def run_mean_field_extended(NRN1, NRN2, NTWK, array_func,\
Ne=8000, Ni=2000, T=5e-3,\
afferent_exc_fraction=0.,
dt=1e-4, tstop=2, extended_output=False,\
ext_drive_change=0.):
# find external drive
M = get_connectivity_and_synapses_matrix(NTWK, SI_units=True)
ext_drive = M[0,0]['ext_drive']
if afferent_exc_fraction<0.5:
afferent_exc_fraction = M[0,0]['afferent_exc_fraction']
X0 = find_fixed_point(NRN1, NRN2, NTWK, exc_aff=ext_drive+ext_drive_change,\
Ne=Ne, Ni=Ni,
verbose=True)
TF1, TF2 = load_transfer_functions(NRN1, NRN2, NTWK)
t = np.arange(int(tstop/dt))*dt
def dX_dt_scalar(X, t=0):
exc_aff = ext_drive+ext_drive_change+(1-afferent_exc_fraction)*array_func(t)
pure_exc_aff = (2*afferent_exc_fraction-1)*array_func(t) # what needs to be added
return build_up_differential_operator(TF1, TF2, Ne=Ne, Ni=Ni, T=T)(X,\
exc_aff=exc_aff, pure_exc_aff=pure_exc_aff)
X = np.zeros((len(t), len(X0)))
X[0,:] = X0
for i in range(len(t)-1):
exc_aff = ext_drive+ext_drive_change+(1-afferent_exc_fraction)*array_func(t[i])
pure_exc_aff = (2*afferent_exc_fraction-1)*array_func(t[i]) # what needs to be added
# X[i+1,:] = X[i,:] + dt*dX_dt_scalar(X[i,:], t=t[i])
X[i+1,:] = X[i,:] + (t[1]-t[0])*build_up_differential_operator(TF1, TF2,\
Ne=Ne, Ni=Ni)(X[i,:], exc_aff=exc_aff, pure_exc_aff=pure_exc_aff)
fe, fi = X[:,0], X[:,1]
sfe, sfei, sfi = [np.sqrt(X[:,i]) for i in range(2,5)]
if extended_output:
params = get_neuron_params(NRN2, SI_units=True)
reformat_syn_parameters(params, M)
exc_aff = ext_drive+ext_drive_change+(1-afferent_exc_fraction)*array_func(t)
pure_exc_aff = (2*afferent_exc_fraction-1)*array_func(t) # what needs to be added
# excitatory neurons have more excitation
muV_e, sV_e, muGn_e, TvN_e = get_fluct_regime_vars(\
fe+exc_aff+pure_exc_aff,\
fi, *pseq_params(params))
muV_i, sV_i, muGn_i, TvN_i = get_fluct_regime_vars(\
fe+exc_aff,\
fi, *pseq_params(params))
muV, sV, muGn, TvN = .8*muV_e+.2*muV_i, .8*sV_e+.2*sV_i,\
.8*muGn_e+.2*muGn_i, .8*TvN_e+.2*TvN_i,
return t, fe, fi, sfe, sfei, sfi, muV, sV, muGn, TvN
else:
return t, fe, fi, sfe, sfei, sfi
def run_mean_field(NRN1, NRN2, NTWK, array_func,\
T=5e-3, dt=1e-4, tstop=2, extended_output=False,\
afferent_exc_fraction=0.,
ext_drive_change=0.):
# find external drive
M = get_connectivity_and_synapses_matrix(NTWK, SI_units=True)
ext_drive = M[0,0]['ext_drive']
if afferent_exc_fraction<0.5:
afferent_exc_fraction = M[0,0]['afferent_exc_fraction']
X0 = find_fixed_point_first_order(NRN1, NRN2, NTWK, exc_aff=ext_drive+ext_drive_change,\
