### A Pluto.jl notebook ###
# v0.20.24

using Markdown
using InteractiveUtils

# ╔═╡ e6e2b124-f53c-11f0-1dd6-e74cdd0384f9
using DifferentialEquations,Plots, LaTeXStrings, Graphs,GraphRecipes, Random, NetworkLayout

# ╔═╡ 52b3f226-d907-4cae-bf86-bb671e244b26
function generatetriadicnetw(n,probp,probt;frange=0.5)#generates a triadic network represented by three directed graphs. 'n' is the number of nodes. The generated network 'g' is a directed pairwise network, where nodes are chosen with probability 'probp'. Among all triplets of nodes which have no connections in g we chose with probability 'probt' a number of triplets and fix randomly the role of the nodes in the triplet: 'b' and 'c' are the connected pair and 'a' modulates their interaction. The network 'tp' contains the pairwise links (b<->c). The network 'tm' has directed links (b->a) and (c->a) whenever 'a' modulates the interaction of 'b' and 'c'.
	rng=MersenneTwister(123)
	#tr=rand(rng)
	w  = (1. -frange) .+ 2. *frange*rand(rng,n) 
	g  = erdos_renyi(n, probp, is_directed=true, seed=123)
	tm = DiGraph(n,0)
	tp = DiGraph(n,0)
	emptytriags = []
	triplets = [] 
	for j1 in 1:n
		for j2 in j1+1:n
			for j3 in j2+1:n
				if  !(j1 in neighbors(g,j2)) && !(j2 in neighbors(g,j1)) &&
					!(j2 in neighbors(g,j3)) && !(j3 in neighbors(g,j2)) &&
					!(j3 in neighbors(g,j1)) && !(j1 in neighbors(g,j3)) 
					push!(emptytriags,(j1,j2,j3))
				end
			end
		end
	end
	for jj in 1:length(emptytriags)
		if rand(rng)<probt
			a=rand(rng,1:3)
			b=mod(a,3)+1
			c=mod(b,3)+1
			push!(triplets,[emptytriags[jj][a],emptytriags[jj][b],emptytriags[jj][c]])
			add_edge!(tp,(emptytriags[jj][b],emptytriags[jj][c]))
			add_edge!(tp,(emptytriags[jj][c],emptytriags[jj][b]))
			add_edge!(tm,(emptytriags[jj][b],emptytriags[jj][a]))
			add_edge!(tm,(emptytriags[jj][c],emptytriags[jj][a]))
		end
	end

(g,tm,tp,w, emptytriags,triplets)
end

# ╔═╡ 3eaa505d-83c2-462f-92ac-4e223e25babf
function largetriadicnetwork!(du,u,p,t) # right hand side for Stuart-Landau network with multiple triadic motifs. Vector of natural frequencies ω, pairwise network g, triplets are represented by two pairwise networks tp and tm, triplet coupling strength α, pairwise coupling strength β, SL parameter λ.
	(ω,g,tp,tm,α,β,λ) = p 
	n = length(ω)
	function sl(u,omega) #Stuart-Landau oscillator 
		(λ + omega * im - abs(u)^2)*u 
	end
	
	function h(u1,u2) 
		(u2 -conj(u1))
	end
	 
	for jj in 1:n
		
		du[jj] = sl(u[jj],ω[jj]) - β/ne(g) * sum(u[jj] .- u[neighbors(g,jj)]) + 
		2*α/ne(tm) * sum(u[neighbors(tm,jj)] .* h.(u[neighbors(tp,jj)] ,u[jj]))
	end
end

# ╔═╡ cdb2b1f3-32c1-49db-89b0-eaef69938816
function randcomp(n) #gives a vector of 'n' random complex numbers uniformly distributed in the unit square.
	u=[]
	for j in 1:n
		push!(u,rand()+ im*rand())
	end
	u 
end

