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SER model

This minimal model of spreading excitations has a rich history in many disciplines, ranging from the propagation of forest-fires, the spread of epidemics, to neuronal dynamics. SER stands for susceptible, excited and refractory.

Installation

pip install ser

Example

import matplotlib.pyplot as plt
import numpy as np
import seaborn as sns

from ser import SER

sns.set_style("white")

# Build a random adjacency matrix (weighted and directed)
n_nodes = 50
adj_mat = np.random.uniform(low=0, high=1, size=(n_nodes, n_nodes))
adj_mat[np.random.random(adj_mat.shape) < .9] = 0  # make sparser

# Instantiate SER model once, use as many times as we want (even on different graphs)
ser_model = SER(n_steps=500,
                prop_e=.1,
                prop_s=.4,
                threshold=.4,
                prob_recovery=.2,
                prob_spont_act=.001)

# Run activity. The output is a matrix (node vs time)
activity = ser_model.run(adj_mat=adj_mat)

#Plot the activity matrix and the global activity level
activity_only_active = activity.copy()
activity_only_active[activity == -1] = 0
n_active_nodes = activity_only_active.sum(axis=0)

fig, (ax1, ax2) = plt.subplots(nrows=2, figsize=(15, 8), sharex=True)
ax1.plot(n_active_nodes, linewidth=4, color="#6D996A", alpha=.8)
ax1.set_ylabel("Number\nactive nodes", fontsize=25)
ax2.imshow(activity, cmap="binary_r")
ax2.set_xlabel("Time", fontsize=25)
ax2.set_ylabel("Nodes", fontsize=25)
ax2.set_aspect("auto")
ax2.grid(False)
sns.despine()
fig.tight_layout()

Implementation

The graph (or network) is represented as an adjacency matrix (numpy array). Dynamics is implemented in numpy and accelerated with numba, so it is fast - quick benchmarks show between 2-3 times faster simulations than pure vectorized numpy versions!

Numba tips and tricks

• Don't use adj_mat with type other than np.float32, np.float64.
• Pro-tip: use np.float32 for adj_mat – it will run faster.

Limitations

• The graph is represented as a numpy array, which is less memory efficient than a list or a dictionary representation. That limits the size of the network you can use (of course, depending on your RAM).

Citing

If you find this package useful for a publication, then please use the following BibTeX to cite it:

@misc{ser,
  author = {Damicelli, Fabrizio},
  title = {Susceptible-Excited-Refractory model in Python: A dynamical model of spreading excitations},
  year = {2019},
  publisher = {GitHub},
  journal = {GitHub repository},
  howpublished = {\url{https://github.com/fabridamicelli/ser}},
}

References

• J. M. Greenberg and S. P. Hastings, SIAM J. Appl. Math. 34, 515 (1978).
• A. Haimovici et al. Phys. Rev. Lett. 110, 178101 (2013).
• Messé et al. PLoS computational biology (2018)