def funbgh2(s, a, b, R, df):
n = len(a)
sqrt_df = np.sqrt(df)
#np.power(s, df-1) * np_exp(-s*s*0.5)
return np_exp((df-1)*np_log(s)-s*s*0.5) \
* mvstdnormcdf(s*a/sqrt_df, s*b/sqrt_df, R[np.tril_indices(n, -1)],
maxpts=1000000, abseps=1e-4)
def funbgh2(s, a, b, R, df):
n = len(a)
sqrt_df = np.sqrt(df)
#np.power(s, df-1) * np_exp(-s*s*0.5)
return np_exp((df-1)*np_log(s)-s*s*0.5) \
* mvstdnormcdf(s*a/sqrt_df, s*b/sqrt_df, R[np.tril_indices(n, -1)],
maxpts=1000000, abseps=1e-4)
def funbgh(s, a, b, R, df):
sqrt_df = np.sqrt(df+0.5)
ret = chi_logpdf(s,df)
ret += np_log(mvstdnormcdf(s*a/sqrt_df, s*b/sqrt_df, R,
maxpts=1000000, abseps=1e-6))
ret = np_exp(ret)
return ret
def inner(start_time, end_time):
mkv_data = pitcache_getter(mkvdata_name,
50).get_tsdata(start_time, end_time)
mask = np_isclose(mkv_data, 0, 0.01)
data = mkv_data.where(~mask)
data = np_log(mkv_data)
if not check_completeness(data.index, start_time, end_time):
raise ValueError('Data missed!')
return data
def funbgh(s, a, b, R, df):
sqrt_df = np.sqrt(df + 0.5)
ret = chi_logpdf(s, df)
ret += np_log(
mvstdnormcdf(s * a / sqrt_df,
s * b / sqrt_df,
R,
maxpts=1000000,
abseps=1e-6))
ret = np_exp(ret)
return ret
def my_dist(a, b):
if a[2] == b[2]:
a_t = (a[0] + np_pi) / 2
b_t = (b[0] + np_pi) / 2
a_r = a[1]
b_r = b[1]
return 10 * ((1. - np_cos(np_abs(a_t - b_t))) +
np_log(np_abs(a_r - b_r) + 1.) / 5.)
else:
return 20.0
def precision(PE):
""" Calculate precision as the inverse variance of the updated prediction error.
return updated precision and updated average_free_energy
"""
with np.errstate(all='raise'):
try:
variance = np_var(PE) # np_var(PE, ddof=1) # mad(PE)
variance = variance if variance > 0.00001 else 0.00001 # so log(var) should max at -5
pi = np_log(1. / variance) # should max at 5
new_precision = 1 / (1 + np.exp(-(pi - 2.5))
) # should be about max. 1
return new_precision # , variance
except Exception as e:
raise Exception("RuntimeWarning in precision(PE):", str(e), "PE:",
PE) from e
def inner(start_time, end_time):
start_time, end_time = trans_date(start_time, end_time)
cache_size = 100
offset = major_mul * minor_mul
threshold = 1e-5
start_time_shifted = get_calendar('stock.sse').\
shift_tradingdays(start_time, -offset - 20)
to_data = pitcache_getter('TO_RATE', cache_size).\
get_tsdata(start_time_shifted, end_time)
data = to_data.rolling(offset,
min_periods=offset).sum().dropna(how='all')
data[data <= threshold] = np_nan
data = data / major_mul
data = np_log(data)
data = data.loc[(data.index >= start_time) & (data.index <= end_time)]
if start_time > trans_date(DATA_START_DATE):
if not check_completeness(data.index, start_time, end_time):
raise ValueError('Data missed!')
