### A Pluto.jl notebook ###
# v0.15.1

using Markdown
using InteractiveUtils

# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
    quote
        local el = $(esc(element))
        global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : missing
        el
    end
end

# ╔═╡ 5f1fe571-3357-49cf-93d6-49ae6b4b9a05
begin
	using OrdinaryDiffEq
	using Plots, LaTeXStrings
	using PlutoUI
	# using CSV
	# using DataFrames, CategoricalArrays
	# using Turing
	# using Dates
end

# ╔═╡ 9997fcae-e8c0-11eb-29d3-19aa2548bb51
md"""
# Within-host modelling of SARS-CoV-2

*C. Contreras, J. Newby, T. Hillen.*
© 2021
"""

# ╔═╡ f02367f9-77ec-4af5-ab95-c216cc61773f


# ╔═╡ a3756580-3ac1-40b5-94ea-9e164c9065e5
md"Importing modules"

# ╔═╡ 4a72dcd8-bb16-4d63-a8a8-e89865b3ff95
md"""
Text
"""

# ╔═╡ 7541a4c5-e8bd-4700-880d-8d7e1b05cdf9


# ╔═╡ 9087b209-8385-4da8-8cfd-6eb7f4a2a0aa
begin
	md"Plot configuration"
	plotly()
	figdir = "figures/"
	# ENV["COLUMNS"]=120
	# ENV["LINES"]=20
end

# ╔═╡ 8e990cf8-3fee-4fde-b044-0e95c90a19a8
md"""
## Standard virus load function

The standard virus load function with three main phases given by

$$V(t)=v_1(t)v_2(t)v_3(t),$$

where $v _1$ describes the initial growth phase between $a _1$ and $a _2$ , $v _2$ the intermediate slow decay
phase between $a _2$ and $b _1$, and $v _3$ the final decay phase between $b _1$ and $b _2$. These functions are given as sigmoid and exponential functions, respectively

$$v_1(t) = 1 + \frac{V_{\max} - 1}{2} \left[ \tanh \left( \frac{6}{a_2 - a_1} \left( t - \frac{a_1 + a_2}{2} \right) \right) - \tanh  \left( -3\frac{a_2 + a_1}{a_2 - a_1} \right) \right]$$

$$v_2(t) = \left\{\begin{aligned}
        & 1 & t < a_2 \\
        & e^{-\alpha (t-a_2)} & t \geq a_2 \\
    \end{aligned} \right.$$

$$v_3(t) = 1 - \frac{1 - V_{\min}}{2} \left[ \tanh \left( \frac{6}{b_2 - b_1} \left( t - \frac{b_1 + b_2}{2} \right) \right) - \tanh  \left( -3\frac{b_2 + b_1}{b_2 - b_1} \right) \right],$$


.
"""

# ╔═╡ 54a73741-2b04-4bb5-9bcb-b594b451d9ec
begin
	H(x) = 0.5*(tanh(1e3*x) + 1.)
	v₁(t, a₁, a₂, Vmax) = 1. + (Vmax - 1.0)*(tanh(6.0*(t - (a₁ + a₂)/2)/(a₂ - a₁)) - tanh(-3.0*(a₂ + a₁)/(a₂ - a₁)))/2
	v₂(t, a₂, α) = 1 - H(t - a₂) + H(t - a₂)*exp(-α*(t - a₂))
	v₃(t, b₁, b₂, Vmin) = 1 - (1.0 - Vmin)*(tanh(6.0*(t - (b₁ + b₂)/2)/(b₂ - b₁)) - tanh(-3.0*(b₂ + b₁)/(b₂ - b₁)))/2
	function VLF(t, a₁, a₂, b₁, b₂, α, Vmax, Vmin)
		v₁(t, a₁, a₂, Vmax)*v₂(t, a₂, α)*v₃(t, b₁, b₂, Vmin)
	end
end

# ╔═╡ 568527c6-0760-405e-a056-98a22f95454c
md"""
## Kinetic model

The within-host model for COVID-19 infections dynamics on the lung epithilium, $E$, is given by

$$\begin{aligned}
    \frac{d E}{dt} & = \mu_E E(1-E) - \delta_E T \frac{V}{V_{max}}.
\end{aligned}$$ 
"""