# ╔═╡ 4911ccf3-3645-4e18-9372-dadda7597922
function runsim(ttrans,trec,p) #Runs a simulation with right hand side 'largetriadicnetwork!' and parameters 'p'. After a start from random initial conditions a trajectory of length 'ttrans' is discarded and then a trajectory of length 'trec' is recorded.
probtrans = ODEProblem(largetriadicnetwork!, 0.3*randcomp(length(p[1])),ttrans,p)
soltrans  = solve(probtrans,save_everystep=false,abstol=1e-4 )

probrec = ODEProblem(largetriadicnetwork!, soltrans.u[end],trec,p)
solrec  = solve(probrec,alg=Tsit5(),abstol=1e-8 )
end

# ╔═╡ 1b12c3d3-88d7-4c94-849a-692ea4735161
function phase(sol,i;ref=1.,step=0.1) #extracts the unwraped phase of oscillator 'i' in a network solution 'sol'. 
	trange = 0.:step:sol.t[end]
	ph(t)=mod(angle(sol(t)[i]),2*pi)
	uwp=[ph(0.)]
	shift  = 0.
	for ii in trange[2:end]
		shift = shift + div(ph(ii) - ph(ii-step),2*pi,RoundNearest)
		push!(uwp,ph(ii) -shift*2*pi)
	end
	trange,uwp
end

# ╔═╡ cd6bc01f-c797-413e-b378-cbafbe5caeac
function alleffr(gg,sol) #extracts all effective frequencies from a given solution 'sol' with underlying network 'gg' (the network is just used for indexing the nodes)
	alfr=[]
	for jj in vertices(gg)
		ph = phase(sol,jj)[2]
		push!(alfr,(ph[end]-ph[1])/sol.t[end])
	end
	alfr
end

# ╔═╡ 4cd1363a-58a3-48f1-988c-a8db7e899156
function effreqtr(tnw,sol) # displays for a given hypernetwork the triplets together with their natural and effective frequencies 
	effr=[]
	natfr=[]
	for jj in 1: length(tnw[6])
		a=tnw[6][jj][1]
		b=tnw[6][jj][2]
		c=tnw[6][jj][3]
		pha, phb, phc = phase(sol,a)[2], phase(sol,b)[2], phase(sol,c)[2]
		push!(effr,[(pha[end]-pha[1])/sol.t[end],(phb[end]-phb[1])/sol.t[end], (phc[end]-phc[1])/sol.t[end]])
		push!(natfr,[tnw[4][a],tnw[4][b],tnw[4][c]])
	end
tnw[6],effr,natfr
end

# ╔═╡ 1b516697-9ad7-4996-8363-92e1b6c9d3fe
function pwphd(sol,j,k;step=0.1)#extracts the unwraped pairwise phase difference of oscillators 'j-k' in a network solution 'sol'. 
	trange = 0.:step:sol.t[end]
	pdiff  = [mod(angle(sol(0.)[j])-angle(sol(0.)[k]),2*pi)]
	shift  = 0.
	for ii in trange[2:end]
		shift=shift+div(mod(angle(sol(ii)[j])-angle(sol(ii)[k]),2*pi)-
		mod(angle(sol(ii-step)[j]) -angle(sol(ii-step)[k]),2*pi),2*pi,RoundNearest)
		push!(pdiff,mod(angle(sol(ii)[j])-angle(sol(ii)[k]),2*pi) - shift*2*pi)
	end
	trange,pdiff
end

# ╔═╡ 4633d5d0-76d9-4ae0-aef0-34ab65cba09e
function trphd(sol,i,j,k;step=0.1)#extracts the unwraped triplet phase of oscillators 'i+j-2k' in a network solution 'sol'. 
	trange = 0.:step:sol.t[end]
	tr(t)=mod(angle(sol(t)[i])+angle(sol(t)[j])-2*angle(sol(t)[k]),2*pi)
	pdiff=[tr(0.)]
	shift  = 0.
	for ii in trange[2:end]
		shift = shift + div(tr(ii) - tr(ii-step),2*pi,RoundNearest)
		push!(pdiff,tr(ii) -shift*2*pi)
	end
	trange,pdiff
end

