2022-01-08 • Lognormal input firing rates
Contents
2022-01-08 • Lognormal input firing rates¶
include("nb_init.jl")
[ Info: import Distributions
[ Info: import PyPlot
[ Info: import DataFrames, PrettyTables
[ Info: import BenchmarkTools, Profile, FilePaths
[ Info: import Unitful, Sciplotlib
[ Info: using VoltageToMap
Distributions¶
We want Poisson firing, i.e. ISIs with an exponential distribution.
Firing rates lognormally distributed (instead of all the same, as before).
"""
`μ` and `σ` are mean and standard deviation of the underlying Gaussian.
`μₓ` is the mean of the log of the Gaussian.
"""
function LogNormal_with_mean(μₓ, σ)
μ = log(μₓ / unit(μₓ)) - σ^2 / 2
LogNormal(μ, σ, unit(μₓ))
end;
input_spike_rate = LogNormal_with_mean(4Hz, √0.6) # our hand-picked params
LogNormal{Float64, Unitful.FreeUnits{(Hz,), 𝐓^-1, nothing}}(μ=1.0862943611198905, σ=0.7745966692414834)
roxin = LogNormal_with_mean(5Hz, √1.04)
LogNormal{Float64, Unitful.FreeUnits{(Hz,), 𝐓^-1, nothing}}(μ=1.0894379124341003, σ=1.019803902718557)
σ² = (σ_X, μ_X) -> log(1 + σ_X^2 / μ_X^2)
σ²_oconnor = σ²(7.4Hz, 12.6Hz)
0.296337
oconnor = LogNormal_with_mean(7.4Hz, √σ²_oconnor)
LogNormal{Float64, Unitful.FreeUnits{(Hz,), 𝐓^-1, nothing}}(μ=1.8533115616194222, σ=0.5443683285987568)
Plot¶
fig, (ax1, ax2, ax3) = plt.subplots(ncols=3, figsize=(8, 2.2))
rlin = (0:0.01:15) * Hz
rlog = (log10(0.04):0.01:log10(41) .|> exp10) * Hz
function plot_firing_rate_distr(distr; kw...)
plot(rlin, pdf.(distr, rlin), ax1; clip_on=false, kw...)
plot(rlog, pdf.(distr, rlog), ax2; clip_on=false, xscale="log", kw...)
plot(rlin, cdf.(distr, rlin), ax3; clip_on=false, ylim=(0,1), kw...)
end
plot_firing_rate_distr(roxin, label="Roxin", c=lighten(C2, 0.4))
plot_firing_rate_distr(oconnor, label="O'Connor", c=lighten(C1, 0.4))
plot_firing_rate_distr(input_spike_rate, label="This study", c=C0, lw=2.7)
set(ax1; xlabel="Input firing rate", ytickstyle=:range, hylabel="Probability density")
set(ax2; xlabel=("(log scale)", :loc=>:center), yaxis=:off)
set(ax3; hylabel="Cumulative probability")
deemph(:yaxis, ax1)
legend(ax2, loc="center", bbox_to_anchor=(-0.14, 0.7), reorder=[3=>1])
ax2.get_legend().set_in_layout(false)
plt.tight_layout(w_pad=1)
savefig("log-normal.pdf", subdir="methods")
![../_images/2022-01-08__lognormal_firing_rates_10_0.png](../_images/2022-01-08__lognormal_firing_rates_10_0.png)
Parameters¶
distrs = [oconnor, roxin, input_spike_rate]
(df = DataFrame(
name=["oconnor", "roxin", "this study"],
σ=stdlogx.(distrs),
mean=mean.(distrs),
median=median.(distrs),
std=std.(distrs),
var=var.(distrs),
)) |> printsimple
name σ mean (Hz) median (Hz) std (Hz) var (Hz²)
────────────────────────────────────────────────────────────────────
oconnor 0.544 7.4 6.38 4.35 18.9
roxin 1.02 5 2.97 6.76 45.7
this study 0.775 4 2.96 3.63 13.2