[MRG] Simulate spikes / action potentials

[ryanhammonds]

This adds action potential cycles as the sum of two inverted asymmetrical gaussians:

import matplotlib.pyplot as plt
import numpy as np
from neurodsp.sim.cycles import sim_ap_cycle

n_seconds = 1
fs = 1000

cycle_params = {'centers': (.25, .5), 'stds':(.15, .12),
                'alphas':(4, .2), 'heights': (15, -5)}

cyc = sim_ap_cycle(n_seconds, fs, **cycle_params)

plt.plot(cyc)

[ryanhammonds]

This func can be used with scipys curve_fit to fit isolated APs from real data (bycycle-tools/bycycle#100). The resulting 8 params could be useful (i.e. dimensionality reduction for APs) and included in df_features returned from bycycle.Spikes.fit().

[TomDonoghue]

This looks super cool!

I had a quick scan of the code, left a coupe comments, and here's a couple quick "higher-level" questions:

• It's not clear to me that the AP sim is a cycle, per se. Would it fit better in sim.transients?
• I presume changing the gaussian code to not use scipy is about getting more control over height, center, etc? Setting height feels like it overlaps with normalizing the signal, and center feels a little weird to have in the cycles, because it makes looks like it 'cuts off' the edge of a gaussian? Am I right in thinking that one would probably never want to set center to a custom value because it would create weird concatenation artifacts?

Between the two comments, I think it's possible it might be a cleaner split to put some stuff in transients, that might work well for generating APs, but might not be quite the same as what one wants for a cycle? What do you think?

[ryanhammonds]

Thanks for the review!

• I think it makes sense to refactor into transients with an alias in cycles so it can still be used with sim_bursty_oscillation.
• The main reason for the sim_gaussian_cycle changes was to have control over the cycle center, which is important only for skewed cycles. Here's an example of how center makes a difference with skewed cycles:

The height param is a bit different from variance. I'm not sure there is a clear mapping between these params unless we were to compute the mean value required to get a zero baseline.

[ryanhammonds]

I've update the code here based on the review. I also update the ap func to take iterables for simulation parameters. This is because 3 gaussians may desired in some cases (i.e. the sum of conductive, sodium and potassium currents). Despite this, 3 currents can be created with only 2 gaussians (where the positive portion has a wide std).

The 3 current model is from this paper. Third column plot:

from neurodsp.sim.cycles import sim_ap_cycle
import matplotlib.pyplot as plt

cycle = sim_ap_cycle(1, 100, (.5, .3, .6), (.1, .1, .1), (0, -1, 1), (-5, 1, 2.5))

plt.plot(cycle)

[ryanhammonds]

@TomDonoghue I made a final round of updates. There have been several changes since the last time you reviewed, but it should be ready to merge. Let me know if you'd like to look over the changes, otherwise I'll merge.

[TomDonoghue]

Edit: hey @ryanhammonds, this looks great! Very cool addition!

Everything looks good to me - you can go ahead and merge when you're ready!