# ╔═╡ dea4b784-87c7-4497-b11b-b1ca1cc83c71
function model!(du, u, p, t)
    E, = u
    a₁, a₂, b₁, b₂, α, Vmax, Vmin, μ_E, δ_E = p
    # Lung damage
    du[1] = dE = μ_E*E*(1.0 - E) - δ_E*E*VLF(t, a₁, a₂, b₁, b₂, α, Vmax, Vmin)/Vmax 
	# Healthy lung epithelium
end

# ╔═╡ 5a3929ad-5719-4021-993c-acc31db4a674
begin
	a₁_slider = @bind a₁ Slider(0.0:0.1:4.0, default=0.4) 
	α_slider = @bind α Slider(0.0:0.1:1.0, default=0.1) 
	md"""Parameter
	
	a1: $(a₁_slider)
	
	alpha: $(α_slider)"""
end

# ╔═╡ b330f75d-125c-4a49-a830-5672ed18c56b
begin
	# initial
	u0 = [
		1.0   # E: Healthy lung epithilium
	]
	tspan = (0.0, 40.0)
	pars = [
		a₁     # a₁
		4.0     # a₂
		13.0    # b₁
		19.0    # b₂
		α     # α
		1e3  # Vmax
		1e-8    # Vmin
		0.01    # μ_E
		0.2     # δ_E
		]
	parnames = [:a₁, :a₂, :b₁, :b₂, :α, :Vmax, :Vmin, :μ_E, :δ_E]
	thresholds = (E = 0.3,);
	prob = ODEProblem(model!, u0, tspan, pars)
end

# ╔═╡ 2f80e9cb-9bd6-4189-9d84-20d5e1c6b0e3
function plot_sol!(sol; kwargs...)
    tt = range(0.0, tspan[2], length=100)
    pars = sol.prob.p
    vv = VLF.(sol.t, pars[1], pars[2], pars[3], pars[4], pars[5], pars[6], pars[7])
    plot!(sol.t, vv, lw=3, xaxis=("Time (days)"), yaxis=("Viral load", extrema(vv).*1.05), subplot=1; kwargs...)
    plot!(sol, vars=1, lw=3, xaxis=("Time (days)"), yaxis=("Healthy lung epithelium", (0, 1.1)), subplot=2; kwargs...) 
    plot!(collect(extrema(sol.t)), [thresholds.E, thresholds.E], color=:black, lw=2, subplot=2)
end

# ╔═╡ 364206c0-954b-45b1-9f20-e5031c34de16
function plot_sol(sol; kwargs...)
    plot(layout=2, legend=:none, grid=:none, size=(600,300))
    plot_sol!(sol; kwargs...) 
end

# ╔═╡ 8864fe08-3dd3-4731-ac26-7ae256835f03
begin
	sol = solve(prob, Tsit5(), dtmax=1e-1)
	plot_sol(sol)
end

# ╔═╡ 5df4f25f-ff30-46ea-b7d1-923001d900fa
md"""
$(a₁)
"""

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
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[compat]
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deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE_jll", "Pkg", "Zlib_jll"]
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[[Grisu]]
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[[HTTP]]
deps = ["Base64", "Dates", "IniFile", "Logging", "MbedTLS", "NetworkOptions", "Sockets", "URIs"]
git-tree-sha1 = "c6a1fff2fd4b1da29d3dccaffb1e1001244d844e"
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[[Hwloc]]
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uuid = "0e44f5e4-bd66-52a0-8798-143a42290a1d"
version = "2.0.0"

[[Hwloc_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "3395d4d4aeb3c9d31f5929d32760d8baeee88aaf"
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[[IfElse]]
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[[Inflate]]
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[[IniFile]]
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[[InteractiveUtils]]
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[[IterTools]]
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[[IterativeSolvers]]
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[[IteratorInterfaceExtensions]]
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[[JLLWrappers]]
deps = ["Preferences"]
git-tree-sha1 = "642a199af8b68253517b80bd3bfd17eb4e84df6e"
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[[JSON]]
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[[JpegTurbo_jll]]
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git-tree-sha1 = "d735490ac75c5cb9f1b00d8b5509c11984dc6943"
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[[LAME_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "f6250b16881adf048549549fba48b1161acdac8c"
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[[LZO_jll]]
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git-tree-sha1 = "e5b909bcf985c5e2605737d2ce278ed791b89be6"
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[[LaTeXStrings]]
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[[LabelledArrays]]
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[[Latexify]]
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[[LibCURL]]
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[[LibCURL_jll]]
deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll", "Zlib_jll", "nghttp2_jll"]
uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0"

