min
  174. x1 = bm.linspace(self.z_min, self.z_max, self.cell_num + 1)
  175. self.x = x1[:-1]
  177. # --- connectivity ---
  178. base_connection = self.make_connection()
  179. noise_connection = np.random.normal(0, params.conn_noise, size=(self.cell_num, self.cell_num))
  180. self.conn_mat = base_connection + noise_connection
  182. # --- state variables ---
  183. self.r = bm.Variable(bm.zeros(self.cell_num))
  184. self.u = bm.Variable(bm.zeros(self.cell_num))
  185. self.v = bm.Variable(bm.zeros(self.cell_num))
  186. self.center = bm.Variable(bm.zeros(1))
  188. # --- integrator ---
  189. self.integral = bp.odeint(method="exp_euler", f=self.derivative)
  191. @property
  192. def derivative(self):
  193. du = lambda u, t, input: (-u + input - self.v) / self.params.tau
  194. dv = lambda v, t: (-v + self.m * self.u) / self.params.tau_v
  195. return bp.JointEq([du, dv])
  197. # ===== utilities =====
  198. def handle_periodic_condition(self, A):
  199. B = bm.where(A > bm.pi, A - 2 * bm.pi, A)
  200. B = bm.where(B < -bm.pi, B + 2 * bm.pi, B)
  201. return B
  203. def calculate_dist(self, d):
  204. d = self.handle_periodic_condition(d)
  205. d = bm.where(d > 0.5 * self.z_range, d - self.z_range, d)
  206. return d
  208. # ===== connectivity =====
  209. def make_connection(self):
  210. @jax.vmap
  211. def get_J(xbins):
  212. d = self.calculate_dist(xbins - self.x)
  213. Jxx = (
  214. self.params.J0
  215. * bm.exp(-0.5 * bm.square(d / self.params.a))
  216. / (bm.sqrt(2 * bm.pi) * self.params.a)
  217. )
  218. return Jxx
  219. return get_J(self.x)
  221. # ===== dynamics =====
  222. def get_bump_center(self, r, x):
  223. exppos = bm.exp(1j * x)
  224. center = bm.angle(bm.sum(exppos * r))
  225. return center.reshape(-1,)
  227. def input_bump(self, head_direction):
  228. return self.params.A * bm.exp(
  229. -0.5 * bm.square(self.calculate_dist(self.x - head_direction) / self.params.a)
  230. )
  232. # ===== update loop =====
  233. def update(self, head_direction, ThetaInput):
  234. self.center.value = self.get_bump_center(r=self.r, x=self.x)
  235. Iext = ThetaInput * self.input_bump(head_direction)
  236. Irec = bm.matmul(self.conn_mat, self.r)
  237. noise = bm.random.randn(self.cell_num) * self.params.noise_strength
  238. input_total = Iext + Irec + noise
  240. # integrate for current step
  241. u, v = self.integral(self.u, self.v, bp.share.load("t"), input_total)
  242. self.u.value = bm.where(u > 0, u, 0)
  243. self.v.value = v
  245. u_sq = bm.square(self.u)
  246. self.r.value = self.params.g * u_sq / (1.0 + self.params.k * bm.sum(u_sq))
  248. @dataclass
  249. class GCParams:
  250. # dynamics
  251. tau: float = 10.0
  252. tau_v: float = 100.0
  253. noise_strength: float = 0.0 #activity noise
  254. conn_noise: float = 0.0 #connectivity noise
  255. k: float = 1.0
  256. adaptation_strength: float = 15.0 # (mbar)
  258. # connectivity / input
  259. a: float = 0.8
  260. A: float = 3.0
  261. J0: float = 5.0
  262. g: float = 1000.0 #scale the firing rate to make it reasonable, no biological meaning
  264. #controlling grid spacing, larger means smaller spacing
  265. mapping_ratio: float = 1
  267. #cntrolling offset length from conjunctive gc layer to gc layer, this is the key to drive the bump to move
  268. phase_offset: float = 1.0 / 20 #relative to -pi~pi range
  270. class GCNet(bp.DynamicalSystem):
  271. """
  272. 2D continuous-attractor grid cell network
  273. Grid size is num_gc_x x num_gc_x (total cells = num_gc_1side**2).
  274. """
  276. def __init__(self, num_dc: int = 100, num_gc_x: int = 100, envsize=1, params: GCParams = GCParams()):
  277. super().__init__()
  279. self.num_dc = num_dc
  280. self.num_gc_1side = num_gc_x
  281. self.envsize = envsize
  282. self.params = params
  284. # ----- derived parameters -----
  285. self.num = num_gc_x * num_gc_x
  286. self.m = params.adaptation_strength * params.tau / params.tau_v
  287. self.Lambda = 2 * bm.pi / params.mapping_ratio #grid spacing
  289. # ----- coordinate transforms (hex vs rect) -----
  290. # Note that coor_transform is to map a parallelogram with a 60-degree angle back to a square
  291. # The logic is to partition the 2D space into parallelograms, each of which contains one lattice of grid cells, and repeat the parallelogram to tile the whole space
  292. self.coor_transform = bm.array([[1.0, -1.0 / bm.sqrt(3.0)],
  293. [0.0, 2.0 / bm.sqrt(3.0)]])
  295. # inverse, which is bm.array([[1.0, 1.0 / 2],[0.0, bm.sqrt(3.0) / 2]])
  296. # Note that coor_transform_inv is to map a square to a parallelogram with a 60-degree angle
  297. self.coor_transform_inv = np.linalg.inv(np.array(self.coor_transform))
  299. # ----- feature space -----
  300. x_bins = bm.linspace(-bm.pi, bm.pi, num_gc_x + 1)
