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mesoscopic_model.py
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mesoscopic_model.py
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# ------------------------------------------------------------------------------ #
# @Author: Victor Buendia Ruiz-Azuaga
# @Email: vbuendiar@onsager.ugr.es
# ------------------------------------------------------------------------------ #
from genericpath import exists
import numpy as np
import pandas as pd
import os
import h5py
import logging
import warnings
logging.basicConfig(level=logging.INFO, format="%(levelname)-8s [%(name)s] %(message)s")
log = logging.getLogger(__name__)
log.setLevel("WARNING")
warnings.filterwarnings("ignore") # suppress numpy warnings
try:
from numba import jit, prange
# raise ImportError
log.info("Using numba for parallelizable functions")
try:
from numba.typed import List
except:
# older numba versions dont have this
def List(*args):
return list(*args)
# silence deprications
try:
from numba.core.errors import (
NumbaDeprecationWarning,
NumbaPendingDeprecationWarning,
)
warnings.simplefilter("ignore", category=NumbaDeprecationWarning)
warnings.simplefilter("ignore", category=NumbaPendingDeprecationWarning)
except:
pass
except ImportError:
log.info("Numba not available, skipping compilation")
# replace numba functions if numba not available:
# we only use jit and prange
# helper needed for decorators with kwargs
def parametrized(dec):
def layer(*args, **kwargs):
def repl(f):
return dec(f, *args, **kwargs)
return repl
return layer
@parametrized
def jit(func, **kwargs):
return func
def prange(*args):
return range(*args)
def List(*args):
return list(*args)
# fmt:off
# see `simulate_model` parameter description
default_pars = dict(
gating_mechanism = True,
max_rsrc = 1.0, # @victor used to be 2
tau_charge = 40.0,
tau_discharge = 5.0,
tau_rate = 1.0,
sigma = 0.1,
w0 = 0.01,
tau_disconnect = 1.0,
tau_connect = 20.0, # @victor used to be 1/50
ext_str = 0.0,
k_inpt = 1.6,
thrs_inpt = 0.2, # @victor used to be 0.4
gain_inpt = 20.0, # @victor used to be 10
thrs_gate = 0.5,
k_gate = 10.0,
dt = 0.01,
rseed = None,
)
# fmt:on
def simulate_model(simulation_time, **kwargs):
"""
Simulate the mesoscopic model with the given parameters.
# Parameters:
simulation_time: float
Duration of the simulation in arbitrary units. use 1000 as a starting point
gating_mechanism : bool, optional
Control whether the gating mechanism is used (default: True).
If False, gates are not updated and activity can pass at all times.
max_rsrc : float, optional
Maximum amount of synaptic resources.
tau_charge : float, optional
Timescale of synaptical resource charging
tau_discharge : float, optional
Timescale of synaptical resource discharge
tau_rate : float, optional
Timescale of firing rate (activity) going to zero (exponential decay)
sigma : float, optional
Strength of background noise fluctuations
w0 : float, optional
Coupling strenght between different nodes
tau_disconnect : float, optional
Timescale of gate becoming inactive, thus not letting activity go through
tau_connect : float, optional
Timescale of gate recovery
ext_str : float or np array of floats, optional
Stimulation strength (for each module)
k_inpt : float, optional
Knee of the input sigmoid
thrs_inpt: float, optional
Threshold for the non-linear sigmoidal function mapping input to rate change
Any activity which falls below this value will not affect the module
gain_inpt : float, optional
Gain that multiplies the result of the sigmoidal function,
thus increasing the effect of the input
thrs_gate : float, optional
Threshold of activity needed in order to be able to affect the gate. Levels
of activity below cannot inactivate a gate.
k_gate : float, optional
Knee of the gate's response sigmoid
dt : float, optional
Timestep of the Euler integrator (default=0.01)
rseed : int, optional
Use a custom random seed to ensure reproducitibility.