verbose=False)
TF1, TF2 = load_transfer_functions(NRN1, NRN2, NTWK)
t = np.arange(int(tstop/dt))*dt
def dX_dt_scalar(X, t=0):
exc_aff = ext_drive+ext_drive_change+(1-afferent_exc_fraction)*array_func(t)
pure_exc_aff = (2*afferent_exc_fraction-1)*array_func(t) # what needs to be added
return build_up_differential_operator_first_order(TF1, TF2, T=T)(X,\
exc_aff=exc_aff, pure_exc_aff=pure_exc_aff)
fe, fi = odeint(dX_dt_scalar, X0, t).T
if extended_output:
params = get_neuron_params(NRN2, SI_units=True)
reformat_syn_parameters(params, M)
exc_aff = ext_drive+ext_drive_change+(1-afferent_exc_fraction)*array_func(t)
pure_exc_aff = (2*afferent_exc_fraction-1)*array_func(t) # what needs to be added
# excitatory neurons have more excitation
muV_e, sV_e, muGn_e, TvN_e = get_fluct_regime_vars(\
fe+exc_aff+pure_exc_aff,\
fi, *pseq_params(params))
muV_i, sV_i, muGn_i, TvN_i = get_fluct_regime_vars(\
fe+exc_aff,\
fi, *pseq_params(params))
muV, sV, muGn, TvN = .8*muV_e+.2*muV_i, .8*sV_e+.2*sV_i,\
.8*muGn_e+.2*muGn_i, .8*TvN_e+.2*TvN_i,
return t, fe, fi, muV, sV, muGn, TvN
else:
return t, fe, fi
def plot_ntwk_sim_output_for_waveform(args,\
BIN=5, min_time=200, bar_ms=50,
zoom_conditions=None, vpeak=-35,\
raster_number=400):
BIN = 8
time_array, rate_array, rate_exc, rate_inh,\
Raster_exc, Raster_inh,\
Vm_exc, Vm_inh, Ge_exc, Ge_inh, Gi_exc, Gi_inh = np.load(args.file,allow_pickle = True)
rate_exc = rate_exc + 0.2
print("ee")
if zoom_conditions is not None:
z = zoom_conditions
else:
z = [time_array[0], time_array[-1]]
cond_t = (time_array > z[0]) & (time_array < z[1])
###### =========================================== ######
############# adding the theoretical eval ###############
###### =========================================== ######
t0 = args.t0 - 4 * args.T1
def rate_func(t):
return double_gaussian(t, 1e-3 * args.t0, 1e-3 * args.T1,
1e-3 * args.T2, args.amp)
t, fe, fi, sfe, sfei, sfi = run_mean_field_extended(args.CONFIG.split('--')[0],\
args.CONFIG.split('--')[1],args.CONFIG.split('--')[2],\
rate_func,dt=5e-4,
tstop=args.tstop*1e-3)
tfirst, fefirst, fifirst = run_mean_field(args.CONFIG.split('--')[0],
args.CONFIG.split('--')[1],
args.CONFIG.split('--')[2],
rate_func,
dt=5e-4,
tstop=args.tstop * 1e-3)
params = get_neuron_params(args.CONFIG.split('--')[0], SI_units=True)
M = get_connectivity_and_synapses_matrix('CONFIG1', SI_units=True)
reformat_syn_parameters(params, M) # merging those parameters
ext_drive = M[0, 0]['ext_drive']
afferent_exc_fraction = M[0, 0]['afferent_exc_fraction']