return data
def rqa_entr(self, th, l_min):
try:
self.rplot
except AttributeError:
return -1
try:
return self.entr[str(th)][str(l_min)]
except KeyError:
try:
self.entr[str(th)]
except KeyError:
self.entr[str(th)] = {}
l, p = self._rqa_lv_dist_min(th,
l_min,
self.rqa_l_freq_dist,
ret_sum=0)
pp = p / np_sum(p)
self.entr[str(th)][str(l_min)] = -pp.dot(np_log(pp))
return self.entr[str(th)][str(l_min)]
import torch
import torch.nn as nn
from torch.autograd import Variable
import torch.nn.functional as F
from convgru import ConvGRUCell
from gen_models import make_conv_net, make_fc_net, make_upconv_net
import rlkit.torch.pytorch_util as ptu
import numpy as np
from numpy import pi
from numpy import log as np_log
log_2pi = np_log(2*pi)
LOG_COV_MAX = 2
LOG_COV_MIN = -5
class MaskedNormalVAE(nn.Module):
def __init__(
self,
maze_dims,
z_dim,
encoder_specs,
decoder_specs
):
super().__init__()
in_ch = maze_dims[0]
in_h = maze_dims[1]
def mk_sencircuit_2cplastic(task_info):
"""
Creates balanced network representing sensory circuit with 2c model in the excitatory neurons.
returns:
groups, synapses, subgroups
groups and synapses have to be added to the "Network" in order to run the simulation
subgroups is used for establishing connections between the sensory and integration circuit;
do not add subgroups to the "Network"
psr following the published Brian1 code in DB model from Wimmer et al. 2015
- brain2 code
- two-compartmental model following Naud & Sprekeler 2018
- implementation runs in cpp_standalone mode, compatible with SNEP
"""
from numpy import log as np_log
# -------------------------------------
# Sensory circuit parameters
# -------------------------------------
# populations
N_E = task_info['sen']['populations']['N_E'] # total number of E neurons
sub = task_info['sen']['populations']['sub'] # fraction corresponding to subpops 1,2
N_E1 = int(N_E * sub) # size of exc subpops that responds to the stimuli
N_I = task_info['sen']['populations']['N_I'] # total number of I neurons
N_X = task_info['sen']['populations']['N_X'] # size of external pop
# local recurrent connections
eps = task_info['sen']['connectivity']['eps'] # connection probability for EE, EI, IE and II
w_p = task_info['sen']['connectivity']['w_p'] # relative synaptic strength within pop E1 and E2
w_m = 2 - w_p # relative synaptic strength across pop E1 and E2
gEEs = task_info['sen']['2c']['gEEs'] # weight of EE synapses, prev: 0.7589*nS
gEI = task_info['sen']['connectivity']['gEI'] # weight of EI synapses, prev: 1.5179*nS
gIEs = task_info['sen']['2c']['gIEs'] # weight of IE synapses, prev: 12.6491*nS
gII = task_info['sen']['connectivity']['gII'] # weight of II synapses
gmax = task_info['sen']['connectivity']['gmax'] # maximum synaptic weight
dE = '0.5*ms + rand()*1.0*ms' # range of transmission delays of E synapses, (0.5:1.5)
dI = '0.1*ms + rand()*0.8*ms' # range of transmission delays of I synapses, (0.1:0.9)
# external connections
epsX = task_info['sen']['connectivity']['epsX'] # connection probability for ext synapses
alphaX = task_info['sen']['connectivity']['alphaX'] # 0: global input, 1: local input
gXEs = task_info['sen']['2c']['gXEs'] # weight of ext to E synapses of soma
gXI = task_info['sen']['connectivity']['gXI'] # weight of ext to I synapses