If None (default), will use whatever Numpy selects
# Returns
time_axis : 1d array,
time stamps for all other timeseries
activity : 2d array,
timeseries of module rate. Shape: (n_module, n_timepoints)
resources : 2d array,
timeseries of module resources. Shape: (n_module, n_timepoints)
"""
pars = default_pars.copy()
for key, value in kwargs.items():
assert key in default_pars.keys(), f"unknown kwarg for mesoscopic model: '{key}'"
pars[key] = value
# make sure ext_str is upcast from float to vector of floats
try:
len(pars["ext_str"])
except TypeError:
log.debug("ext_str is a float, upcasting to array")
pars["ext_str"] = np.array([pars["ext_str"]])
if len(pars["ext_str"]) == 1:
pars["ext_str"] = pars["ext_str"] * np.ones(4)
elif len(pars["ext_str"]) == 4:
pass
else:
raise ValueError("ext_str must be a float or a vector of length 4")
log.debug(f"ext_str: {pars['ext_str']}")
return _simulate_model(simulation_time, **pars)
@jit(nopython=True, parallel=False, fastmath=False, cache=True)
def _simulate_model(
simulation_time,
gating_mechanism,
max_rsrc,
tau_charge,
tau_discharge,
tau_rate,
sigma,
w0,
tau_disconnect,
tau_connect,
# to do partial stimulation, we need this to be a vector.
# wrap correctly on the python side.
ext_str,
k_inpt,
thrs_inpt,
gain_inpt,
thrs_gate,
k_gate,
dt,
rseed,
):
"""
This guy is wrapped, so we can set default arguments via the dictionary.
Numba does not like this.
"""
# Set random seed
if rseed != None:
np.random.seed(rseed)
thermalization_time = simulation_time * 0.1
simulation_time = simulation_time + thermalization_time
# Binnings associated to such a time
nt = int(simulation_time / dt)
GATE_CONNECTED = 1 # allow transmission
GATE_DISCONNECTED = 0 # nothing goes through
# time series of variables
# activity (firing rate), init to random
rate = np.ones(shape=(4, nt), dtype="float") * np.nan
rate[:, 0] = np.random.rand(4)
# resources
rsrc = np.ones(shape=(4, nt), dtype="float") * np.nan
rsrc[:, 0] = np.random.rand(4) * max_rsrc
# state of each gate at this time (directed) gate[from, to]
gate = np.ones(shape=(4, 4), dtype="int") * GATE_CONNECTED
# keep track of geates. lets keep the shape simple and set all non-existing gates to zero.
gate_history = np.zeros(shape=(4, 4, nt), dtype="int")
# Coupling matrix
Aij = np.zeros(shape=(4, 4), dtype="int") # Adjacency matrix
Aij[0, 1] = 1
Aij[1, 0] = 1
Aij[0, 2] = 1
Aij[2, 0] = 1
Aij[1, 3] = 1
Aij[3, 1] = 1
Aij[2, 3] = 1
Aij[3, 2] = 1
# Auxiliary shortcut to pre-compute this constant
# which is used in sigmoid transfer function
aux_thrsig = np.exp(k_inpt * thrs_inpt)
# -------------
# Simulation
# -------------
# Main computation loop: Milstein algorithm, assuming Ito interpretation
for t in range(nt - 1):
# Update each module, `src` -> source module, `tar` -> target module
for tar in range(4):
# Collect the part of input that arrives from other modules
module_input = 0.0
for src in range(4):
# connection matrix. [from, to]. ajj is 0.
if Aij[src, tar] == 1:
# Sum input to module tar, only through open gates
if gate[src, tar] == GATE_CONNECTED:
module_input += w0 * rate[src, t] * rsrc[src, t]