fe_e, fe_i = fe + ext_drive + rate_func(t), fe + ext_drive
muV_e, sV_e, muGn_e, TvN_e = get_fluct_regime_vars(fe_e, fi,
*pseq_params(params))
muV_i, sV_i, muGn_i, TvN_i = get_fluct_regime_vars(fe_i, fi,
*pseq_params(params))
Ne = Raster_inh[1].min()
FIGS = []
# plotting
FIGS.append(plt.figure(figsize=(5, 4)))
cond = (Raster_exc[0] > z[0]) & (Raster_exc[0] < z[1]) & (
Raster_exc[1] > Ne - raster_number)
plt.plot(Raster_exc[0][cond], Raster_exc[1][cond], '.g')
cond = (Raster_inh[0] > z[0]) & (Raster_inh[0] < z[1]) & (
Raster_inh[1] < Ne + .2 * raster_number)
plt.plot(Raster_inh[0][cond], Raster_inh[1][cond], '.r')
'''
plt.plot([z[0],z[0]+bar_ms], [Ne, Ne], 'k-', lw=5)
plt.annotate(str(bar_ms)+'ms', (z[0]+bar_ms, Ne))
'''
#set_plot(plt.gca(), ['left'], ylabel='Neuron index', xticks=[])
FIGS.append(plt.figure(figsize=(5, 5)))
ax1 = plt.subplot2grid((3, 1), (0, 0), rowspan=2)
ax2 = plt.subplot2grid((3, 1), (2, 0))
for i in range(len(Vm_exc)):
ax1.plot(time_array[cond_t], Vm_exc[i][cond_t], 'g-', lw=.5)
spk = np.where((Vm_exc[i][cond_t][:-1] > -50)
& (Vm_exc[i][cond_t][1:] < -55))[0]
for ispk in spk:
ax1.plot(time_array[cond_t][ispk] * np.ones(2),
[Vm_exc[i][cond_t][ispk], vpeak], 'g--')
ax2.plot(time_array[cond_t], Ge_exc[i][cond_t], 'g-', lw=.5)
ax2.plot(time_array[cond_t], Gi_exc[i][cond_t], 'r-', lw=.5)
# vm
ax1.plot(1e3 * t[1e3 * t > t0], 1e3 * muV_e[1e3 * t > t0], 'g-', lw=2)
ax1.fill_between(1e3*t[1e3*t>t0], 1e3*(muV_e[1e3*t>t0]-sV_e[1e3*t>t0]),\
1e3*(muV_e[1e3*t>t0]+sV_e[1e3*t>t0]), color='g', alpha=.4)
# ge
ge_th = 1e9 * fe_e[1e3 * t > t0] * params['Qe'] * params['Te'] * (
1 - params['gei']) * params['pconnec'] * params['Ntot']
sge_th = 1e9 * params['Qe'] * np.sqrt(
fe_e[1e3 * t > t0] * params['Te'] *
(1 - params['gei']) * params['pconnec'] * params['Ntot'])
ax2.plot(1e3 * t[1e3 * t > t0], ge_th, 'g-', lw=2)
ax2.fill_between(1e3 * t[1e3 * t > t0],
ge_th - sge_th,
ge_th + sge_th,
color='g',
alpha=.4)
gi_th = 1e9 * fi[1e3 * t > t0] * params['Qi'] * params['Ti'] * params[
'gei'] * params['pconnec'] * params['Ntot']
sgi_th = 1e9 * params['Qi'] * np.sqrt(
fi[1e3 * t > t0] * params['Ti'] * params['gei'] * params['pconnec'] *
params['Ntot'])
ax2.plot(1e3 * t[1e3 * t > t0], gi_th, 'r-', lw=2)
ax2.fill_between(1e3 * t[1e3 * t > t0],
gi_th - sgi_th,
gi_th + sgi_th,
color='r',
alpha=.4)
ax1.plot(time_array[cond_t][0] * np.ones(2), [-65, -55], lw=4, color='k')
ax1.annotate('10mV', (time_array[cond_t][0], -65))
#set_plot(ax1, [], xticks=[], yticks=[])