# ╔═╡ a5430ebc-31b4-48fc-8913-5dfc063c77c7
function plottrnw(tnw) #plots a triadic network structure produced by 'generatetriadicnetw'.
	function extractxy(pos)
		x=[]
		y=[]
		for jj in 1: length(pos)
			push!(x,pos[jj][1])
			push!(y,pos[jj][2])
		end
		x,y
	end
	pos = stress(tnw[1])
	x,y=extractxy(pos)
	m=length(tnw[6])
	mg=DiGraph(2*m,0)
	xmod=[]
	xmodt=[]
	ymod=[]
	ymodt=[]
		for jj in 1:m
			add_edge!(mg,(jj,m+jj))
			push!(xmod, x[tnw[6][jj][1]])
			push!(ymod, y[tnw[6][jj][1]])
			push!(xmodt, (x[tnw[6][jj][2]]+x[tnw[6][jj][3]])/2.)
			push!(ymodt, (y[tnw[6][jj][2]]+y[tnw[6][jj][3]])/2.)
		end
	p1=graphplot(mg,x=append!(xmod,xmodt), y=append!(ymod,ymodt), edgecolor=:blue,linewidth=2, curvature=0.0,markersize = 0.001,style=:dash,size=(200,200),annotation=(-1.2,1.5,"(a)"),annotationfontsizes=12)
	
	graphplot!(p1,tnw[3],x=x,y=y,edgecolor=:blue,linewidth=2, curvature=0.0,markersize = 0.001,arrow=:none)

	graphplot!(p1,tnw[1], x=x, y=y,curves=true, nodeshape=:circle, markersize = 0.35, fontsize=10,nodecolor=[:red,:blue,:blue,:blue,:red,:blue,:blue,:blue,:blue,:blue, :blue,:blue,:red,:blue,:blue,:blue,:blue,:blue,:blue,:blue], 
	names=["a"," "," "," ","b"," "," "," "," "," "," "," ","c"," "," "," "," "," "," "," "])
end

# ╔═╡ 0d0a0938-67f9-4d70-a17c-479d522bde77
md"### Test system with $n=3$
Just for testing we recover the results for the triadic motif."

# ╔═╡ 68ec7863-abd5-4b40-933b-29101875939f
gg=complete_graph(3) #network of pairwise links 

# ╔═╡ 4c0c9c36-12e3-41ff-a1ba-c2b38e2dea4c
trnwtest=generatetriadicnetw(3,0.,1.) #network defining the single higher order link