[[LibGit2]]
deps = ["Base64", "NetworkOptions", "Printf", "SHA"]
uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"

[[LibSSH2_jll]]
deps = ["Artifacts", "Libdl", "MbedTLS_jll"]
uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8"

[[LibVPX_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "12ee7e23fa4d18361e7c2cde8f8337d4c3101bc7"
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[[Libdl]]
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[[Libffi_jll]]
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git-tree-sha1 = "761a393aeccd6aa92ec3515e428c26bf99575b3b"
uuid = "e9f186c6-92d2-5b65-8a66-fee21dc1b490"
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[[Libgcrypt_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgpg_error_jll", "Pkg"]
git-tree-sha1 = "64613c82a59c120435c067c2b809fc61cf5166ae"
uuid = "d4300ac3-e22c-5743-9152-c294e39db1e4"
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[[Libglvnd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll", "Xorg_libXext_jll"]
git-tree-sha1 = "7739f837d6447403596a75d19ed01fd08d6f56bf"
uuid = "7e76a0d4-f3c7-5321-8279-8d96eeed0f29"
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[[Libgpg_error_jll]]
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git-tree-sha1 = "c333716e46366857753e273ce6a69ee0945a6db9"
uuid = "7add5ba3-2f88-524e-9cd5-f83b8a55f7b8"
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[[Libiconv_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "42b62845d70a619f063a7da093d995ec8e15e778"
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[[Libmount_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "9c30530bf0effd46e15e0fdcf2b8636e78cbbd73"
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[[Libtiff_jll]]
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git-tree-sha1 = "340e257aada13f95f98ee352d316c3bed37c8ab9"
uuid = "89763e89-9b03-5906-acba-b20f662cd828"
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[[Libuuid_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "7f3efec06033682db852f8b3bc3c1d2b0a0ab066"
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[[LightGraphs]]
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[[LineSearches]]
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[[LinearAlgebra]]
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[[LogExpFunctions]]
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[[Logging]]
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[[LoopVectorization]]
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[[MacroTools]]
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[[ManualMemory]]
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[[Markdown]]
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[[MbedTLS]]
deps = ["Dates", "MbedTLS_jll", "Random", "Sockets"]
git-tree-sha1 = "1c38e51c3d08ef2278062ebceade0e46cefc96fe"
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[[MbedTLS_jll]]
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[[Measures]]
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[[Missings]]
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[[Mmap]]
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[[MozillaCACerts_jll]]
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[[MuladdMacro]]
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[[NLSolversBase]]
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[[NLsolve]]
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[[NaNMath]]
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[[NetworkOptions]]
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[[NonlinearSolve]]
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[[OffsetArrays]]
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[[Ogg_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "7937eda4681660b4d6aeeecc2f7e1c81c8ee4e2f"
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[[OpenSSL_jll]]
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git-tree-sha1 = "15003dcb7d8db3c6c857fda14891a539a8f2705a"
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[[OpenSpecFun_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "13652491f6856acfd2db29360e1bbcd4565d04f1"
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[[Opus_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "51a08fb14ec28da2ec7a927c4337e4332c2a4720"
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[[OrderedCollections]]
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[[OrdinaryDiffEq]]
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uuid = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
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[[PCRE_jll]]
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git-tree-sha1 = "b2a7af664e098055a7529ad1a900ded962bca488"
uuid = "2f80f16e-611a-54ab-bc61-aa92de5b98fc"
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[[Parameters]]
deps = ["OrderedCollections", "UnPack"]
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[[Parsers]]
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[[Pixman_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b4f5d02549a10e20780a24fce72bea96b6329e29"
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[[Pkg]]
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uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"

[[PlotThemes]]
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[[PlotUtils]]
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[[Plots]]
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[[PlutoUI]]
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[[Polyester]]
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[[Preferences]]
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[[Printf]]
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[[Qt5Base_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "Fontconfig_jll", "Glib_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "OpenSSL_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libxcb_jll", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_keysyms_jll", "Xorg_xcb_util_renderutil_jll", "Xorg_xcb_util_wm_jll", "Zlib_jll", "xkbcommon_jll"]
git-tree-sha1 = "ad368663a5e20dbb8d6dc2fddeefe4dae0781ae8"
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[[REPL]]
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uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"