  301. x_grid, y_grid = bm.meshgrid(x_bins[:-1], x_bins[:-1])
  302. self.x_grid = x_grid.reshape(-1)
  303. self.y_grid = y_grid.reshape(-1)
  305. # positions in (x,y) space and transformed space
  306. self.value_grid = bm.stack([self.x_grid, self.y_grid], axis=1) # (N, 2)
  307. self.value_bump = self.value_grid * 4
  308. # ----- candidate centers (for center snapping) -----
  309. self.candidate_centers = self.make_candidate_centers(self.Lambda)
  311. # ----- connectivity -----
  312. base_connection = self.make_connection()
  313. noise_connection = np.random.normal(0.0, params.conn_noise, size=(self.num, self.num))
  314. self.conn_mat = base_connection + noise_connection
  316. # ----- state variables -----
  317. self.r = bm.Variable(bm.zeros(self.num))
  318. self.u = bm.Variable(bm.zeros(self.num))
  319. self.v = bm.Variable(bm.zeros(self.num))
  320. self.gc_bump = bm.Variable(bm.zeros(self.num))
  321. self.conj_input = bm.Variable(bm.zeros(self.num))
  322. self.sensory_input = bm.Variable(bm.zeros(self.num))
  323. self.center_phase = bm.Variable(bm.zeros(2))
  324. self.center_position = bm.Variable(bm.zeros(2))
  325. self.conj_center = bm.Variable(bm.zeros(2))
  326. self.sensory_center = bm.Variable(bm.zeros(2))
  328. # ----- integrator -----
  329. self.integral = bp.odeint(method="exp_euler", f=self.derivative)
  331. # ========================= Dynamics =========================
  332. @property
  333. def derivative(self):
  334. # pass total input (Irec + external + noise) as 'inp'
  335. du = lambda u, t, inp: (-u + inp - self.v) / self.params.tau
  336. dv = lambda v, t: (-v + self.m * self.u) / self.params.tau_v
  337. return bp.JointEq([du, dv])
  339. # ========================= Utilities =========================
  340. def handle_periodic_condition(self, d):
  341. d = bm.where(d > bm.pi, d - 2.0 * bm.pi, d)
  342. d = bm.where(d < -bm.pi, d + 2.0 * bm.pi, d)
  343. return d
  345. def calculate_dist(self, d):
  346. """
  347. d: (..., 2) displacement in original (x,y).
  348. Return Euclidean distance after transform (hex/rect).
  349. """
  350. #consider the periodic boundary condition
  351. d = self.handle_periodic_condition(d)
  352. # transform to lattice axes
  353. dist = (bm.matmul(self.coor_transform_inv, d.T)).T #This means the bump on the parallelogram lattice is a Gaussian, while in the square space it is a twisted Gaussian
  354. return bm.sqrt(dist[:, 0] ** 2 + dist[:, 1] ** 2)
  356. def make_candidate_centers(self, Lambda):
  357. #This will generate a massivly large number of candidate centers, so that cover the simulated environmental size sufficiently
  358. N_c = bm.int(bm.ceil(self.envsize/Lambda)+1) * 2 #number of candidates along one dimension
  359. cc = bm.zeros((N_c, N_c, 2))
  361. for i in range(N_c):
  362. for j in range(N_c):
  363. cc = cc.at[i, j, 0].set((-N_c // 2 + i) * Lambda)
  364. cc = cc.at[i, j, 1].set((-N_c // 2 + j) * Lambda)
  366. cc_tranformed = bm.dot(self.coor_transform_inv, cc.reshape(N_c * N_c, 2).T).T
  368. return cc_tranformed
  370. # ========================= Connectivity =========================
  371. def make_connection(self):
  372. @jax.vmap
  373. def kernel(v):
  374. # v: (2,) location in (x,y)
  375. d = self.calculate_dist(v - self.value_grid) # (N,)
  376. return (
  377. (self.params.J0 / self.params.g)
  378. * bm.exp(-0.5 * bm.square(d / self.params.a))
  379. / (bm.sqrt(2.0 * bm.pi) * self.params.a)
  380. )
  381. return kernel(self.value_grid) # (N, N)
  383. # ========================= Inputs =========================
  384. def position2phase(self, position):
  385. """
  386. map position->phase; phase is wrapped to [-pi, pi] per-axis
  387. """
  388. mapped_pos = position * self.params.mapping_ratio
  389. phase = bm.matmul(self.coor_transform, mapped_pos) + bm.pi
  390. px = bm.mod(phase[0], 2.0 * bm.pi) - bm.pi
  391. py = bm.mod(phase[1], 2.0 * bm.pi) - bm.pi
  392. return bm.array([px, py])
  394. def calculate_input_from_conjgc(self, animal_pos, direction_activity, theta_modulation):
  395. """Get input from conjunctive grid cell layer → grid cell layer; returns (N,) vector."""
  396. assert bm.size(animal_pos) == 2
  397. num_dc = self.num_dc
  398. num_gc = self.num
  399. direction_bin = bm.linspace(-bm.pi, bm.pi, num_dc)
  401. # # # lag relative to head direction
  402. # lagvec = -bm.array([bm.cos(head_direction), bm.sin(head_direction)]) * self.params.phase_offset * 0.0
  403. # offset = bm.array([bm.cos(direction_bin), bm.sin(direction_bin)]) * self.params.phase_offset + lagvec.reshape(-1, 1)
  405. offset = bm.array([bm.cos(direction_bin), bm.sin(direction_bin)]) * self.params.phase_offset
  407. center_conj = self.position2phase(animal_pos.reshape(-1, 1) + offset.reshape(-1, num_dc))
  409. conj_input = bm.zeros((num_dc, num_gc))
