def non_linear_calcium(u, v, w0, seed):
"""
Same as ~cbsp.population_1.linear_calcium(u, v, w0, seed) for the non linear calcium model.
"""
# Calcium
tau_Ca = 0.01893044
Cpre = 0.86467
Cpost = 2.30815
xi = (2 * (Cpost + Cpre) - Cpost) / Cpre - 1
# Plasticity
thetaD = 1
thetaP = 4.99780
drate = 111.82515
prate = 894.23695
sigma = 2.8284
tau = 707.02258
sqrttau = np.sqrt(tau)
# Optional, for current approximation
tau_m = 5.e-3
c_N = 0.4
R = 50e6
Iconst = c_N * tau_m / R
np.random.seed(seed)
time = np.linspace(0., cbsp.SIMULATION_TIME,
int(cbsp.SIMULATION_TIME / cbsp.TIMESTEP) + 1)
N = 1000
cpre = np.zeros(N)
cpost = np.zeros(N)
c = np.zeros(N)
w = np.zeros(N)
w[:] = w0
w_rec_pop = np.zeros((N, len(time)))
u_rec_pop = np.zeros((N, len(time)))
v_rec = np.zeros_like(time)
I_rec = np.zeros_like(time)
c_rec_pop = np.zeros((N, len(time)))
for i, t in enumerate(time):
u_sp = utils.spike_train(N, u, cbsp.TIMESTEP)
v_sp = utils.spike_train(1, v, cbsp.TIMESTEP)
n = utils.standard_normal(N, cbsp.TIMESTEP)
Hp = utils.heaviside(c - thetaP)
Hd = utils.heaviside(c - thetaD)
cpre = cpre - cbsp.TIMESTEP * cpre / tau_Ca + Cpre * u_sp
cpost = cpost - cbsp.TIMESTEP * cpost / tau_Ca + Cpost * v_sp + xi * v_sp * cpre
c = cpre + cpost
w = w + cbsp.TIMESTEP / tau * (prate * (1 - w) * Hp - drate * w * Hd +
np.sqrt(Hp + Hd) * sigma * sqrttau * n)
w_rec_pop[:, i] = w
u_rec_pop[:, i] = u_sp
v_rec[i] = v_sp.item()
I_rec[i] = Iconst * np.dot(w, u_sp)
c_rec_pop[:, i] = c
return w_rec_pop, time, (u_rec_pop, v_rec, I_rec, c_rec_pop)
def linear_calcium_mat(u1, w1, u2, w2, seed):
"""Integrates the spike-timing dependent synaptic strength.
Args:
u1 (float): presynaptic firing rate of the first population.
w1 (float): initial synapse strength of the first population.
u2 (float): presynaptic firing rate of the second population.
w2 (float): initial synapse strength of the second population.
seed (int): random state.
Returns:
tuple: ((w1, w2), t, (u1, u2, v, I, c1, c2))
with
array: w1, change of synapse strengths in the first population. Shape (#synapses, #timesteps).
array: w2, change of synapse strengths in the second population. Shape (#synapses, #timesteps).
array: t, time.
array: u1, presynaptic spike trains in the first population. Shape (#synapses, #timesteps).
array: u2, presynaptic spike trains in the second population. Shape (#synapses, #timesteps).
array: v, postsynaptic spike train. Shape (#timesteps).
array: I, postsynaptic current. Shape (#timesteps).
array: c1, calcium traces in the first population. Shape (#synapses, #timesteps).
array: c2, calcium traces in the second population. Shape (#synapses, #timesteps).
"""
# Calcium
tau_Ca = 0.02227212
Cpre = 0.84410
Cpost = 1.62138
# Plasticity
thetaD = 1
thetaP = 2.009289
drate = 137.7586
prate = 597.08922
sigma = 2.8284
tau = 520.76129
sqrttau = np.sqrt(tau)
# MAT model
tau_m, tau_1, tau_2 = 5.e-3, 10.e-3, 200.e-3
trefr = 2.e-3
c_N = 0.2
R = 50e6
alpha1, alpha2, w_mat = 30.e-3, 2.e-3, 20.e-3
Iconst = c_N * tau_m / R
time = np.linspace(0., cbsp.SIMULATION_TIME,
int(cbsp.SIMULATION_TIME / cbsp.TIMESTEP) + 1)
N1 = 1000
N2 = 1000
V = 0.
theta1, theta2 = 0., 0.
