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# -*- coding: utf-8 -*- | |
""" | |
A two dimensional dynamic system with leak current, persistent sodium current | |
and transient potassium current. Exhibits spiking behavior and some other cool | |
stuff. The equations and their paremeters come from "Dynamical Systems in | |
Neuroscience: The Geometry of Excitability and Bursting" by Izhikevich, | |
Eugene M. There it says: "This model is equivalent in many respects to the | |
well-known and widely used ICa+Ik-model proposed by Morris and Lecar (1981) | |
to describe voltage oscillations in the barnacle giant muscle fiber." (p.89) |
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# -*- coding: utf-8 -*- | |
""" | |
A Python implementation of the Izhikevich Neuron as described in Izhikevich E.M. (2003) | |
Tested in Python 3.7.3 | |
Author: @scidanm | |
""" | |
import numpy as np |
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# -*- coding: utf-8 -*- | |
""" | |
Python implementation of a Hodgkin-Huxley model of a cortical pyramidal neuron. | |
Code taken in large parts from https://gist.github.com/giuseppebonaccorso/60ce3eb3a829b94abf64ab2b7a56aaef | |
Adapted to work with solve_ivp. | |
Parameters changed to a cortical pyramidal neuron as described in https://neuronaldynamics.epfl.ch/online/Ch2.S2.html | |
Tested in Python 3.7.3 |
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# -*- coding: utf-8 -*- | |
""" | |
Uses python with NEURON to simulate voltage clamping a ball-and-stick cell. | |
Tested in Python 3.7.3 and NEURON 7.6.7 | |
Author: @scidanm | |
""" | |
from neuron import h, gui |
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# -*- coding: utf-8 -*- | |
""" | |
Voltage spikes, also known as action potentials, are considered the key unit of information flow in | |
the nervous system. One of the first quantitative descriptions of the action potential is the | |
Hodgkin-Huxley Model, named after nobel prize winning physiologists Alan Lloyd Hodgkin and Andrew | |
Fielding Huxley. This matplotlib animation shows the result of simulating the Hodgkin-Huxley model | |
in python with parameters that are set in a way, that the model resembles a cortical pyramidal cell. | |
At 50ms a current is injected, making the model spike. The upper panel shows the dynamical systems | |
view of the action potential. Before the current injection, the model stays at the resting | |
potential. When the current is injected a bifurcation occurs. The system finds a limit cycle. |
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import numpy as np | |
from matplotlib.animation import FuncAnimation | |
import matplotlib.pyplot as plt | |
x = np.arange(0, 10*np.pi, 0.01) | |
y = np.sin(x) | |
fig = plt.figure() | |
ax = plt.subplot(1, 1, 1) |
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import numpy as np | |
from matplotlib.animation import FuncAnimation | |
import matplotlib.pyplot as plt | |
x = np.arange(0, 10*np.pi, 0.01) | |
y_sin = np.sin(x) | |
y_cos = np.cos(x) | |
fig = plt.figure() | |
ax1 = plt.subplot(2, 1, 1) |
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# -*- coding: utf-8 -*- | |
""" | |
@author: Daniel Müller-Komorowska | |
""" | |
import numpy as np | |
import scipy.signal as signal | |
def amp_crosscorr(eeg1, eeg2, samp_freq, low_freq, high_freq): | |
""" |
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""" | |
The functions in this code are taken from a Neuromatch Academy Tutorial about dimensionality | |
reduction by Alex Cayco Gajic & John Murray: | |
https://github.com/NeuromatchAcademy/course-content/tree/master/tutorials/W1D5_DimensionalityReduction | |
Neuromatch Academy content is licensed under a Creative Commons Attribution 4.0 International | |
https://github.com/NeuromatchAcademy/course-content/blob/master/LICENSE.md | |
I use these functions to create an animation showing a subset of MNIST samples | |
reconstructed from an increasing number of principal components. |
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import torch | |
import pandas as pd | |
from sklearn.preprocessing import StandardScaler | |
from sklearn.model_selection import train_test_split | |
import numpy as np | |
import matplotlib.pyplot as plt | |
import seaborn as sns | |
np.random.seed(10000) |
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