  410. for i in range(num_dc):
  411. d = self.calculate_dist(bm.asarray(center_conj[:, i]) - self.value_grid)
  412. conj_input = conj_input.at[i].set(self.params.A * bm.exp(-0.5 * bm.square(d / self.params.a)))
  414. # weighting by direction bump activity: keep top one-third (by max) then normalize, I thinking using all direction_activity should also be fine
  415. weight = bm.where(direction_activity > bm.max(direction_activity) / 3, direction_activity, 0.0)
  416. weight = weight / (bm.sum(weight) + 1e-12) # avoid div-by-zero, dim: (num_dc,)
  419. return (bm.matmul(conj_input.T, weight).reshape(-1) * theta_modulation) #dim: (num_gc, num_dc) x (num_dc,) -> (num_gc,)
  421. def calculate_sensory_input(self, animal_pos, theta_modulation):
  422. """Get sensory input to grid cell layer based on animal position; returns (N,) vector."""
  423. center_phase = self.position2phase(animal_pos)
  424. d = self.calculate_dist(center_phase - self.value_grid)
  425. sensory_input = self.params.A * bm.exp(-0.5 * bm.square(d / self.params.a))
  426. return sensory_input* theta_modulation #dim: (num_gc,)
  428. # ========================= Bump center (phase/pos) =========================
  429. def get_unique_activity_bump(self, network_activity, animal_position):
  430. """
  431. Estimate a unique bump (activity peak) from the current network state,
  432. given the animal's actual position.
  434. Returns
  435. -------
  436. center_phase : (2,) array
  437. Phase coordinates of bump center on the manifold.
  438. center_position : (2,) array
  439. Real-space position of the bump (nearest candidate).
  440. bump : (N,) array
  441. Gaussian bump template centered at center_position.
  442. """
  444. # --- find bump center in phase space ---
  445. exppos_x = bm.exp(1j * self.x_grid)
  446. exppos_y = bm.exp(1j * self.y_grid)
  447. activity_masked = bm.where(network_activity > bm.max(network_activity) * 0.1, network_activity, 0.0)
  449. center_phase = bm.zeros((2,))
  450. center_phase = center_phase.at[0].set(bm.angle(bm.sum(exppos_x * activity_masked)))
  451. center_phase = center_phase.at[1].set(bm.angle(bm.sum(exppos_y * activity_masked)))
  453. # --- map back to real space, snap to nearest candidate ---
  454. center_phase_residual = bm.matmul(self.coor_transform_inv, center_phase) / self.params.mapping_ratio
  455. candidate_pos_all = self.candidate_centers + center_phase_residual
  456. distances = bm.linalg.norm(candidate_pos_all - animal_position, axis=1)
  457. center_position = candidate_pos_all[bm.argmin(distances)]
  459. # --- build Gaussian bump template ---
  460. d = bm.asarray(center_position) - self.value_bump
  461. dist = bm.sqrt(d[:, 0] ** 2 + d[:, 1] ** 2)
  462. gc_bump = self.params.A * bm.exp(-bm.square(dist / self.params.a))
  464. return center_phase, center_position, gc_bump
  466. # one-step update (main)
  467. def update(self, animal_posistion, direction_activity, theta_modulation_conj2gc, theta_modulation_sensory2gc):
  469. # get bump activity in real space info from network activity on the manifold ---
  470. center_phase, center_position, gc_bump = self.get_unique_activity_bump(self.r, animal_posistion)
  471. self.center_phase.value = center_phase
  472. self.center_position.value = center_position
  473. self.gc_bump.value = gc_bump
  476. # get external input to grid cell layer from conjunctive grid cell layer
  477. # note that this conjunctive input will be theta modulated. When speed is high, theta modulation is high, thus input is stronger
  478. # This is how we get longer theta sweeps when speed is high
  479. conj_input = self.calculate_input_from_conjgc(animal_posistion, direction_activity, theta_modulation_conj2gc)
  480. sensory_input = self.calculate_sensory_input(animal_posistion, theta_modulation_sensory2gc)
  482. self.conj_input.value = conj_input
  483. self.sensory_input.value = sensory_input
  485. #get conj_input center and sensory_input center for monitoring
  486. _, conj_center_pos, _ = self.get_unique_activity_bump(conj_input, animal_posistion)
  487. _, sensory_center_pos, _ = self.get_unique_activity_bump(sensory_input, animal_posistion)
  488. self.conj_center.value = conj_center_pos
  489. self.sensory_center.value = sensory_center_pos
  491. # recurrent + noise
  492. Irec = bm.matmul(self.conn_mat, self.r)
  493. input_noise = bm.random.randn(self.num) * self.params.noise_strength
  494. total_net_input = Irec + conj_input + sensory_input + input_noise
  496. # integrate
  497. u, v = self.integral(self.u, self.v, bp.share.load("t"), total_net_input)
  498. self.u.value = bm.where(u > 0.0, u, 0.0)
  499. self.v.value = v
  501. # get neuron firing by global inhibition
  502. u_sq = bm.square(self.u)
  503. self.r.value = self.params.g * u_sq / (1.0 + self.params.k * bm.sum(u_sq))