dX = '0.5*ms + rand()*1.0*ms' # range of transmission delays of X synapses, (0.5:1.5)
# neuron model
CmI = task_info['sen']['neuron']['CmI'] # membrane capacitance of I neurons
gleakI = task_info['sen']['neuron']['gleakI'] # leak conductance of I neurons
Vl = task_info['sen']['neuron']['Vl'] # reversal potential
Vt = task_info['sen']['neuron']['Vt'] # threshold potential
Vr = task_info['sen']['neuron']['Vr'] # reset potential, only for inh
tau_refI = task_info['sen']['neuron']['tau_refI'] # absolute refractory period of I neurons
nu_ext = task_info['sen']['neuron']['nu_ext'] # rate of external Poisson neurons, prev: 12.5*Hz
# soma
taus = task_info['sen']['2c']['taus'] # timescale of membrane potential
Cms = task_info['sen']['2c']['Cms'] # capacitance
gleakEs = Cms/taus
tauws = task_info['sen']['2c']['tauws'] # timescale of recovery ("slow") variable
bws = task_info['sen']['2c']['bws'] # strength of spike-triggered facilitation (bws < 0)
gCas = task_info['sen']['2c']['gCas'] # strenght of forward calcium spike propagation
tau_refE = task_info['sen']['2c']['tau_refE'] # refractory period
# dendrite
taud = task_info['sen']['2c']['taud']
Cmd = task_info['sen']['2c']['Cmd']
gleakEd = Cmd/taud
tauwd = task_info['sen']['2c']['tauwd'] # timescale of recovery ("slow") variable
awd = task_info['sen']['2c']['awd'] # stregth of subthreshold facilitations (awd < 0)
gCad = task_info['sen']['2c']['gCad'] # strength of local regenerative activity
bpA = task_info['sen']['2c']['bpA'] # strength of backpropagation activity (c variable)
k1 = task_info['sen']['2c']['k1'] # rectangular kernel for backpropagating activity
k2 = task_info['sen']['2c']['k2'] # if t in [0.5, 2.0] we'll have backpropagating current
muOUs = task_info['sen']['2c']['muOUs'] # OU parameters for background noise of soma
#muOUd = task_info['sen']['2c']['muOUd'] # OU parameters for background noise of dendrites
sigmaOU = task_info['sen']['2c']['sigmaOU']
tauOU = task_info['sen']['2c']['tauOU']
# synapse models
VrevE = task_info['sen']['synapse']['VrevE'] # reversal potential for E synapses
VrevI = task_info['sen']['synapse']['VrevI'] # reversal potential for I synapses in inh
tau_decay = task_info['sen']['synapse']['tau_decay'] # decay constant of AMPA, GABA
tau_rise = task_info['sen']['synapse']['tau_rise'] # rise constant of AMPA, GABA for inh
VrevIsd = task_info['sen']['synapse']['VrevIsd'] # rev potential for I synapses in soma, dend
# plasticity in dendrites
eta0 = task_info['sen']['2c']['eta0']
tauB = task_info['sen']['2c']['tauB']
targetB = task_info['targetB']
B0 = tauB*targetB
tau_update = task_info['sen']['2c']['tau_update']
eta = eta0 * tau_update / tauB
validburst = task_info['sen']['2c']['validburst'] # if tau_burst = 4*ms, at 16 ms stopburst = 0.0183
min_burst_stop = task_info['sen']['2c']['min_burst_stop'] # thus, we will set it at critrefburst = 0.02
tau_burst = -validburst / np_log(min_burst_stop) * second
param2c = {'gEE': gEEs, 'gEI': gEI, 'gIE': gIEs, 'gII': gII, 'gmax': gmax, 'gXEs': gXEs, 'gXI': gXI,
'gleakEs': gleakEs, 'gleakEd': gleakEd, 'gleakI': gleakI, 'Cms': Cms, 'Cmd': Cmd, 'CmI': CmI,
'Vl': Vl, 'Vt': Vt, 'Vr': Vr, 'VrevE': VrevE, 'VrevIsd': VrevIsd, 'VrevI': VrevI,
'taus': taus, 'taud': taud, 'tau_refE': tau_refE, 'tau_refI': tau_refI,
