+10 XP

Population Statistics with NumPy

np.mean(V, axis=0) averages over neurons (rows). np.std(V, axis=0) does the same for standard deviation. The result shape is (T,) — one stat per time step.

Axis intuition for V[N, T]:
• np.mean(V, axis=0) → collapse rows → shape (T,) → mean voltage at each time
• np.mean(V, axis=1) → collapse columns → shape (N,) → mean voltage of each neuron over time
• np.mean(V) → grand mean → one number

python
import numpy as np
import matplotlib.pyplot as plt
np.random.seed(42)
N, T = 20, 150
dt=1e-3; tau=20e-3; el=-60e-3; vr=-70e-3; vth=-50e-3
r=100e6; i_mean=25e-11; i_std=0.5e-11
V = np.zeros((N, T))
V[:, 0] = el
for n in range(N):
    np.random.seed(n)
    for t_step in range(T - 1):
        t = t_step * dt
        i_t = i_mean + i_std * np.random.normal() * np.sqrt(dt)
→ V[n, t+1] = next step value; V[n, t] = current value for RHS
        V[n, t_step+1] = V[n, t_step] + (dt/tau)*(el - V[n,t_step] + r*i_t)
        if V[n, t_step+1] >= vth:
            V[n, t_step+1] = vr
→ np.mean(V, axis=0): average over N neurons → shape (T,)
t_ms = np.arange(T) * dt * 1000
v_mean = np.mean(V, axis=0) * 1000
v_std  = np.std(V,  axis=0) * 1000
→ fill_between: shaded band from mean-std to mean+std
fig, ax = plt.subplots(figsize=(8, 3))
ax.plot(t_ms, v_mean, color='#1CB0F6', label='Mean V')
ax.fill_between(t_ms, v_mean-v_std, v_mean+v_std,
                alpha=0.3, color='#1CB0F6', label='±1 std')
ax.set_xlabel('Time (ms)'); ax.set_ylabel('V (mV)')
ax.set_title(f'Population Average: N={N}')
ax.legend(); plt.show()

The shaded band shows trial-to-trial variability across 20 neurons. Wider band = more variable population.