network_models.py at commit 8c1af28, no license · at the source

Overview

Authors: Zilong Ji1,2, Huiwen Zhang1, Callum Marshall1, Rokas Stonis3, Neil Burgess1,2,3
ORCID iDs: Zilong Ji, Huiwen Zhang, Rokas Stonis, Neil Burgess
  1. UCL Institute of Cognitive Neuroscience, University College London, London, UK
  2. UCL Queen Square Institute of Neurology, University College London, London, UK
  3. UCL Sainsbury Wellcome Centre for Neural Circuits and Behaviour, University College London, London, UK
Institutions: UCL Queen Square Institute of Neurology (United Kingdom); University College London (United Kingdom); Sainsbury Wellcome Centre (United Kingdom)
Journal: Science advances, volume 12, issue 36, article eaeg6797
Dates: received 24 February 2026; accepted 20 July 2026; published online 4 September 2026; in print September 2026
Type: Research article · Language: English
License: CC BY-NC
Identifiers: DOI 10.1126/sciadv.aeg6797 · PMID 42696579 · PMCID PMC13544234 · OpenAlex W7134250837
Open access: gold, a free copy (OpenAlex)
Preprint: doi:10.64898/2026.03.08.710351
Status: code verified
Categories: none (in silico) (organism), systems (subfield)
Methods: Spectral & time-frequency, Smoothing, state filtering, decompositions, Machine learning, Connectivity, Statistics, Single-unit activity, calcium imaging
MeSH: Entorhinal Cortex*, Theta Rhythm*, Action Potentials, Animals, Computer Simulation, Grid Cells, Models, Neurological (* major topic)
Journal subjects: Neuroscience, Neurophysiology
Topic: Memory and Neural Mechanisms (Cognitive Neuroscience, Neuroscience), according to OpenAlex
Funding: Wellcome Principle Research Fellowship (222457/Z/21/Z)
Citations: not cited yet (Europe PMC); 36 references in the paper