'tau_decay': tau_decay, 'tau_rise': tau_rise, 'tau_ws': tauws, 'tau_wd': tauwd,
'bws': bws, 'awd': awd, 'gCas': gCas, 'gCad': gCad, 'bpA': bpA, 'k1': k1, 'k2': k2,
'muOUs': muOUs, 'tauOU': tauOU, 'sigmaOU': sigmaOU,
'w_p': w_p, 'w_m': w_m, 'sub': sub, 'eps': eps, 'epsX': epsX, 'alphaX': alphaX,
'eta': eta, 'B0': B0, 'tauB': tauB, 'tau_burst': tau_burst, 'min_burst_stop': min_burst_stop}
# numerical integration method
nummethod = task_info['simulation']['nummethod']
# -------------------------------------
# Set up model and connections
# -------------------------------------
# neuron equations
eqss = '''
dV/dt = (-g_ea*(V-VrevE) -g_i*(V-VrevIsd) -(V-Vl))/tau + (gCas/(1+exp(-(V_d/mV + 38)/6)) + w_s + I)/Cm : volt (unless refractory)
dg_ea/dt = (-g_ea + x_ea) / tau_decay : 1
dx_ea/dt = -x_ea / tau_rise : 1
dg_i/dt = (-g_i + x_i) / tau_decay : 1
dx_i/dt = -x_i / tau_rise : 1
dw_s/dt = -w_s / tau_ws : amp
tau = taus : second
Cm = Cms : farad
I = Irec(t, i) : amp
V_d : volt (linked)
B : 1 (linked)
burst_start : 1 (linked)
burst_stop : 1 (linked)
muOUd : amp (linked)
'''
# dIbg/dt = (muOUs - Ibg) / tauOU + (sigmaOU * xi) / sqrt(tauOU / 2) : amp --> they have I_Ext
eqsd = '''
dV_d/dt = (-g_ea*(V_d-VrevE) -(V_d-Vl))/tau + (gCad/(1+exp(-(V_d/mV + 38)/6)) + w_d + K + Ibg)/Cm : volt
dg_ea/dt = (-g_ea + x_ea) / tau_decay : 1
dx_ea/dt = -x_ea / tau_rise : 1
dw_d/dt = (-w_d + awd*(V_d - Vl))/tau_wd : amp
dIbg/dt = (muOUd - Ibg) / tauOU + (sigmaOU * xi) / sqrt(tauOU / 2) : amp
K = bpA * (((t-lastspike_soma) >= k1) * ((t-lastspike_soma) <= k2)) : amp
dB/dt = -B / tauB : 1
dburst_start/dt = -burst_start / tau_burst : 1 (unless refractory)
dburst_stop/dt = -burst_stop / tau_burst : 1
tau = taud : second
Cm = Cmd : farad
muOUd : amp
lastspike_soma : second (linked)
'''
eqsI = '''
dV/dt = (-g_ea*(V-VrevE) -g_i*(V-VrevI) -(V-Vl))/tau + I/Cm : volt (unless refractory)
dg_ea/dt = (-g_ea + x_ea) / tau_decay : 1
dx_ea/dt = -x_ea / tau_rise : 1
dg_i/dt = (-g_i + x_i) / tau_decay : 1
dx_i/dt = -x_i / tau_rise : 1
tau = CmI/gleakI : second
Cm = CmI : farad
I : amp
'''
# neuron groups
soma = NeuronGroup(N_E, model=eqss, method=nummethod, threshold='V>=Vt',
reset='''V = Vl
w_s += bws
burst_start += 1
burst_stop = 1''',
refractory=tau_refE, namespace=param2c, name='soma')
dend = NeuronGroup(N_E, model=eqsd, method=nummethod, threshold='burst_start > 1 + min_burst_stop',
reset='''B += 1
burst_start = 0''',
refractory='burst_stop >= min_burst_stop',
namespace=param2c, name='dend')
senI = NeuronGroup(N_I, model=eqsI, method=nummethod, threshold='V>=Vt', reset='V=Vr',
refractory=tau_refI, namespace=param2c, name='senI')
# linked variables
soma.V_d = linked_var(dend, 'V_d')
soma.B = linked_var(dend, 'B')
soma.burst_start = linked_var(dend, 'burst_start')
soma.burst_stop = linked_var(dend, 'burst_stop')
soma.muOUd = linked_var(dend, 'muOUd')
dend.lastspike_soma = linked_var(soma, 'lastspike')
# subgroups
soma1 = soma[:N_E1]
dend1 = dend[:N_E1]
soma2 = soma[N_E1:]
dend2 = dend[N_E1:]
# update muOUd with plasticity rule
dend1.muOUd = '-50*pA - rand()*100*pA' # random initialisation of weights -50:-150 pA
dend1.run_regularly('muOUd = clip(muOUd - eta * (B - B0), -100*amp, 0)', dt=tau_update)