[[Random]]
deps = ["Serialization"]
uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"

[[RecipesBase]]
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[[RecipesPipeline]]
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[[RecursiveArrayTools]]
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[[RecursiveFactorization]]
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[[Reexport]]
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uuid = "189a3867-3050-52da-a836-e630ba90ab69"
version = "1.1.0"

[[Requires]]
deps = ["UUIDs"]
git-tree-sha1 = "4036a3bd08ac7e968e27c203d45f5fff15020621"
uuid = "ae029012-a4dd-5104-9daa-d747884805df"
version = "1.1.3"

[[SHA]]
uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"

[[SLEEFPirates]]
deps = ["IfElse", "Static", "VectorizationBase"]
git-tree-sha1 = "da6d214ffc85b1292f300649ef86d3c4f9aaf25d"
uuid = "476501e8-09a2-5ece-8869-fb82de89a1fa"
version = "0.6.22"

[[SciMLBase]]
deps = ["ArrayInterface", "CommonSolve", "ConstructionBase", "Distributed", "DocStringExtensions", "IteratorInterfaceExtensions", "LinearAlgebra", "Logging", "RecipesBase", "RecursiveArrayTools", "StaticArrays", "Statistics", "Tables", "TreeViews"]
git-tree-sha1 = "932aaae93e81686e6473f27b5a11c403576a2183"
uuid = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
version = "1.18.0"

[[Scratch]]
deps = ["Dates"]
git-tree-sha1 = "0b4b7f1393cff97c33891da2a0bf69c6ed241fda"
uuid = "6c6a2e73-6563-6170-7368-637461726353"
version = "1.1.0"

[[Serialization]]
uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"

[[Setfield]]
deps = ["ConstructionBase", "Future", "MacroTools", "Requires"]
git-tree-sha1 = "d5640fc570fb1b6c54512f0bd3853866bd298b3e"
uuid = "efcf1570-3423-57d1-acb7-fd33fddbac46"
version = "0.7.0"

[[SharedArrays]]
deps = ["Distributed", "Mmap", "Random", "Serialization"]
uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"

[[Showoff]]
deps = ["Dates", "Grisu"]
git-tree-sha1 = "91eddf657aca81df9ae6ceb20b959ae5653ad1de"
uuid = "992d4aef-0814-514b-bc4d-f2e9a6c4116f"
version = "1.0.3"

[[SimpleTraits]]
deps = ["InteractiveUtils", "MacroTools"]
git-tree-sha1 = "5d7e3f4e11935503d3ecaf7186eac40602e7d231"
uuid = "699a6c99-e7fa-54fc-8d76-47d257e15c1d"
version = "0.9.4"

[[Sockets]]
uuid = "6462fe0b-24de-5631-8697-dd941f90decc"

[[SortingAlgorithms]]
deps = ["DataStructures"]
git-tree-sha1 = "b3363d7460f7d098ca0912c69b082f75625d7508"
uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
version = "1.0.1"

[[SparseArrays]]
deps = ["LinearAlgebra", "Random"]
uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"

[[SparseDiffTools]]
deps = ["Adapt", "ArrayInterface", "Compat", "DataStructures", "FiniteDiff", "ForwardDiff", "LightGraphs", "LinearAlgebra", "Requires", "SparseArrays", "StaticArrays", "VertexSafeGraphs"]
git-tree-sha1 = "cc8703d09d1e7337fb794dbf6c9634afaa4f49c7"
uuid = "47a9eef4-7e08-11e9-0b38-333d64bd3804"
version = "1.14.1"

[[SpecialFunctions]]
deps = ["ChainRulesCore", "LogExpFunctions", "OpenSpecFun_jll"]
git-tree-sha1 = "a50550fa3164a8c46747e62063b4d774ac1bcf49"
uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
version = "1.5.1"

[[Static]]
deps = ["IfElse"]
git-tree-sha1 = "2740ea27b66a41f9d213561a04573da5d3823d4b"
uuid = "aedffcd0-7271-4cad-89d0-dc628f76c6d3"
version = "0.2.5"

