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assets/literate/intro_diffeq.md

@@ -154,21 +154,19 @@ Since `I` will change dynamically in time, it will be a time-dependent variable
 
 ````julia:ex9
 @variables v(t)=-65 u(t)=-13 I(t)
-# The following parameter values correspond to regular spiking.
-@parameters a=0.02 b=0.2 c=-65 d=8
+@parameters a=0.02 b=0.2 c=-65 d=8 ## These parameter values correspond to regular spiking.
 
 eqs = [D(v) ~ 0.04 * v ^ 2 + 5 * v + 140 - u + I,
         D(u) ~ a * (b * v - u),
         I ~ 10*sin(0.5*t)]
 
 event = (v > 30.0) => [u ~ u + d, v ~ c]
 
-# Notice how `I` was moved from the parameter list to the variable list in the following call.
 @named izh_system = ODESystem(eqs, t, [v, u, I], [a, b, c, d]; discrete_events = event)
 izh_simple = structural_simplify(izh_system)
 ````
 
-Let's display the equations of the original and the simplified system to see the effect of `structural_simplify`.
+Notice how `I` was moved from the parameter list to the variable list above. Let's display the equations of the original and the simplified system to see the effect of `structural_simplify`.
 
 ````julia:ex10
 equations(izh_system)

assets/literate/intro_diffeq_script.jl

@@ -81,16 +81,14 @@ fig
 save(joinpath(@OUTPUT, "mtk4.svg"), fig); # hide
 
 @variables v(t)=-65 u(t)=-13 I(t)
-# The following parameter values correspond to regular spiking.
-@parameters a=0.02 b=0.2 c=-65 d=8
+@parameters a=0.02 b=0.2 c=-65 d=8 ## These parameter values correspond to regular spiking.
 
 eqs = [D(v) ~ 0.04 * v ^ 2 + 5 * v + 140 - u + I,
         D(u) ~ a * (b * v - u),
         I ~ 10*sin(0.5*t)]
 
 event = (v > 30.0) => [u ~ u + d, v ~ c]
 
-# Notice how `I` was moved from the parameter list to the variable list in the following call.
 @named izh_system = ODESystem(eqs, t, [v, u, I], [a, b, c, d]; discrete_events = event)
 izh_simple = structural_simplify(izh_system)
 

assets/literate/intro_plot.md

@@ -43,8 +43,7 @@ When defining an `Axis` there are multiple options to affect its appearance and
 We can also change an `Axis` after it has been constructed. For instance we could hide the x-axis label and ticks on the top plot above, since it is a duplicate of the x-axis of the bottom plot. We will keep the grid lines though, because it is easier to read the x-axis values this way.
 
 ````julia:ex2
-# `grid=false` avoids hiding the x grid lines
-hidexdecorations!(axs[1], grid=false)
+hidexdecorations!(axs[1], grid=false) ## `grid=false` avoids hiding the x grid lines
 
 # Now we can display the figure again with the updated axes
 fig
@@ -65,8 +64,7 @@ using ModelingToolkit: t_nounits as t, D_nounits as D
 using OrdinaryDiffEq
 
 @variables v(t)=-65 u(t)=-13
-# Parameters for fast spiking.
-@parameters a=0.1 b=0.2 c=-65 d=2 I=10
+@parameters a=0.1 b=0.2 c=-65 d=2 I=10 ## Parameters for fast spiking.
 
 eqs = [D(v) ~ 0.04 * v ^ 2 + 5 * v + 140 - u + I,
         D(u) ~ a * (b * v - u)]
@@ -96,12 +94,17 @@ t_window = 20
 t_range = first(tspan):t_window:last(tspan)
 # initialize an empty vector to hold the spike values.
 spikes = zeros(length(t_range) - 1)
+````
+
+To find spikes we need to
+- loop over the timepoints at which every time window begins
+- find the indices of timepoints that fall within the current time window
+- count the number of spikes within the same window
 
-# loop over the timepoints at which every time window begins
+````julia:ex4
 for i in eachindex(t_range[1:end-1])
-    # find the indices of timepoints that fall within the current time window
     idxs = findall(t -> t_range[i] <= t <= t_range[i+1], timepoints)
-    # count the number of spikes within the same window
+
     spikes[i] = count(V_izh[idxs] .> spike_threshold) ## counts the number of True elements in a Boolean vector
 end
 

assets/literate/intro_plot_script.jl

@@ -16,8 +16,7 @@ scatter!(axs[2], seconds, measurements)
 fig
 save(joinpath(@OUTPUT, "layout.svg"), fig); # hide
 
-# `grid=false` avoids hiding the x grid lines
-hidexdecorations!(axs[1], grid=false)
+hidexdecorations!(axs[1], grid=false) ## `grid=false` avoids hiding the x grid lines
 
 # Now we can display the figure again with the updated axes
 fig
@@ -28,8 +27,7 @@ using ModelingToolkit: t_nounits as t, D_nounits as D
 using OrdinaryDiffEq
 
 @variables v(t)=-65 u(t)=-13
-# Parameters for fast spiking.
-@parameters a=0.1 b=0.2 c=-65 d=2 I=10
+@parameters a=0.1 b=0.2 c=-65 d=2 I=10 ## Parameters for fast spiking.
 
 eqs = [D(v) ~ 0.04 * v ^ 2 + 5 * v + 140 - u + I,
         D(u) ~ a * (b * v - u)]
@@ -60,11 +58,9 @@ t_range = first(tspan):t_window:last(tspan)
 # initialize an empty vector to hold the spike values.
 spikes = zeros(length(t_range) - 1)
 
-# loop over the timepoints at which every time window begins
 for i in eachindex(t_range[1:end-1])
-    # find the indices of timepoints that fall within the current time window
     idxs = findall(t -> t_range[i] <= t <= t_range[i+1], timepoints)
-    # count the number of spikes within the same window
+
     spikes[i] = count(V_izh[idxs] .> spike_threshold) ## counts the number of True elements in a Boolean vector
 end