Theta = 0.
trest = 0.
I = 0.
v_sp = 0.
np.random.seed(seed)
c = np.zeros(N1 + N2)
w = np.zeros(N1 + N2)
u_sp = np.zeros(N1 + N2)
w[:N1] = w1 # np.random.normal(w0, w0_std, N)
w[N1:] = w2
w1_rec_pop = np.zeros((N1, len(time)))
w2_rec_pop = np.zeros((N2, len(time)))
u1_rec_pop = np.zeros((N1, len(time)))
u2_rec_pop = np.zeros((N2, len(time)))
v_rec = np.zeros_like(time)
I_rec = np.zeros_like(time)
c1_rec_pop = np.zeros((N1, len(time)))
c2_rec_pop = np.zeros((N2, len(time)))
for i, t in enumerate(time):
# import pdb; pdb.set_trace()
u_sp[:N1] = utils.spike_train(N1, u1, cbsp.TIMESTEP)
u_sp[N2:] = utils.spike_train(N2, u2, cbsp.TIMESTEP)
n = utils.standard_normal(N1 + N2, cbsp.TIMESTEP)
Hp = utils.heaviside(c - thetaP)
Hd = utils.heaviside(c - thetaD)
c = c - cbsp.TIMESTEP * c / tau_Ca + Cpre * u_sp + Cpost * v_sp
w = w + cbsp.TIMESTEP / tau * (prate * (1 - w) * Hp - drate * w * Hd +
np.sqrt(Hp + Hd) * sigma * sqrttau * n)
I = Iconst * np.dot(w, u_sp)
V = V + cbsp.TIMESTEP * (-V / tau_m + R / tau_m * I)
theta1 = theta1 + cbsp.TIMESTEP * (-theta1 / tau_1) + alpha1 * v_sp
theta2 = theta2 + cbsp.TIMESTEP * (-theta2 / tau_2) + alpha2 * v_sp
Theta = theta1 + theta2 + w_mat
if V > Theta and t > trest:
v_sp = 1.
trest = t + trefr
else:
v_sp = 0.
w1_rec_pop[:, i] = w[:N1]
u1_rec_pop[:, i] = u_sp[:N1]
w2_rec_pop[:, i] = w[N1:]
u2_rec_pop[:, i] = u_sp[N1:]
v_rec[i] = v_sp
I_rec[i] = I
c1_rec_pop[:, i] = c[:N1]
c2_rec_pop[:, i] = c[N1:]
return (w1_rec_pop, w2_rec_pop), time, (u1_rec_pop, u2_rec_pop, v_rec,
I_rec, c1_rec_pop, c2_rec_pop)
def linear_calcium_aeif(u1, w1, u2, w2, seed):
"""
Same as ~cbsp.population_3.linear_calcium_mat(u1, w1, u2, w2, seed) for the AEIF model.
"""
# Calcium
tau_Ca = 0.02227212
Cpre = 0.84410
Cpost = 1.62138
# Plasticity
thetaD = 1
thetaP = 2.009289
drate = 137.7586
prate = 597.08922
sigma = 2.8284
tau = 520.76129
sqrttau = np.sqrt(tau)
# AEIF model (ranamed w->z)
C = 2.81e-10 # 2.81e-9 # pF
g_L = 30e-9 # nS
E_L = -70.6e-3 # mV
V_T = -50.4e-3 # mV
D_T = 2e-3 # mV
tau_z = 0.144 # s
a = 4e-9 # nS
b = 0.0805e-9 # nA
R = 1 / g_L
tau_v = R * C
c_N = 0.085 # 17 # 0.0375
Iconst = c_N * tau_v / R
time = np.linspace(0., cbsp.SIMULATION_TIME,
int(cbsp.SIMULATION_TIME / cbsp.TIMESTEP) + 1)
N1 = 1000
N2 = 1000
V = E_L
z = 0.