# ╔═╡ 03ac5976-dc02-4f2a-bb68-fbc36a816ab1
graphplot(trnwtest[2],curves=false, names = 1:3 )

# ╔═╡ c4f4a4df-1cbe-4116-a312-52b1ac2a9e3e
graphplot(trnwtest[3],curves=false, names = 1:3 )

# ╔═╡ f2dd9a65-8228-4493-a2a0-60861be05000
ww=[0.98,0.95,1.05]; #natural frequencies

# ╔═╡ 358b33bd-d522-4198-86bd-a1d4ddc0072c
soltest  = runsim(500,100,(ww,gg,trnwtest[3],trnwtest[2],0.3,0.0,0.2));

# ╔═╡ e9f32600-1488-47b3-b70e-5464d3e29423
function plotp(sol;step=0.1) #plots pairwise phase differences of solution 'sol'
	trange=0.:step:sol.t[end]
	pdiff12=[mod(angle(sol(0.)[1])-angle(sol(0.)[2]),2*pi)]
	pdiff23=[mod(angle(sol(0.)[2])-angle(sol(0.)[3]),2*pi)]
	pdiff31=[mod(angle(sol(0.)[3])-angle(sol(0.)[1]),2*pi)]
	shift12=0.
	shift23=0.
	shift31=0.
	for ii in trange[2:end]
		shift12=shift12+div(mod(angle(sol(ii)[1])-angle(sol(ii)[2]),2*pi)-
		mod(angle(sol(ii-step)[1]) -angle(sol(ii-step)[2]),2*pi),2*pi,RoundNearest)
		shift23=shift23+div(mod(angle(sol(ii)[2])-angle(sol(ii)[3]),2*pi)-
		mod(angle(sol(ii-step)[2]) -angle(sol(ii-step)[3]),2*pi),2*pi,RoundNearest)
		shift31=shift31+div(mod(angle(sol(ii)[3])-angle(sol(ii)[1]),2*pi)-
		mod(angle(sol(ii-step)[3]) -angle(sol(ii-step)[1]),2*pi),2*pi,RoundNearest)
		push!(pdiff12,mod(angle(sol(ii)[1])-angle(sol(ii)[2]),2*pi) -shift12*2*pi)
		push!(pdiff23,mod(angle(sol(ii)[2])-angle(sol(ii)[3]),2*pi) -shift23*2*pi)
		push!(pdiff31,mod(angle(sol(ii)[3])-angle(sol(ii)[1]),2*pi) -shift31*2*pi)
		end
	plot(trange,[pdiff12,pdiff23,pdiff31],color=[:purple :orange :cyan],framestyle=:box,labels=[L"\hat\phi_1-\hat\phi_2" L"\hat\phi_2-\hat\phi_3" L"\hat\phi_3-\hat\phi_1"], yrange=[-7,7], size=(600,200),xticks=false,grid=false,legend_position=:bottomright, yticks=[-5.,0.,5.],annotation=(1,5.4,"(b)"),annotationfontsizes=12,legendfontsize=12,linewidth=2)
end

# ╔═╡ d151ef53-846c-4f82-8300-fd4be387fd9e
function plott(sol;step=0.1) #plots unwrapped triple phase differences of solution 'sol'

	tr1(t)=mod(angle(sol(t)[1])+angle(sol(t)[2])-2*angle(sol(t)[3]),2*pi)
	tr2(t)=mod(angle(sol(t)[2])+angle(sol(t)[3])-2*angle(sol(t)[1]),2*pi)
	tr3(t)=mod(angle(sol(t)[3])+angle(sol(t)[1])-2*angle(sol(t)[2]),2*pi)
	
	trange=0.:step:sol.t[end]

	pdiff1=[tr1(0.)]
	pdiff2=[tr2(0.)]
	pdiff3=[tr3(0.)]
	shift1=0.
	shift2=0.
	shift3=0.
	for ii in trange[2:end]
		shift1 = shift1 + div(tr1(ii) - tr1(ii-step),2*pi,RoundNearest)
		shift2 = shift2 + div(tr2(ii) - tr2(ii-step),2*pi,RoundNearest)
		shift3 = shift3 + div(tr3(ii) - tr3(ii-step),2*pi,RoundNearest)
		
		push!(pdiff1,tr1(ii) -shift1*2*pi)
		push!(pdiff2,tr2(ii) -shift2*2*pi)
		push!(pdiff3,tr3(ii) -shift3*2*pi)
	end
plot(trange,[pdiff1,pdiff2,pdiff3],framestyle=:box,labels=[L"\hat\phi_1+\hat\phi_2-2\hat\phi_3" L"\hat\phi_2+\hat\phi_3-2\hat\phi_1" L"\hat\phi_3+\hat\phi_1-2\hat\phi_2"], yrange=[-12,12] ,size=(600,200),grid=false,legend_position=:bottomright,color=[:deeppink :darkgreen  :navy], xlabel=L"t", yticks=[-10,0,10],annotation=(1,10.,"(c)"),annotationfontsizes=12,legendfontsize=12, linewidth=2,xguidefontsize=12)
end

# ╔═╡ 1d85b4b1-8822-4328-9f7d-3aac5299328c
rp(t,u)=(t,real(u)) #function for plotting (extracts real part of a component vs time)