Abstract

During random foraging, the positional signal decoded from entorhinal grid cells exhibits left-right theta sweeps, alternating from one side of the head direction to the other across successive theta cycles. Here, we report that theta sweeps are topographically organized along the dorsoventral axis of the medial entorhinal cortex, with the angular deviation from head direction increasing gradually from dorsal (smaller scale) to ventral (larger scale) modules. This gradient coexists with a corresponding dorsoventral increase in angular deviation decoded from theta-modulated direction cells, which drive grid cell theta sweeps. These phenomena parallel a broadening of head direction tuning and increasing occurrence of theta cycle skipping in single-cell firing along the dorsoventral axis. Computational modeling demonstrates that these patterns are consistent with continuous attractor dynamics and a dorsoventral gradient in firing rate adaptation. These results highlight how theta sweeps can simultaneously represent multiple potential future locations and reveal a clear neural mechanism underlying this process.

Reproduced under the paper's license (CC BY-NC), 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.

Zenodo 21427119

License: CC-BY-4.0
State: the link answers, verified on 26 September 2026
Evidence: files inventoried
Size: 1 file
Software Heritage: not checked
Found in: “Data, code, and materials availability:”
Not found: README, license file, CITATION.cff, environment file, tests, continuous integration, documentation
Availability: 1 check, the latest on 26 September 2026: the link answers (HTTP 200)
  • 26 September 2026: the link answers (HTTP 200)
At the source: doi.org/10.5281/zenodo.21427119

zilongji/topographythetasweeps

License: none: the authors keep all their rights
State: the link answers, verified on 26 September 2026
Evidence: files inventoried
Commit: 8c1af287e1110d396ca3a20afa107343d15697f6, 31 May 2026
Languages: Jupyter (36), Python (2)
Size: 250 files, 38 scripts
Software Heritage: not archived
Found in: the Zenodo archive record
Holds: README, 36 notebooks
Not found: license file, CITATION.cff, environment file, tests, continuous integration, documentation
Tools: NumPy (38 files), Matplotlib (37 files), SciPy (26 files), pandas (14 files), seaborn (14 files), statsmodels (10 files), JAX (3 files), scikit-learn (2 files), UMAP (2 files), h5py (1 file), NetworkX (1 file)
Availability: 1 check, the latest on 26 September 2026: the link answers
  • 26 September 2026: the link answers
39 files
At the source: github.com/ZilongJi/TopographyThetaSweeps/tree/paper-release

The paper's code and data availability statement is in the Data section.

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  • 2 repositories of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
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Data

Datasets cited

Data, code, and materials availability

All data and code needed to evaluate and reproduce the results in the paper are present in the paper and/or the Supplementary Materials. This study did not generate new materials. Data are publicly available at: https://doi.org/10.25493/R5FR-EDG. Code for reproducing all the results in the main text is available at: https://doi.org/10.5281/zenodo.21427119.

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

Versions

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Version 1, 27 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 5 authors, 7 MeSH terms, 1 funder, 35 references.

Cite

This paper

Ji, Z., Zhang, H., Marshall, C., Stonis, R., & Burgess, N. (2026). Dorsoventral gradient of theta sweeps in the medial entorhinal cortex. Science advances, 12(36), eaeg6797. https://doi.org/10.1126/sciadv.aeg6797

BibTeX

@article{ji2026dorsoventral,
author = {Ji, Zilong and Zhang, Huiwen and Marshall, Callum and Stonis, Rokas and Burgess, Neil},
title = {{Dorsoventral gradient of theta sweeps in the medial entorhinal cortex}},
journal = {Science advances},
year = {2026},
month = sep,
volume = {12},
number = {36},
pages = {eaeg6797},
publisher = {American Association for the Advancement of Science},
issn = {2375-2548},
doi = {10.1126/sciadv.aeg6797},
url = {https://doi.org/10.1126/sciadv.aeg6797},
pmid = {42696579},
pmcid = {PMC13544234}
}

RIS

TY - JOUR
AU - Ji, Zilong
AU - Zhang, Huiwen
AU - Marshall, Callum
AU - Stonis, Rokas
AU - Burgess, Neil
TI - Dorsoventral gradient of theta sweeps in the medial entorhinal cortex
T2 - Science advances
J2 - Sci Adv
PY - 2026
DA - 2026/09/04
VL - 12
IS - 36
SP - eaeg6797
SN - 2375-2548
PB - American Association for the Advancement of Science
DO - 10.1126/sciadv.aeg6797
UR - https://doi.org/10.1126/sciadv.aeg6797
LA - en
ER -

CSL-JSON

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