#set_plot(ax2, ['left'], ylabel='$G$ (nS)', xticks=[])
FIGS.append(plt.figure(figsize=(5, 5)))
ax1 = plt.subplot2grid((3, 1), (0, 0), rowspan=2)
ax2 = plt.subplot2grid((3, 1), (2, 0))
for i in range(len(Vm_inh)):
ax1.plot(time_array[cond_t], Vm_inh[i][cond_t], 'r-', lw=.5)
spk = np.where((Vm_inh[i][cond_t][:-1] > -51)
& (Vm_inh[i][cond_t][1:] < -55))[0]
for ispk in spk:
ax1.plot(time_array[cond_t][ispk] * np.ones(2),
[Vm_inh[i][cond_t][ispk], vpeak], 'r--')
ax2.plot(time_array[cond_t], Ge_inh[i][cond_t], 'g-', lw=.5)
ax2.plot(time_array[cond_t], Gi_inh[i][cond_t], 'r-', lw=.5)
# vm
ax1.plot(1e3 * t[1e3 * t > t0], 1e3 * muV_i[1e3 * t > t0], 'r-', lw=2)
ax1.fill_between(1e3*t[1e3*t>t0], 1e3*(muV_i[1e3*t>t0]-sV_i[1e3*t>t0]),\
1e3*(muV_i[1e3*t>t0]+sV_i[1e3*t>t0]), color='r', alpha=.4)
ge_th = 1e9 * fe_i[1e3 * t > t0] * params['Qe'] * params['Te'] * (
1 - params['gei']) * params['pconnec'] * params['Ntot']
sge_th = 1e9 * params['Qe'] * np.sqrt(
fe_i[1e3 * t > t0] * params['Te'] *
(1 - params['gei']) * params['pconnec'] * params['Ntot'])
ax2.plot(1e3 * t[1e3 * t > t0], ge_th, 'g-', lw=2)
ax2.fill_between(1e3 * t[1e3 * t > t0],
ge_th - sge_th,
ge_th + sge_th,
color='g',
alpha=.4)
ax2.plot(1e3 * t[1e3 * t > t0], gi_th, 'r-', lw=2)
ax2.fill_between(1e3 * t[1e3 * t > t0],
gi_th - sgi_th,
gi_th + sgi_th,
color='r',
alpha=.4)
ax1.plot(time_array[cond_t][0] * np.ones(2), [-65, -55], lw=4, color='k')
ax1.annotate('10mV', (time_array[cond_t][0], -65))
#set_plot(ax1, [], xticks=[], yticks=[])
#set_plot(ax2, ['left'], ylabel='$G$ (nS)', xticks=[])
fig, AX = plt.subplots(figsize=(5, 3))
# we bin the population rate
rate_exc = bin_array(rate_exc[cond_t], BIN, time_array[cond_t])
rate_inh = bin_array(rate_inh[cond_t], BIN, time_array[cond_t])
rate_array = bin_array(rate_array[cond_t], BIN, time_array[cond_t])
time_array = bin_array(time_array[cond_t], BIN, time_array[cond_t])
AX.plot(time_array, rate_exc, 'g-', lw=.6, label='$\\nu_e(t)$')
AX.plot(time_array, rate_inh, 'r-', lw=.6, label='$\\nu_i(t)$')
AX.plot(1000 * tfirst, fifirst, 'r--', lw=.6, label='$\\nu_i(t)$')
np.save('HH_response', [
1000 * tfirst, fefirst, fifirst, t, fe, fi, sfe, sfi,
rate_func(tfirst)
])
#AX.plot(time_array, .8*rate_exc+.2*rate_inh, 'k-', lw=2, label='$\\nu(t)$')
AX.plot(1e3 * t[1e3 * t > t0], fi[1e3 * t > t0], 'r-', label='num. sim.')
AX.plot(1e3*t[1e3*t>t0], rate_func(t[1e3*t>t0]), 'k:',\
lw=2, label='$\\nu_e^{aff}(t)$ \n $\\nu_e^{drive}$')
AX.plot(1e3 * t[1e3 * t > t0],
fe[1e3 * t > t0],
'g-',
label='mean field \n pred.')