# this should not happen.
# @victor, can you confirm, that we do not need this?
# module_input *= 0.5
# Collect pieces to update our firing rate, Milstein algorithm
# Spontaneous decay, firing rate to zero
term1 = dt * (-rate[tar, t] / tau_rate)
# Input from all sources, recurrent, neighbours, external
total_input = rsrc[tar, t] * rate[tar, t] + module_input + ext_str[tar]
term2 = dt * transfer_function(
total_input,
gain_inpt,
k_inpt,
thrs_inpt,
aux_thrsig,
)
# additive noise
# @victor: noise only gets added with sqrt dt?
term3 = np.sqrt(dt) * np.random.standard_normal() * sigma
rate[tar, t + 1] = rate[tar, t] + term1 + term2 + term3
# resources are easier
rsrc[tar, t + 1] = rsrc[tar, t] + dt * (
-(rate[tar, t] * rsrc[tar, t]) / tau_discharge
+ (max_rsrc - rsrc[tar, t]) / tau_charge
)
# update gates for next time step
old_gate = gate.copy()
for src in range(4):
for tar in range(4):
# Store gate history for export, before updating [from, to, time]
gate_history[src, tar, t] = gate[src, tar]
gate_history[src, tar, t] = gate[src, tar]
# update outgoing(!) gates, but only if the mechanism is enabled
if not gating_mechanism:
continue
# dont touch non-existing gate
# we could skip before saving the gate history, but this helps debugging
if Aij[src, tar] == 0:
continue
# Disconnect gate depending on activity of source
if old_gate[src, tar] == GATE_CONNECTED:
prob = _probability_to_disconnect(
rsrc[src, t], dt, thrs_gate, k_gate, tau_disconnect
)
if np.random.rand() < prob:
gate[src, tar] = GATE_DISCONNECTED
# Connect gate with a characteristic time
else:
prob = 1.0 - np.exp(-dt / tau_connect)
if np.random.rand() < prob:
gate[src, tar] = GATE_CONNECTED
# this is a bit hacky...
# to thermalize, simply chop off the indices that correspond to thermalization time
rec_start = int(thermalization_time / dt)
rate = rate[:, rec_start:]
rsrc = rsrc[:, rec_start:]
gate_history = gate_history[:, :, rec_start:]
time_axis = np.arange(0, nt - rec_start) * dt
return time_axis, rate, rsrc, gate_history
def probability_to_disconnect(resources, **kwargs):
"""
Returns the probability of the gate to be closed depending on sigmoid response and currently available resources
#Parameters:
resources : float
Level of resources
dt : float
Integration timestep
thrs_gate : float
Threshold for sigmoidal. Below this value output is low, but not cut to zero
k_gate : float
Knee of the sigmoidal
tau_disconnect : float
Time scale at which the gate disconnects when no resources are available
# Returns
prob_close: float
Probability of gate closing for the currently available number of resources.
"""
pars = default_pars.copy()
for key, value in kwargs.items():
assert key in default_pars.keys(), f"unknown kwarg for mesoscopic model: '{key}'"
pars[key] = value
return _probability_to_disconnect(
resources, pars["dt"], pars["thrs_gate"], pars["k_gate"], pars["tau_disconnect"]
)
@jit(nopython=True, parallel=False, fastmath=False, cache=True)
def _probability_to_disconnect(resources, dt, thrs_gate, k_gate, tau_disconnect):
return 1.0 - np.exp(
-dt
* ((1 / tau_disconnect) - gate_sigm(resources, thrs_gate, k_gate, tau_disconnect))
)
# Sigmoid for gate response
@jit(nopython=True, parallel=False, fastmath=False, cache=True)
def gate_sigm(inpt, thrs_gate, k_gate, tau_disconnect):
"""
Sigmoid that gives the response of the gate to the current level of resources
#Parameters:
inpt : float
Level of resources
thrs_gate : float
Threshold. Below this value output is low, but not cut to zero
k_gate : float
Knee of the sigmoidal
tau_disconnect : float
Time scale at which the gate disconnects when no resources are available
# Returns
tau_disconnect_effective : float
Rate of gate closing for the currently available number of resources.
"""
return (1 / tau_disconnect) / (1.0 + np.exp(-k_gate * (inpt - thrs_gate)))
#
@jit(nopython=True, parallel=False, fastmath=False, cache=True)
def transfer_function(total_input, gain_inpt, k_inpt, thrs_inpt, aux_thrsig=None):
"""
Gets the input to a module, given its input
x/b = (1-exp( -k(rx+h-t) ) )/(1+exp(kt)*exp(-k(xr+h-t)))
#Parameters
inpt : float, or array of floats
Neuronal activity input to the transfer function
gain_inpt : float
Maximum value returned by sigmoid for large inputs
k_inpt : float
Knee of the sigmoid
thrs_inpt : float
Threshold. Below this value, function returns 0
aux_thrsig : float, optional
Auxiliary variable defined as exp(k_inpt * thrs_inpt), can be precomputed
#Returns
feedback : float
The result of applying the transfer function
"""
if aux_thrsig is None:
aux_thrsig = np.exp(k_inpt * thrs_inpt)
expinpt = np.exp(-k_inpt * (total_input - thrs_inpt))
if total_input >= thrs_inpt:
return gain_inpt * (1.0 - expinpt) / (aux_thrsig * expinpt + 1.0)
else:
# we need to get consistent shapes.
return total_input * 0.0
def single_module_odes(y, t, **pars):
"""
Defines the coupled ODEs of the mesoscopic model.
Use with numeric solver to explore nullclines and plot trajectories.
Note that the `simulate_meso` function does not use this, and the ODEs are
hard-coded in both places.
# Parameters
y : array-like
(rate, resource)
t : float
time at which to evaluate the ODE, only needed for the solver, not used in def
**pars : dict
Parameters of the model, as a dict.
at least needs to contain those keys:
- "ext_str"
- "thrs_inpt"
- "gain_inpt"
- "k_inpt"
- "tau_discharge"
- "tau_charge"
- "tau_rate"
- "max_rsrc"
# Example
```
pars = mm.default_pars.copy()
ode_with_kwargs = functools.partial(single_module_odes, **pars)
trajectory = scipy.integrate.odeint(
func=ode_with_kwargs,
y0=np.array([0.5, 1.0]),
t=np.linspace(0, 1000, 5000),
)
```
"""
rate, rsrc = y
# fmt:off
rate_ode = \
- rate / pars["tau_rate"] + 0.0 \
+ transfer_function(
total_input = rate * rsrc + pars["ext_str"],
gain_inpt = pars["gain_inpt"],
k_inpt = pars["k_inpt"],
thrs_inpt = pars["thrs_inpt"],
)
rsrc_ode = \
- rsrc * rate / pars["tau_discharge"] \
+ (pars["max_rsrc"] - rsrc) / pars["tau_charge"]
# fmt:on
return np.array([rate_ode, rsrc_ode])
def simulate_and_save(output_filename, meta_data=None, **kwargs):
"""
Perform a simulation of the system and save it to the indicated path
#Parameters
output_filename : str
Path to the output file. Extension (.hdf5) will be added automatically.
meta_data : dict, optional
key value pairs to save into the hdf5 file in the `/meta/` group.
(use for parameters so they can be read back in)
**kwargs : dict
Any parameters that can be given to mesoscopic_model.simulate_model
"""
# Perform model simulation
time, activity, resources, gate_history = simulate_model(**kwargs)
# Create the path if needed
os.makedirs(os.path.dirname(output_filename), exist_ok=True)
# Create a DataFrame easy to read in our workflow and export as HDF
df = pd.DataFrame(columns=["time"] + [f"mod_{m_cd}" for m_cd in range(1, 5)])
df["time"] = time
for m_cd in range(4):
df[f"mod_{m_cd+1}"] = activity[m_cd, :]
df[f"mod_{m_cd+1}_res"] = resources[m_cd, :]
# For the first module, store also the dynamics of its gate
# for gateind in range(2):
# df[f"mod_gate_{gateind+1}"] = gate_history[gateind, :]
# overwrite data if it already exists
if ".hdf5" not in output_filename.lower():
output_filename += ".hdf5"
if os.path.exists(f"{output_filename}"):
os.remove(f"{output_filename}")
df.to_hdf(f"{output_filename}", f"/dataframe", complevel=9)
# This is quite inconsistent, most data is saved with pandas, only this is
# native hdf5. fixing requires a rewrite of meso_helper
file = h5py.File(f"{output_filename}", "r+")
file.create_dataset(f"/data/gate_history", data=gate_history, compression="gzip")
file.close()
if meta_data is not None:
file = h5py.File(f"{output_filename}", "r+")
for key in meta_data.keys():
try:
file.create_dataset(f"/meta/{key}", data=meta_data[key])
except Exception as e:
log.exception(e)
file.close()