# ╔═╡ 01471628-7089-41a2-b6d8-a684ca3e88d9
begin
	
	p1=plot(soltest, idxs = [(rp, 0, 1),(rp, 0, 2),(rp, 0, 3)], xticks=false, 
	xlabel="", framestyle=:box, grid=false,size=(600,200), yrange=(-1.5,1.5), yticks=[-1.,0.,1.], labels=[L"\mathrm{Re} (z_1)" L"\mathrm{Re}(z_2)" L"\mathrm{Re}(z_3)"], annotation=(4,1.2,"(a)"), annotationfontsizes=12, legendfontsize=12,linewidth=2,guidefontsize=14); #plots time traces of real parts

	p2=plotp(soltest); #plots pairwise phase differences

	p3=plott(soltest); #plots triplet phases

	fig1=plot(p1,p2,p3,layout=(3,1),size=(600,600)) # combined plot
end

# ╔═╡ 810d442b-1b30-44ed-b109-fe4ab0c0dd93
md" ### Network with pairwise and triadic coupling
We simulate now a hypernetwork with randomly chosen pairwise directed links and triadic hyperlinks. The triadic links a chosen from triplets of nodes that have no pairwise connections among them, but are linked to the other nodes by pairwise and, possibly, also by one of the other triadic links.

"

# ╔═╡ 9a976ce0-a318-43b8-b934-274a2790be89
tnw=generatetriadicnetw(20,0.2,0.05,frange=0.3)

# ╔═╡ 2f73156a-a8b2-4d81-8afe-5d0561b8a4f1
md"
This hypernetwork has $n=20$ nodes with directed pairwise links indicated by the black arrows and triadic hyperlinks indicated in blue. The dashed arrows pointing not to a node but to another blue solid link indicate, where a third node modulates  a pairwise connection, generating together a triplet hyperlink. Within the triplet of red nodes will adapt the natural frequencies such that together they are sufficiently close to full resonance. All other natural frequencies are chosen with equal probability from the interval $[0.7,1.3]$.
" 

# ╔═╡ fc263a9d-a07e-4fb4-bba5-b43cef24c250
md"First, we simulate the network with only the pairwise links, i.e. $\beta=0$. "

# ╔═╡ c5238c84-a689-49be-8946-beea93c7eb33
sol0=runsim(1000,500,(tnw[4],tnw[1],tnw[3],tnw[2],0.0,1.,0.3));#only paiwise links

# ╔═╡ a103e0e1-a916-49ed-8203-ac3c2303b69b
md"  The effective frequencies show that for the given coupling strength there is a pairwise locking among some of the nodes. This depends on their random connectedness and natural frequencies. "

# ╔═╡ 4b7b5165-0e6c-47e2-9cdf-ecf8a22de58d
sort(alleffr(tnw[1],sol0))

# ╔═╡ 7764f4bc-a159-4277-964d-367230a5d8e4
md"Now we inspect the effective frequencies of the oscillators in the triplet hyperlinks. " 

# ╔═╡ da41ed56-9094-4f54-88cf-63c1dcc4ce62
effreqtr(tnw,sol0)

# ╔═╡ 91564504-554d-4292-9184-99f53d8f7dca
md" We adapt now two of the frequencies in the first triplet to bring it close to full resonance."

# ╔═╡ e550ba23-adf4-4779-8a35-d17f16e9daff
w=copy(tnw[4])

# ╔═╡ 9847f76f-269f-48ab-b743-c7f99cbf8d22
w[1],w[5]=0.94,1.03

# ╔═╡ 475e441f-d144-41d8-9a21-12d8807c3586
sol1=runsim(1000,500,(w,tnw[1],tnw[3],tnw[2],0.0,1.,0.3));# adapted frequencies 'w', no triplet coupling

# ╔═╡ 7404a469-11d3-434c-83c6-2331b5928a2c
effreqtr(tnw,sol1)

# ╔═╡ 8187154e-4194-4fd5-8252-6aec0887516a
md"Finally, we simulate the full network system with pairwise and triplet links and the adapted natural frequencies."