AX.fill_between(1e3*t[1e3*t>t0], fe[1e3*t>t0]-sfe[1e3*t>t0], fe[1e3*t>t0]+sfe[1e3*t>t0],\
color='g', alpha=.3, label='mean field \n pred.')
AX.fill_between(1e3*t[1e3*t>t0], fi[1e3*t>t0]-sfi[1e3*t>t0], fi[1e3*t>t0]+sfi[1e3*t>t0],\
color='r', alpha=.3)
# AX.plot(1e3*t[1e3*t>t0], .8*fe[1e3*t>t0]+.2*fi[1e3*t>t0], 'k-', label='..')
AX.legend(prop={'size': 'xx-small'})
#set_plot(AX, ['left'], ylabel='$\\nu$ (Hz)', xticks=[], num_yticks=3)
FIGS.append(fig)
print('excitatory rate: ', rate_exc[len(rate_exc) / 2:].mean(), 'Hz')
print('inhibitory rate: ', rate_inh[len(rate_exc) / 2:].mean(), 'Hz')
print(sfe[0], sfe[-1])
plt.show()
return FIGS
def plot_ntwk_sim_output(time_array, rate_array, rate_exc, rate_inh,\
Raster_exc, Raster_inh,\
Vm_exc, Vm_inh, Ge_exc, Ge_inh, Gi_exc, Gi_inh,\
BIN=5, min_time=2000):
BIN = 15.
cond_t = (time_array > min_time) # transient behavior after 400 ms
params = get_neuron_params(args.CONFIG.split('--')[0], SI_units=True)
M = get_connectivity_and_synapses_matrix('CONFIG1', SI_units=True)
EXC_AFF = M[0, 0]['ext_drive']
print('starting fixed point')
fe0, fi0, sfe, sfie, sfi = find_fixed_point(args.CONFIG.split('--')[0], args.CONFIG.split('--')[1], 'CONFIG1',\
exc_aff=EXC_AFF, Ne=8000, Ni=2000, verbose=True)
print('end fixed point')
reformat_syn_parameters(params, M) # merging those parameters
xfe = fe0 + np.linspace(-4, 4) * sfe
fe_pred = gaussian_func(xfe, fe0, sfe)
xfi = fi0 + np.linspace(-4, 4) * sfi
fi_pred = gaussian_func(xfi, fi0, sfi)
mGe, mGi, sGe, sGi = mean_and_var_conductance(fe0 + EXC_AFF, fi0,
*pseq_params(params))
muV, sV, muGn, TvN = get_fluct_regime_vars(fe0 + EXC_AFF, fi0,
*pseq_params(params))
print("eee", muV)
FE, FI = np.meshgrid(xfe, xfi)
pFE, pFI = np.meshgrid(fe_pred, fi_pred)
MUV, SV, _, _ = get_fluct_regime_vars(
FE + EXC_AFF, FI, *pseq_params(params)) * pFE * pFI / np.sum(pFE * pFI)
### MEMBRANE POTENTIAL
MEAN_VM, STD_VM, KYRT_VM = [], [], []
for i in range(len(Vm_exc)):
MEAN_VM.append(Vm_exc[i][(time_array > min_time) & (Vm_exc[i] != -65) &
(Vm_exc[i] < -50)].mean())
MEAN_VM.append(Vm_inh[i][(time_array > min_time) & (Vm_inh[i] != -65) &
(Vm_inh[i] < -50)].mean())
for vv in [
Vm_exc[i][(time_array > min_time)],
Vm_inh[i][(time_array > min_time)]
]:
i0 = np.where((vv[:-1] > -52) & (vv[1:] < -60))[0]
print(i0)
sv = []
if len(i0) == 0:
STD_VM.append(vv.std())
elif len(i0) == 1:
STD_VM.append(vv[0].std())
else:
for i1, i2 in zip(i0[:-1], i0[1:]):
if i2 - i1 > 60:
sv.append(vv[i1 + 30:i2 - 30].std())
STD_VM.append(np.array(sv).mean())
