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Copy file name to clipboardExpand all lines: docs/src/tutorials/LMA_example.md
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@@ -20,20 +20,22 @@ using Catalyst
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# how the nonlinear reactions are to be transformed using LMA
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rn_nonlinear =@reaction_networkbegin
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@parameters σ_b σ_u ρ_b ρ_u
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σ_b, g + p →0
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σ_u*(1-g), 0⇒ g + p
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ρ_u, g → g + p
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ρ_b*(1-g), 0⇒ p
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1, p →0
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endσ_b σ_u ρ_b ρ_u
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end
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rn_linear =@reaction_networkbegin
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@parameters σ_b_LMA σ_u ρ_b ρ_u
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σ_b_LMA, g →0# typing ̄σ_b is not allowed it seems
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σ_u*(1-g), 0⇒ g
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ρ_u, g → g+p
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(ρ_b*(1-g)), 0⇒ p
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1, p →0
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endσ_b_LMA σ_u ρ_b ρ_u
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end
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```
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We can now apply the LMA to find the effective parameter $\bar{σ}_b$ and generate the corresponding moment equations of the linear GRN using MomentClosure's [`linear_mapping_approximation`](@ref):

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@@ -141,11 +143,12 @@ As pointed out by the authors in [1], a more efficient way is to expand the gene
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However, TaylorSeries only supports elementary function operations at the time and hence evaluating the Kummer's function $M(\cdot,\cdot,\cdot)$ requires some more work (these specialised numerics are readily available in more established scientific computing frameworks such as Mathematica but there's no fun in that). We can extend the TaylorSeries framework by constructing a function `t_pFq` that implements a recurrence relation between the Taylor coefficients for the generalized hypergeometric function `pFq` as defined in [HypergeometricFunctions.jl](https://github.com/JuliaMath/HypergeometricFunctions.jl). This can be done as follows (note that our construction is valid only for a single-variable Taylor series [`Taylor1`](https://juliadiff.org/TaylorSeries.jl/stable/api/#TaylorSeries.Taylor1)):
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```julia
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using TaylorSeries, HypergeometricFunctions
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using HypergeometricFunctions: pFqweniger
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# please let me know if a simpler and more efficient way to do this exists!
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