# ╔═╡ fed71c68-671a-4126-84ca-48d4024a02d5
sol  = runsim(1000,500,(w,tnw[1],tnw[3],tnw[2],1.5,1.,0.3)); #adapted frequencies and triplet coupling

# ╔═╡ e4b0d5cc-69c1-4bce-a1b2-b955e470346a
begin
	pa=plottrnw(tnw)
	
	pb=plot([pwphd(sol,1,5),pwphd(sol,5,13),pwphd(sol,13,1)], framestyle=:box, grid=false, size=(600,200), labels=[L"\hat\phi_a-\hat\phi_b" L"\hat\phi_b-\hat\phi_c" L"\hat\phi_c-\hat\phi_a"], legend_position=:topright, color=[:purple :orange :cyan], xticks=false, yticks=[-40.,0.,40.], yrange=[-50.,50], annotation=(5,41,"(b)"), annotationfontsizes=12, legendfontsize=12,linewidth=2)
	plot!(pb,[pwphd(sol1,1,5),pwphd(sol1,5,13),pwphd(sol1,13,1)],color=[:purple :orange :cyan], opacity=0.5,labels=:none)
	
	pc=plot([trphd(sol,1,5,13),trphd(sol,5,13,1),trphd(sol,13,1,5)], framestyle=:box, grid=false, size=(600,280), labels=[L"\hat\phi_a+\hat\phi_b-2\hat\phi_c" L"\hat\phi_b+\hat\phi_c-2\hat\phi_a" L"\hat\phi_c+\hat\phi_a-2\hat\phi_b"], yrange=[-100,100], legend_position=:bottomright, color=[:darkgreen  :deeppink :navy], xlabel=L"t", annotation=(5,87,"(c)"), annotationfontsizes=12, legendfontsize=12,linewidth=2,guidefontsize=12);
	plot!(pc,[trphd(sol1,1,5,13),trphd(sol1,5,13,1),trphd(sol1,13,1,5)],
		 color=[:darkgreen  :deeppink :navy], opacity=0.5,labels=:none);
	
	fig6=plot(pa,pb,pc,layout=Plots.grid(3,1,heights=[0.64,0.16,0.20]), size=(600,1000))

end

# ╔═╡ 82d530e5-99ae-466f-bdf2-9929e8a63074
savefig(fig6,"./Figs/Fig6.png")

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git-tree-sha1 = "52858d64353db33a56e13c341d7bf44cd0d7b309"
uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
version = "1.1.6+0"

[[deps.Xorg_libXext_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
git-tree-sha1 = "a4c0ee07ad36bf8bbce1c3bb52d21fb1e0b987fb"
uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
version = "1.3.7+0"

[[deps.Xorg_libXfixes_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
git-tree-sha1 = "9caba99d38404b285db8801d5c45ef4f4f425a6d"
uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
version = "6.0.1+0"

[[deps.Xorg_libXi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
git-tree-sha1 = "a376af5c7ae60d29825164db40787f15c80c7c54"
uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
version = "1.8.3+0"

[[deps.Xorg_libXinerama_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libXext_jll"]
git-tree-sha1 = "a5bc75478d323358a90dc36766f3c99ba7feb024"
uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
version = "1.1.6+0"

[[deps.Xorg_libXrandr_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "aff463c82a773cb86061bce8d53a0d976854923e"
uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
version = "1.5.5+0"

[[deps.Xorg_libXrender_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
git-tree-sha1 = "7ed9347888fac59a618302ee38216dd0379c480d"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.12+0"

[[deps.Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libXau_jll", "Xorg_libXdmcp_jll"]
git-tree-sha1 = "bfcaf7ec088eaba362093393fe11aa141fa15422"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.17.1+0"