[[StaticArrays]]
deps = ["LinearAlgebra", "Random", "Statistics"]
git-tree-sha1 = "1b9a0f17ee0adde9e538227de093467348992397"
uuid = "90137ffa-7385-5640-81b9-e52037218182"
version = "1.2.7"

[[Statistics]]
deps = ["LinearAlgebra", "SparseArrays"]
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"

[[StatsAPI]]
git-tree-sha1 = "1958272568dc176a1d881acb797beb909c785510"
uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
version = "1.0.0"

[[StatsBase]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "2f6792d523d7448bbe2fec99eca9218f06cc746d"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.33.8"

[[StrideArraysCore]]
deps = ["ArrayInterface", "ManualMemory", "Requires", "ThreadingUtilities", "VectorizationBase"]
git-tree-sha1 = "2525850b6887e217c3cc149ab29eb2a7a6360d37"
uuid = "7792a7ef-975c-4747-a70f-980b88e8d1da"
version = "0.1.16"

[[StructArrays]]
deps = ["Adapt", "DataAPI", "StaticArrays", "Tables"]
git-tree-sha1 = "000e168f5cc9aded17b6999a560b7c11dda69095"
uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
version = "0.6.0"

[[SuiteSparse]]
deps = ["Libdl", "LinearAlgebra", "Serialization", "SparseArrays"]
uuid = "4607b0f0-06f3-5cda-b6b1-a6196a1729e9"

[[Suppressor]]
git-tree-sha1 = "a819d77f31f83e5792a76081eee1ea6342ab8787"
uuid = "fd094767-a336-5f1f-9728-57cf17d0bbfb"
version = "0.2.0"

[[TOML]]
deps = ["Dates"]
uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"

[[TableTraits]]
deps = ["IteratorInterfaceExtensions"]
git-tree-sha1 = "c06b2f539df1c6efa794486abfb6ed2022561a39"
uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c"
version = "1.0.1"

[[Tables]]
deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "TableTraits", "Test"]
git-tree-sha1 = "8ed4a3ea724dac32670b062be3ef1c1de6773ae8"
uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
version = "1.4.4"

[[Tar]]
deps = ["ArgTools", "SHA"]
uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"

[[Test]]
deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

[[ThreadingUtilities]]
deps = ["ManualMemory"]
git-tree-sha1 = "593009385e6536dc50baedc2c8bc1a3717ef358f"
uuid = "8290d209-cae3-49c0-8002-c8c24d57dab5"
version = "0.4.5"

[[TreeViews]]
deps = ["Test"]
git-tree-sha1 = "8d0d7a3fe2f30d6a7f833a5f19f7c7a5b396eae6"
uuid = "a2a6695c-b41b-5b7d-aed9-dbfdeacea5d7"
version = "0.3.0"

[[URIs]]
git-tree-sha1 = "97bbe755a53fe859669cd907f2d96aee8d2c1355"
uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
version = "1.3.0"

[[UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

[[UnPack]]
git-tree-sha1 = "387c1f73762231e86e0c9c5443ce3b4a0a9a0c2b"
uuid = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
version = "1.0.2"

[[Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"

[[VectorizationBase]]
deps = ["ArrayInterface", "Hwloc", "IfElse", "Libdl", "LinearAlgebra", "Static"]
git-tree-sha1 = "b609848b41158b8cc13a72dc6deb9511f9a96187"
uuid = "3d5dd08c-fd9d-11e8-17fa-ed2836048c2f"
version = "0.20.22"

[[VertexSafeGraphs]]
deps = ["LightGraphs"]
git-tree-sha1 = "b9b450c99a3ca1cc1c6836f560d8d887bcbe356e"
uuid = "19fa3120-7c27-5ec5-8db8-b0b0aa330d6f"
version = "0.1.2"

[[Wayland_jll]]
deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "3e61f0b86f90dacb0bc0e73a0c5a83f6a8636e23"
uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
version = "1.19.0+0"

[[Wayland_protocols_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll"]
git-tree-sha1 = "2839f1c1296940218e35df0bbb220f2a79686670"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.18.0+4"

[[XML2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "1acf5bdf07aa0907e0a37d3718bb88d4b687b74a"
uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
version = "2.9.12+0"