I = 0.
v_sp = 0.
np.random.seed(seed)
c = np.zeros(N1 + N2)
w = np.zeros(N1 + N2)
u_sp = np.zeros(N1 + N2)
w[:N1] = w1 # np.random.normal(w0, w0_std, N)
w[N1:] = w2
w1_rec_pop = np.zeros((N1, len(time)))
w2_rec_pop = np.zeros((N2, len(time)))
u1_rec_pop = np.zeros((N1, len(time)))
u2_rec_pop = np.zeros((N2, len(time)))
v_rec = np.zeros_like(time)
I_rec = np.zeros_like(time)
c1_rec_pop = np.zeros((N1, len(time)))
c2_rec_pop = np.zeros((N2, len(time)))
for i, t in enumerate(time):
u_sp[:N1] = utils.spike_train(N1, u1, cbsp.TIMESTEP)
u_sp[N1:] = utils.spike_train(N2, u2, cbsp.TIMESTEP)
n = utils.standard_normal(N1 + N2, cbsp.TIMESTEP)
Hp = utils.heaviside(c - thetaP)
Hd = utils.heaviside(c - thetaD)
c = c - cbsp.TIMESTEP * c / tau_Ca + Cpre * u_sp + Cpost * v_sp
w = w + cbsp.TIMESTEP / tau * (prate * (1 - w) * Hp - drate * w * Hd +
np.sqrt(Hp + Hd) * sigma * sqrttau * n)
I = Iconst * np.dot(w, u_sp)
V = V + cbsp.TIMESTEP / tau_v * (-V + E_L + D_T * np.exp(
(V - V_T) / D_T) - R * z + R * I)
z = z + cbsp.TIMESTEP / tau_z * (a * (V - E_L) - z)
if V > V_T:
v_sp = 1.
V = V - (V_T - E_L)
z = z + b
else:
v_sp = 0.
w1_rec_pop[:, i] = w[:N1]
u1_rec_pop[:, i] = u_sp[:N1]
w2_rec_pop[:, i] = w[N1:]
u2_rec_pop[:, i] = u_sp[N1:]
v_rec[i] = v_sp
I_rec[i] = I
c1_rec_pop[:, i] = c[:N1]
c2_rec_pop[:, i] = c[N1:]
return (w1_rec_pop, w2_rec_pop), time, (u1_rec_pop, u2_rec_pop, v_rec,
I_rec, c1_rec_pop, c2_rec_pop)
def non_linear_calcium_mat(u1, w1, u2, w2, seed):
"""
Same as ~cbsp.population_3.linear_calcium_mat(u1, w1, u2, w2, seed) for the non linear calcium model.
"""
# Calcium
tau_Ca = 0.01893044
Cpre = 0.86467
Cpost = 2.30815
xi = (2 * (Cpost + Cpre) - Cpost) / Cpre - 1
# Plasticity
thetaD = 1
thetaP = 4.99780
drate = 111.82515
prate = 894.23695
sigma = 2.8284
tau = 707.02258
sqrttau = np.sqrt(tau)
# MAT model
tau_m, tau_1, tau_2 = 5.e-3, 10.e-3, 200.e-3
trefr = 2.e-3
c_N = 0.2
R = 50e6
alpha1, alpha2, w_mat = 30.e-3, 2.e-3, 20.e-3
Iconst = c_N * tau_m / R
time = np.linspace(0., cbsp.SIMULATION_TIME,
int(cbsp.SIMULATION_TIME / cbsp.TIMESTEP) + 1)
N1 = 1000
N2 = 1000
V = 0.
theta1, theta2 = 0., 0.
Theta = 0.
trest = 0.