# TODO: check the target vs burst rate convergence
# TODO: try tau_B = 50,000 sec, but mayb\e this is not the case because you do reach the target
# synapses
# weight according the different subgroups
condsame = '(i<N_pre*sub and j<N_post*sub) or (i>=N_pre*sub and j>=N_post*sub)'
conddiff = '(i<N_pre*sub and j>=N_post*sub) or (i>=N_pre*sub and j<N_post*sub)'
# AMPA: exc --> exc
synSESE = Synapses(soma, soma, model='w : 1', method=nummethod,
on_pre='''x_ea += w
w = clip(w, 0, gmax)''',
namespace=param2c, name='synSESE')
synSESE.connect(p='eps')
synSESE.w[condsame] = 'w_p * gEE/gleakEs * (1 + randn()*0.5)'
synSESE.w[conddiff] = 'w_m * gEE/gleakEs * (1 + randn()*0.5)'
synSESE.delay = dE
# AMPA: exc --> inh
synSESI = Synapses(soma, senI, model='w : 1', method=nummethod,
on_pre='''x_ea += w
w = clip(w, 0, gmax)''',
namespace=param2c, name='synSESI')
synSESI.connect(p='eps')
synSESI.w = 'gEI/gleakI * (1 + randn()*0.5)'
synSESI.delay = dE
# GABA: inh --> exc
synSISE = Synapses(senI, soma, model='w : 1', method=nummethod,
on_pre='''x_i += w
w = clip(w, 0, gmax)''',
namespace=param2c, name='synSISE')
synSISE.connect(p='eps')
synSISE.w = 'gIE/gleakEs * (1 + randn()*0.5)'
synSISE.delay = dI
# GABA: inh --> inh
synSISI = Synapses(senI, senI, model='w : 1', method=nummethod,
on_pre='''x_i += w
w = clip(w, 0, gmax)''',
namespace=param2c, name='synSISI')
synSISI.connect(p='eps')
synSISI.w = 'gII/gleakI * (1 + randn()*0.5)'
synSISI.delay = dI
# external inputs and synapses
extS = PoissonGroup(N_X, rates=nu_ext)
synSXSEs = Synapses(extS, soma, model='w : 1', method=nummethod,
on_pre='''x_ea += w
w = clip(w, 0, gmax)''',
namespace=param2c, name='synSXSEs')
synSXSEs.connect(condition=condsame, p='epsX * (1 + alphaX)')
synSXSEs.connect(condition=conddiff, p='epsX * (1 - alphaX)')
synSXSEs.w = 'gXEs/gleakEs * (1 + randn()*0.5)'
synSXSEs.delay = dX
synSXSI = Synapses(extS, senI, model='w : 1', method=nummethod,
on_pre='''x_ea += w
w = clip(w, 0, gmax)''',
namespace=param2c, name='synSXSI')
synSXSI.connect(p='epsX')
synSXSI.w = 'gXI/gleakI * (1 + randn()*0.5)'
synSXSI.delay = dX
# external inputs to dendrites mimicking decision circuit
subDE = 240
rateDE = 40*Hz # TODO: lower rate --> 40 or 30
d = 1*ms
wDS = 0.06
XDE = PoissonGroup(subDE, rates=rateDE)
synXDEdend = Synapses(XDE, dend1, model='w : 1', method=nummethod, delay=d,
on_pre='x_ea += w',
namespace=param2c, name='synXDEdend')
synXDEdend.connect(p=0.2)
synXDEdend.w = 'wDS'
# variables to return
groups = {'soma': soma, 'dend': dend, 'SI': senI, 'SX': extS, 'XDE': XDE}
subgroups = {'soma1': soma1, 'soma2': soma2,
'dend1': dend1, 'dend2': dend2}
synapses = {'synSESE': synSESE, 'synSESI': synSESI,
'synSISE': synSISE, 'synSISI': synSISI,
'synSXSI': synSXSI, 'synSXSEs': synSXSEs,
'synXDEdend': synXDEdend}
return groups, synapses, subgroups
def chi_logpdf(x, df):
tmp = (df-1.)*np_log(x) + (-x*x*0.5) - (df*0.5-1)*np_log(2.0) \
- sps_gammaln(df*0.5)
return tmp
def chi_logpdf(x, df):
tmp = (df-1.)*np_log(x) + (-x*x*0.5) - (df*0.5-1)*np_log(2.0) \
- sps_gammaln(df*0.5)
return tmp
def kl_div(P, Q):
# optimized KLD
kld = np_sum(_p * np_log(_p / _q) for _p, _q in zip(P, Q) if _p != 0)
return kld if kld != np.inf else 0.
def log_(n, base=3):
return np_log(n) / np_log(base)
def logarithmize(self):
result_df = np_log(self._df)
return Curve("", self._df.X, result_df.Y)