STD_VM.append(Vm_inh[i][(time_array > min_time)
& (Vm_inh[i] < -50)].std())
fig1, AX1 = plt.subplots(1, 3, figsize=(3, 2)) # for means
fig2, AX2 = plt.subplots(1, 3, figsize=(3, 2)) # for std
AX1[0].bar([0],
np.array(MEAN_VM).mean() + 65,
yerr=np.array(MEAN_VM).std(),
color='w',
edgecolor='k',
lw=3,
error_kw=dict(elinewidth=3, ecolor='k'))
AX2[0].bar([0],
np.array(STD_VM).mean(),
yerr=np.array(STD_VM).std(),
color='w',
edgecolor='k',
lw=3,
error_kw=dict(elinewidth=3, ecolor='k'),
label='$V_m$')
AX1[0].bar([1], [1e3 * muV + 65], color='gray', alpha=.5, label='$V_m$')
AX2[0].bar([1], [1e3 * sV], color='gray', alpha=.5)
#set_plot(AX1[0], ['left'], xticks=[], ylim=[0,11], yticks=[0, 5, 10], yticks_labels=['-65', '-60', '-55'], ylabel='mean (mV)')
#set_plot(AX2[0], ['left'], xticks=[], ylim=[0,5], yticks=[0, 2, 4], ylabel='std. dev. (mV)')
### EXCITATORY CONDUCTANCE
MEAN_GE, STD_GE, KYRT_GE = [], [], []
for i in range(len(Ge_exc)):
MEAN_GE.append(Ge_exc[i][(time_array > min_time)].mean())
MEAN_GE.append(Ge_inh[i][(time_array > min_time)].mean())
STD_GE.append(Ge_exc[i][(time_array > min_time)].std())
STD_GE.append(Ge_inh[i][(time_array > min_time)].std())
AX1[1].bar([0],
np.array(MEAN_GE).mean(),
yerr=np.array(MEAN_GE).std(),
color='w',
edgecolor='g',
lw=3,
error_kw=dict(elinewidth=3, ecolor='g'),
label='num. sim.')
AX2[1].bar([0],
np.array(STD_GE).mean(),
yerr=np.array(STD_GE).std(),
color='w',
edgecolor='g',
lw=3,
error_kw=dict(elinewidth=3, ecolor='g'),
label='exc.')
AX1[1].bar([1], [1e9 * mGe], color='g', label='mean field \n pred.')
AX2[1].bar([1], [1e9 * sGe], color='g', label='exc.')
#set_plot(AX1[1], ['left'], xticks=[], yticks=[0,15,30], ylabel='mean (nS)')
#set_plot(AX2[1], ['left'], xticks=[], yticks=[0,5,10], ylabel='std. dev. (nS)')
### INHIBITORY CONDUCTANCE
MEAN_GI, STD_GI, KYRT_GI = [], [], []
for i in range(len(Gi_exc)):
MEAN_GI.append(Gi_exc[i][(time_array > min_time)].mean())
MEAN_GI.append(Gi_inh[i][(time_array > min_time)].mean())
STD_GI.append(Gi_exc[i][(time_array > min_time)].std())
STD_GI.append(Gi_inh[i][(time_array > min_time)].std())
AX1[2].bar([0],
np.array(MEAN_GI).mean(),
yerr=np.array(MEAN_GI).std(),
color='w',
edgecolor='r',
lw=3,
error_kw=dict(elinewidth=3, ecolor='r'),
label='num. sim.')
AX2[2].bar([0],
np.array(STD_GI).mean(),
yerr=np.array(STD_GI).std(),
color='w',
edgecolor='r',
lw=3,
error_kw=dict(elinewidth=3, ecolor='r'),
label='inh.')
AX1[2].bar([1], [1e9 * mGi], color='r', label='mean field \n pred.')
AX2[2].bar([1], [1e9 * sGi], color='r', label='inh.')