[[deps.Xorg_libxkbfile_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
git-tree-sha1 = "e3150c7400c41e207012b41659591f083f3ef795"
uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
version = "1.1.3+0"

[[deps.Xorg_xcb_util_cursor_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_jll", "Xorg_xcb_util_renderutil_jll"]
git-tree-sha1 = "c5bf2dad6a03dfef57ea0a170a1fe493601603f2"
uuid = "e920d4aa-a673-5f3a-b3d7-f755a4d47c43"
version = "0.1.5+0"

[[deps.Xorg_xcb_util_image_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xcb_util_jll"]
git-tree-sha1 = "f4fc02e384b74418679983a97385644b67e1263b"
uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
version = "0.4.1+0"

[[deps.Xorg_xcb_util_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxcb_jll"]
git-tree-sha1 = "68da27247e7d8d8dafd1fcf0c3654ad6506f5f97"
uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
version = "0.4.1+0"

[[deps.Xorg_xcb_util_keysyms_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xcb_util_jll"]
git-tree-sha1 = "44ec54b0e2acd408b0fb361e1e9244c60c9c3dd4"
uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
version = "0.4.1+0"

[[deps.Xorg_xcb_util_renderutil_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xcb_util_jll"]
git-tree-sha1 = "5b0263b6d080716a02544c55fdff2c8d7f9a16a0"
uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
version = "0.3.10+0"

[[deps.Xorg_xcb_util_wm_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xcb_util_jll"]
git-tree-sha1 = "f233c83cad1fa0e70b7771e0e21b061a116f2763"
uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
version = "0.4.2+0"

[[deps.Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "801a858fc9fb90c11ffddee1801bb06a738bda9b"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.7+0"

[[deps.Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "00af7ebdc563c9217ecc67776d1bbf037dbcebf4"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.44.0+0"

[[deps.Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "a63799ff68005991f9d9491b6e95bd3478d783cb"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.6.0+0"

[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.3.1+2"

[[deps.Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "446b23e73536f84e8037f5dce465e92275f6a308"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.7+1"

[[deps.eudev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "c3b0e6196d50eab0c5ed34021aaa0bb463489510"
uuid = "35ca27e7-8b34-5b7f-bca9-bdc33f59eb06"
version = "3.2.14+0"

[[deps.fzf_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "b6a34e0e0960190ac2a4363a1bd003504772d631"
uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09"
version = "0.61.1+0"

[[deps.libaom_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "4bba74fa59ab0755167ad24f98800fe5d727175b"
uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
version = "3.12.1+0"

[[deps.libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "125eedcb0a4a0bba65b657251ce1d27c8714e9d6"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.17.4+0"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.15.0+0"

[[deps.libdecor_jll]]
deps = ["Artifacts", "Dbus_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "Pango_jll", "Wayland_jll", "xkbcommon_jll"]
git-tree-sha1 = "9bf7903af251d2050b467f76bdbe57ce541f7f4f"
uuid = "1183f4f0-6f2a-5f1a-908b-139f9cdfea6f"
version = "0.2.2+0"

[[deps.libevdev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "56d643b57b188d30cccc25e331d416d3d358e557"
uuid = "2db6ffa8-e38f-5e21-84af-90c45d0032cc"
version = "1.13.4+0"

[[deps.libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "646634dd19587a56ee2f1199563ec056c5f228df"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.4+0"

[[deps.libinput_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "eudev_jll", "libevdev_jll", "mtdev_jll"]
git-tree-sha1 = "91d05d7f4a9f67205bd6cf395e488009fe85b499"
uuid = "36db933b-70db-51c0-b978-0f229ee0e533"
version = "1.28.1+0"

[[deps.libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "07b6a107d926093898e82b3b1db657ebe33134ec"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.50+0"

[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll"]
git-tree-sha1 = "11e1772e7f3cc987e9d3de991dd4f6b2602663a5"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.8+0"