[[XSLT_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "Pkg", "XML2_jll", "Zlib_jll"]
git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a"
uuid = "aed1982a-8fda-507f-9586-7b0439959a61"
version = "1.1.34+0"

[[Xorg_libX11_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
git-tree-sha1 = "5be649d550f3f4b95308bf0183b82e2582876527"
uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
version = "1.6.9+4"

[[Xorg_libXau_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4e490d5c960c314f33885790ed410ff3a94ce67e"
uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
version = "1.0.9+4"

[[Xorg_libXcursor_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd"
uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724"
version = "1.2.0+4"

[[Xorg_libXdmcp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fe47bd2247248125c428978740e18a681372dd4"
uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
version = "1.1.3+4"

[[Xorg_libXext_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "b7c0aa8c376b31e4852b360222848637f481f8c3"
uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
version = "1.3.4+4"

[[Xorg_libXfixes_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4"
uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
version = "5.0.3+4"

[[Xorg_libXi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
version = "1.7.10+4"

[[Xorg_libXinerama_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
version = "1.1.4+4"

[[Xorg_libXrandr_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
version = "1.5.2+4"

[[Xorg_libXrender_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.10+4"

[[Xorg_libpthread_stubs_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "6783737e45d3c59a4a4c4091f5f88cdcf0908cbb"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
version = "0.1.0+3"

[[Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
git-tree-sha1 = "daf17f441228e7a3833846cd048892861cff16d6"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.13.0+3"

[[Xorg_libxkbfile_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "926af861744212db0eb001d9e40b5d16292080b2"
uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
version = "1.1.0+4"

[[Xorg_xcb_util_image_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
version = "0.4.0+1"

[[Xorg_xcb_util_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"]
git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
version = "0.4.0+1"

[[Xorg_xcb_util_keysyms_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
version = "0.4.0+1"

[[Xorg_xcb_util_renderutil_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
version = "0.3.9+1"

[[Xorg_xcb_util_wm_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
version = "0.4.1+1"

[[Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "4bcbf660f6c2e714f87e960a171b119d06ee163b"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.2+4"

[[Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "5c8424f8a67c3f2209646d4425f3d415fee5931d"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.27.0+4"

[[Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.4.0+3"

[[Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"

[[Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "cc4bf3fdde8b7e3e9fa0351bdeedba1cf3b7f6e6"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.0+0"

[[ZygoteRules]]
deps = ["MacroTools"]
git-tree-sha1 = "9e7a1e8ca60b742e508a315c17eef5211e7fbfd7"
uuid = "700de1a5-db45-46bc-99cf-38207098b444"
version = "0.2.1"

[[libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "acc685bcf777b2202a904cdcb49ad34c2fa1880c"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.14.0+4"

[[libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "7a5780a0d9c6864184b3a2eeeb833a0c871f00ab"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "0.1.6+4"

[[libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.38+0"

[[libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "c45f4e40e7aafe9d086379e5578947ec8b95a8fb"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+0"

[[nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"

[[p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"

[[x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "d713c1ce4deac133e3334ee12f4adff07f81778f"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2020.7.14+2"

[[x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "487da2f8f2f0c8ee0e83f39d13037d6bbf0a45ab"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.0.0+3"

[[xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "ece2350174195bb31de1a63bea3a41ae1aa593b6"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "0.9.1+5"
"""

# ╔═╡ Cell order:
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# ╠═4a72dcd8-bb16-4d63-a8a8-e89865b3ff95
# ╠═7541a4c5-e8bd-4700-880d-8d7e1b05cdf9
# ╠═9087b209-8385-4da8-8cfd-6eb7f4a2a0aa
# ╠═8e990cf8-3fee-4fde-b044-0e95c90a19a8
# ╠═54a73741-2b04-4bb5-9bcb-b594b451d9ec
# ╠═568527c6-0760-405e-a056-98a22f95454c
# ╠═dea4b784-87c7-4497-b11b-b1ca1cc83c71
# ╠═b330f75d-125c-4a49-a830-5672ed18c56b
# ╠═364206c0-954b-45b1-9f20-e5031c34de16
# ╠═2f80e9cb-9bd6-4189-9d84-20d5e1c6b0e3
# ╠═8864fe08-3dd3-4731-ac26-7ae256835f03
# ╠═5a3929ad-5719-4021-993c-acc31db4a674
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