I = 0.
v_sp = 0.
np.random.seed(seed)
cpre = np.zeros(N1 + N2)
cpost = np.zeros(N1 + N2)
c = np.zeros(N1 + N2)
w = np.zeros(N1 + N2)
u_sp = np.zeros(N1 + N2)
w[:N1] = w1 # np.random.normal(w0, w0_std, N)
w[N1:] = w2
w1_rec_pop = np.zeros((N1, len(time)))
w2_rec_pop = np.zeros((N2, len(time)))
u1_rec_pop = np.zeros((N1, len(time)))
u2_rec_pop = np.zeros((N2, len(time)))
v_rec = np.zeros_like(time)
I_rec = np.zeros_like(time)
c1_rec_pop = np.zeros((N1, len(time)))
c2_rec_pop = np.zeros((N2, len(time)))
for i, t in enumerate(time):
# import pdb; pdb.set_trace()
u_sp[:N1] = utils.spike_train(N1, u1, cbsp.TIMESTEP)
u_sp[N2:] = utils.spike_train(N2, u2, cbsp.TIMESTEP)
n = utils.standard_normal(N1 + N2, cbsp.TIMESTEP)
Hp = utils.heaviside(c - thetaP)
Hd = utils.heaviside(c - thetaD)
cpre = cpre - cbsp.TIMESTEP * cpre / tau_Ca + Cpre * u_sp
cpost = cpost - cbsp.TIMESTEP * cpost / tau_Ca + Cpost * v_sp + xi * v_sp * cpre
c = cpre + cpost
w = w + cbsp.TIMESTEP / tau * (prate * (1 - w) * Hp - drate * w * Hd +
np.sqrt(Hp + Hd) * sigma * sqrttau * n)
I = Iconst * np.dot(w, u_sp)
V = V + cbsp.TIMESTEP * (-V / tau_m + R / tau_m * I)
theta1 = theta1 + cbsp.TIMESTEP * (-theta1 / tau_1) + alpha1 * v_sp
theta2 = theta2 + cbsp.TIMESTEP * (-theta2 / tau_2) + alpha2 * v_sp
Theta = theta1 + theta2 + w_mat
if V > Theta and t > trest:
v_sp = 1.
trest = t + trefr
else:
v_sp = 0.
w1_rec_pop[:, i] = w[:N1]
u1_rec_pop[:, i] = u_sp[:N1]
w2_rec_pop[:, i] = w[N1:]
u2_rec_pop[:, i] = u_sp[N1:]
v_rec[i] = v_sp
I_rec[i] = I
c1_rec_pop[:, i] = c[:N1]
c2_rec_pop[:, i] = c[N1:]
return (w1_rec_pop, w2_rec_pop), time, (u1_rec_pop, u2_rec_pop, v_rec,
I_rec, c1_rec_pop, c2_rec_pop)
def linear_calcium_mat(u, w0, seed):
"""Integrates the spike-timing dependent synaptic strength.
Args:
u (float): presynaptic firing rate.
w0 (float): initial synapse strength.
seed (int): random state.
Returns:
tuple: (w, t, (u, v, I, c))
with
array: w, change of synapse strengths. Shape (#synapses, #timesteps).
array: t, time.
array: u, presynaptic spike trains. Shape (#synapses, #timesteps).
array: v, postsynaptic spike train. Shape (#timesteps).
array: I, postsynaptic current. Shape (#timesteps).
array: c, calcium traces. Shape (#synapses, #timesteps).
"""
# Calcium
tau_Ca = 0.02227212
Cpre = 0.84410
Cpost = 1.62138
# Plasticity
thetaD = 1
thetaP = 2.009289
drate = 137.7586
prate = 597.08922
sigma = 2.8284
tau = 520.76129
sqrttau = np.sqrt(tau)
# MAT model
tau_m, tau_1, tau_2 = 5.e-3, 10.e-3, 200.e-3
trefr = 2.e-3
c_N = 0.4
R = 50e6
alpha1, alpha2, w_mat = 30.e-3, 2.e-3, 20.e-3
Iconst = c_N * tau_m / R
time = np.linspace(0., cbsp.SIMULATION_TIME,
int(cbsp.SIMULATION_TIME / cbsp.TIMESTEP) + 1)
N = 1000
V = 0.
theta1, theta2 = 0., 0.
Theta = 0.
trest = 0.