[[deps.mtdev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "b4d631fd51f2e9cdd93724ae25b2efc198b059b1"
uuid = "009596ad-96f7-51b1-9f1b-5ce2d5e8a71e"
version = "1.1.7+0"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.64.0+1"

[[deps.oneTBB_jll]]
deps = ["Artifacts", "JLLWrappers", "LazyArtifacts", "Libdl"]
git-tree-sha1 = "d5a767a3bb77135a99e433afe0eb14cd7f6914c3"
uuid = "1317d2d5-d96f-522e-a858-c73665f53c3e"
version = "2022.0.0+0"

[[deps.p7zip_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.7.0+0"

[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "14cc7083fc6dff3cc44f2bc435ee96d06ed79aa7"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "10164.0.1+0"

[[deps.x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "e7b67590c14d487e734dcb925924c5dc43ec85f3"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "4.1.0+0"

[[deps.xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "fbf139bce07a534df0e699dbb5f5cc9346f95cc1"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "1.9.2+0"
"""

# ╔═╡ Cell order:
# ╠═e6e2b124-f53c-11f0-1dd6-e74cdd0384f9
# ╟─52b3f226-d907-4cae-bf86-bb671e244b26
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# ╟─cd6bc01f-c797-413e-b378-cbafbe5caeac
# ╟─4cd1363a-58a3-48f1-988c-a8db7e899156
# ╟─1b516697-9ad7-4996-8363-92e1b6c9d3fe
# ╟─4633d5d0-76d9-4ae0-aef0-34ab65cba09e
# ╟─a5430ebc-31b4-48fc-8913-5dfc063c77c7
# ╟─0d0a0938-67f9-4d70-a17c-479d522bde77
# ╠═68ec7863-abd5-4b40-933b-29101875939f
# ╠═4c0c9c36-12e3-41ff-a1ba-c2b38e2dea4c
# ╠═03ac5976-dc02-4f2a-bb68-fbc36a816ab1
# ╠═c4f4a4df-1cbe-4116-a312-52b1ac2a9e3e
# ╠═f2dd9a65-8228-4493-a2a0-60861be05000
# ╠═358b33bd-d522-4198-86bd-a1d4ddc0072c
# ╟─e9f32600-1488-47b3-b70e-5464d3e29423
# ╟─d151ef53-846c-4f82-8300-fd4be387fd9e
# ╟─1d85b4b1-8822-4328-9f7d-3aac5299328c
# ╠═01471628-7089-41a2-b6d8-a684ca3e88d9
# ╟─810d442b-1b30-44ed-b109-fe4ab0c0dd93
# ╠═9a976ce0-a318-43b8-b934-274a2790be89
# ╟─2f73156a-a8b2-4d81-8afe-5d0561b8a4f1
# ╟─fc263a9d-a07e-4fb4-bba5-b43cef24c250
# ╠═c5238c84-a689-49be-8946-beea93c7eb33
# ╟─a103e0e1-a916-49ed-8203-ac3c2303b69b
# ╠═4b7b5165-0e6c-47e2-9cdf-ecf8a22de58d
# ╟─7764f4bc-a159-4277-964d-367230a5d8e4
# ╠═da41ed56-9094-4f54-88cf-63c1dcc4ce62
# ╟─91564504-554d-4292-9184-99f53d8f7dca
# ╠═e550ba23-adf4-4779-8a35-d17f16e9daff
# ╠═9847f76f-269f-48ab-b743-c7f99cbf8d22
# ╠═475e441f-d144-41d8-9a21-12d8807c3586
# ╠═7404a469-11d3-434c-83c6-2331b5928a2c
# ╟─8187154e-4194-4fd5-8252-6aec0887516a
# ╠═fed71c68-671a-4126-84ca-48d4024a02d5
# ╠═e4b0d5cc-69c1-4bce-a1b2-b955e470346a
# ╠═82d530e5-99ae-466f-bdf2-9929e8a63074
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002