#set_plot(AX1[2], ['left'], xticks=[], yticks=[0,15,30], ylabel='mean (nS)')
#set_plot(AX2[2], ['left'], xticks=[], yticks=[0,5,10], ylabel='std. dev. (nS)')
### POPULATION RATE ###
fig, ax = plt.subplots(figsize=(4, 3))
# we bin the population rate
N0 = int(BIN / (time_array[1] - time_array[0]))
N1 = int((time_array[cond_t][-1] - time_array[cond_t][0]) / BIN)
time_array = time_array[cond_t][:N0 * N1].reshape((N1, N0)).mean(axis=1)
rate_exc = rate_exc[cond_t][:N0 * N1].reshape((N1, N0)).mean(axis=1)
rate_inh = rate_inh[cond_t][:N0 * N1].reshape((N1, N0)).mean(axis=1)
rate_array = rate_array[cond_t][:N0 * N1].reshape((N1, N0)).mean(axis=1)
hh, bb = np.histogram(rate_exc, bins=3, normed=True)
ax.bar(.5 * (bb[:-1] + bb[1:]),
hh,
color='w',
width=bb[1] - bb[0],
edgecolor='g',
lw=3,
label='exc.',
alpha=.7)
hh, bb = np.histogram(rate_inh, bins=5, normed=True)
ax.bar(.5 * (bb[:-1] + bb[1:]),
hh,
color='w',
width=bb[1] - bb[0],
edgecolor='r',
lw=3,
label='inh',
alpha=.7)
ax.fill_between(xfe, 0 * fe_pred, fe_pred, color='g', alpha=.8)
ax.fill_between(xfi, 0 * fi_pred, fi_pred, color='r', alpha=.8)
#set_plot(plt.gca(), ['bottom', 'left'], xlabel='pop. activity (Hz)', yticks=[], ylabel='density')
for ax in AX1:
ax.legend()
for ax in AX2:
ax.legend()
return [fig, fig1, fig2]
def Euler_method_for_ring_model(NRN1, NRN2, NTWK, RING, STIM, BIN=5e-3,\
custom_ring_params={}, custom_stim_params={}):
"""
Given two afferent rate input excitatory and inhibitory respectively
this function computes the prediction of a first order rate model
(e.g. Wilson and Cowan in the 70s, or 1st order of El Boustani and
Destexhe 2009) by implementing a simple Euler method
IN A 2D GRID WITH LATERAL CONNECTIVITY
the number of laterally connected units is 'connected_neighbors'
there is an exponential decay of the strength 'decay_connect'
----------------------------------------------------------------
the core of the formalism is the transfer function, see Zerlaut et al. 2015
it can also be Kuhn et al. 2004 or Amit & Brunel 1997
-----------------------------------------------------------------
nu_0 is the starting value value of the recurrent network activity
it should be the fixed point of the network dynamics
-----------------------------------------------------------------
t is the discretization used to solve the euler method
BIN is the initial sampling bin that should correspond to the
markovian time scale where the formalism holds (~5ms)
conduction_velocity=0e-3, in ms per pixel !!!
"""
print('----- loading parameters [...]')
M = get_connectivity_and_synapses_matrix(NTWK, SI_units=True)
ext_drive = M[0, 0]['ext_drive']
params = get_neuron_params(NRN2, SI_units=True)
reformat_syn_parameters(params, M)
afferent_exc_fraction = M[0, 0]['afferent_exc_fraction']
print('----- ## we look for the fixed point [...]')
try:
fe0, fi0, muV0 = np.load("fixed_point_data_TO_BE_REMOVED.npy")
print(
"/!\\ STORED FIXED POINT DATA LOADED, check if not a different config /!\\"
)
except IOError:
fe0, fi0 = find_fixed_point_first_order(NRN1,
NRN2,
NTWK,
exc_aff=ext_drive)
muV0, _, _, _ = get_fluct_regime_vars(fe0 + ext_drive, fi0,
*pseq_params(params))
np.save('fixed_point_data_TO_BE_REMOVED.npy', [fe0, fi0, muV0])
print('----- ## we load the transfer functions [...]')