I = 0.
v_sp = 0.
np.random.seed(seed)
c = np.zeros(N)
w = np.zeros(N)
w[:] = w0 # np.random.normal(w0, w0_std, N)
w_rec_pop = np.zeros((N, len(time)))
u_rec_pop = np.zeros((N, len(time)))
v_rec = np.zeros_like(time)
I_rec = np.zeros_like(time)
c_rec_pop = np.zeros((N, len(time)))
for i, t in enumerate(time):
u_sp = utils.spike_train(N, u, cbsp.TIMESTEP)
n = utils.standard_normal(N, cbsp.TIMESTEP)
Hp = utils.heaviside(c - thetaP)
Hd = utils.heaviside(c - thetaD)
c = c - cbsp.TIMESTEP * c / tau_Ca + Cpre * u_sp + Cpost * v_sp
w = w + cbsp.TIMESTEP / tau * (prate * (1 - w) * Hp - drate * w * Hd +
np.sqrt(Hp + Hd) * sigma * sqrttau * n)
I = Iconst * np.dot(w, u_sp)
V = V + cbsp.TIMESTEP * (-V / tau_m + R / tau_m * I)
theta1 = theta1 + cbsp.TIMESTEP * (-theta1 / tau_1) + alpha1 * v_sp
theta2 = theta2 + cbsp.TIMESTEP * (-theta2 / tau_2) + alpha2 * v_sp
Theta = theta1 + theta2 + w_mat
if V > Theta and t > trest:
v_sp = 1.
trest = t + trefr
else:
v_sp = 0.
w_rec_pop[:, i] = w
u_rec_pop[:, i] = u_sp
v_rec[i] = v_sp
I_rec[i] = I
c_rec_pop[:, i] = c
return w_rec_pop, time, (u_rec_pop, v_rec, I_rec, c_rec_pop)
def linear_calcium(u, v, w0, seed):
"""Integrates the spike-timing dependent synaptic strength.
Args:
u (float): presynaptic firing rate.
v (float): postsynaptic firing rate.
w0 (float): initial synapse strength.
seed (int): random state.
Returns:
tuple: (w, t, (u, v, I, c))
with
array: w, change of synapse strengths. Shape (#synapses, #timesteps).
array: t, time.
array: u, presynaptic spike trains. Shape (#synapses, #timesteps).
array: v, postsynaptic spike train. Shape (#timesteps).
array: I, postsynaptic current. Shape (#timesteps).
array: c, calcium traces. Shape (#synapses, #timesteps).
"""
# Calcium
tau_Ca = 0.02227212
Cpre = 0.84410
Cpost = 1.62138
# Plasticity
thetaD = 1
thetaP = 2.009289
drate = 137.7586
prate = 597.08922
sigma = 2.8284
tau = 520.76129
sqrttau = np.sqrt(tau)
# Optional, for current approximation
tau_m = 5.e-3
c_N = 0.4
R = 50e6
Iconst = c_N * tau_m / R
np.random.seed(seed)
time = np.linspace(0., cbsp.SIMULATION_TIME,
int(cbsp.SIMULATION_TIME / cbsp.TIMESTEP) + 1)
N = 1000
cpre = np.zeros(N)
cpost = np.zeros(N)
c = np.zeros(N)
w = np.zeros(N)
w[:] = w0 # np.random.normal(w0, w0_std, N)
w_rec_pop = np.zeros((N, len(time)))
u_rec_pop = np.zeros((N, len(time)))
v_rec = np.zeros_like(time)
I_rec = np.zeros_like(time)
c_rec_pop = np.zeros((N, len(time)))
for i, t in enumerate(time):
u_sp = utils.spike_train(N, u, cbsp.TIMESTEP)
v_sp = utils.spike_train(1, v, cbsp.TIMESTEP)
n = utils.standard_normal(N, cbsp.TIMESTEP)
Hp = utils.heaviside(c - thetaP)
Hd = utils.heaviside(c - thetaD)
c = c - cbsp.TIMESTEP * c / tau_Ca + Cpre * u_sp + Cpost * v_sp
w = w + cbsp.TIMESTEP / tau * (prate * (1 - w) * Hp - drate * w * Hd +
np.sqrt(Hp + Hd) * sigma * sqrttau * n)
w_rec_pop[:, i] = w
u_rec_pop[:, i] = u_sp
v_rec[i] = v_sp.item()
I_rec[i] = Iconst * np.dot(w, u_sp)
c_rec_pop[:, i] = c
return w_rec_pop, time, (u_rec_pop, v_rec, I_rec, c_rec_pop)