TF1, TF2 = load_transfer_functions(NRN1, NRN2, NTWK)
print('----- ## ring initialisation [...]')
X, Xn_exc, Xn_inh, exc_connected_neighbors, exc_decay_connect, inh_connected_neighbors,\
inh_decay_connect, conduction_velocity = ring.pseq_ring_params(RING, custom=custom_ring_params)
print('----- ## stimulation initialisation [...]')
t, Fe_aff = stim.get_stimulation(X, STIM, custom=custom_stim_params)
Fi_aff = 0 * Fe_aff # no afferent inhibition yet
print('----- ## model initialisation [...]')
Fe, Fi, muVn = 0 * Fe_aff + fe0, 0 * Fe_aff + fi0, 0 * Fe_aff + muV0
print('----- starting the temporal loop [...]')
dt = t[1] - t[0]
# constructing the Euler method for the activity rate
for i_t in range(len(t) - 1): # loop over time
for i_x in range(len(X)): # loop over pixels
# afferent excitation + exc DRIVE
fe = (1 - afferent_exc_fraction) * Fe_aff[
i_t, i_x] + ext_drive # common both to exc and inh
fe_pure_exc = (2 * afferent_exc_fraction -
1) * Fe_aff[i_t, i_x] # only for excitatory pop
fi = 0 # 0 for now.. !
# EXC --- we add the recurrent activity and the lateral interactions
for i_xn in Xn_exc: # loop over neighboring excitatory pixels
# calculus of the weight
exc_weight = ring.gaussian_connectivity(
i_xn, 0., exc_decay_connect)
# then we have folded boundary conditions (else they donot
# have all the same number of active neighbors !!)
i_xC = (i_x + i_xn) % (len(X))
if i_t > int(abs(i_xn) / conduction_velocity / dt):
it_delayed = i_t - int(
abs(i_xn) / conduction_velocity / dt)
else:
it_delayed = 0
fe += exc_weight * Fe[it_delayed, i_xC]
# INH --- we add the recurrent activity and the lateral interactions
for i_xn in Xn_inh: # loop over neighboring inhibitory pixels
# calculus of the weight
inh_weight = ring.gaussian_connectivity(
i_xn, 0., inh_decay_connect)
# then we have folded boundary conditions (else they donot
# have all the same number of active neighbors !!)
i_xC = (i_x + i_xn) % (len(X))
if i_t > int(abs(i_xn) / conduction_velocity / dt):
it_delayed = i_t - int(
abs(i_xn) / conduction_velocity / dt)
else:
it_delayed = 0
fi += inh_weight * Fi[it_delayed, i_xC]
## NOTE THAT NO NEED TO SCALE : fi*= gei*pconnec*Ntot and fe *= (1-gei)*pconnec*Ntot
## THIS IS DONE IN THE TRANSFER FUNCTIONS !!!!
# now we can guess the rate model output
muVn[i_t + 1,
i_x], _, _, _ = get_fluct_regime_vars(fe, fi,
*pseq_params(params))
Fe[i_t + 1,
i_x] = Fe[i_t, i_x] + dt / BIN * (TF1(fe + fe_pure_exc, fi) -
Fe[i_t, i_x])
Fi[i_t + 1,
i_x] = Fi[i_t, i_x] + dt / BIN * (TF2(fe, fi) - Fi[i_t, i_x])
print('----- temporal loop over !')
return t, X, Fe_aff, Fe, Fi, np.abs((muVn - muV0) / muV0)
def TF2(fe, fi):
return TF_my_template(fe, fi, *pseq_params(params2))
def TF1(fe, fi):
return TF_my_template(fe, fi, *pseq_params(params1))