naming.jl

### A Pluto.jl notebook ###
# v0.17.4

using Markdown
using InteractiveUtils

# ╔═╡ a9584c19-2516-4b15-b074-094e478831ae
begin
	using Agents
	using NestedSamplers
	using Graphs
	using GraphPlot
	using Compose
	using Distributions
	using StatsPlots
	using StatsFuns
	using LaTeXStrings
	using Random
	using DataFramesMeta
	using StatsBase
	using LinearAlgebra
	using DataStructures
	using PlutoUI
	TableOfContents()
end

# ╔═╡ 9967a91d-5c6a-4642-be6d-7d5d6e129d1f
md"Note: unfinished work"

# ╔═╡ 37c410c8-f563-4c5f-a0c1-a135c7fed73a
md"""
# Next level naming game

!!! terminology "Problem definition"
    What structure, if any, is there to the networks that maximize the **convergence** of a simple naming game at given time $T$? Do succesful communication strategies emerge, and how do the networks that implement them look like?

## MEANS formulation

!!! terminology
    MEANS = Maximum entropy as nested sampling
	
	Advantages over conventional MCMC methods:
    - Inclusion of prior information
    - Simulate any temperature for free if only one constraint!
	- No burn-in required, good convergence measures
    - Can evaluate (derivatives of) $\log Z$, can evaluate $H$, density of states, etc.
	- General superior "mapping out of the problem" ability compared to MCMC, though presumably limited to small amount of dimensions compared to MCMC

Generate networks $A \sim \pi(A)$ from the prior and likelihood $\exp(\lambda c(A))$ and solve the $D$-dimensional problem with nested sampling *once* for $\lambda = 1$, then reweigh for any other value of $\lambda$ to vary the constraint $\langle c(A) \rangle = C$.

Set $C$ to high values for a given $T$. How do the posterior samples $A \sim P(A|\lambda)$ look like? Are there any favored structures?

!!! warning
    This is a **noisy likelihood** problem, because at a given point $A$ the value of $c(A)$ depends on some extra random numbers not accessible to the nested sampler. Instead, we have a distribution $p(c|A)$ from which we sample only value. We can also evaluate a Monte Carlo estimate of the mean of this distribution to get more smooth constraints or let the nested sampler control the decisions in the ABM by augmenting the problem dimensionality $D$ with extra dimensions, one for each decision made by the ABM.

## Network prior $\pi(A)$

Undirected $ER(N,p)$-network where $N$ is fixed and $O(5)$ and $p \sim Beta(.5,.5)$ to allow for a richer prior. This gives $D = N(N-1)/2 + 1$ dimensions.

## Convergence measure

Let $p_i^{(T)}$ be the normalized distribution of unique words $i = 1:N$ found in the lexicons of the $N$ agents at a given time step $T$, which depends implicitly on a given network $A$ (suppressed in the notation).
Let $u_i = p_i^{(0)} = 1/N$ be that initial distribution and $\delta_i = \delta_{ij}$ the discrete delta distribution which represents absolute convergence (agreement) on the final word $j$.
Then **define convergence** as
````math
c(T) = {KL(p^{(T)}|u) \over KL(\delta|u)} \in [0,1]
````
Here $KL(p|q)$ is the Kullback-Leibler divergence from $q$ to $p$. Concretely $c(T) = 1 - {H(p_i^{(T)}) \over \log N}$, but the above expression expresses the philosophy behind the measure, with $H(p)$ the discrete entropy of $p$.

I think $c$ is a much more interesting measure than the success rate $S$ because it will, for example, not be equal to $1$ when there are two disconnected components which have converged fully amongst themselves.
"""

# ╔═╡ fd47f9b1-ad53-4aab-a53c-a0c7e11419bc
begin
	function erdosrenyi(N, p, u)
		v = quantile(Bernoulli(p), u) .|> Int
		# Could also use TriangularIndices.jl for populating `U` from `v`
		linearindex(i, j) = (N*(N-1)÷2) - (N-i)*((N-i)-1)÷2 + j - i - 1
		U = [i < j ? v[linearindex(i, j)] : 0 for i = 1:N, j = 1:N]
		A = Hermitian(U)
	end

	"""
	Number of dimensions of a random network in our problem, i.e., the number of random numbers (RNs) needed to sample a random adjacency matrix `A` in our scheme:
	  - Sample a random Bernouilli probability from a Beta distribution (1 RN)
	  - Sample a symmetrical (0,1) matrix with zeros on the diagonal ((N*(N-1))÷2 RNs)
	"""
	ndim(N) = 1 + (N*(N-1))÷2

	prior(N; k...) = prior(N, rand(ndim(N)); k...)

	"""
	Sample the adjacency matrix of a random DAG `A ∼ π(A)` using the `ndim(N)` random numbers `u`. The hyperparameters `α, β` control the sparsity of the DAGs through a `Beta(α, β)` prior for the Bernouilli probability controlling the placement of edges between nodes.
	"""
	function prior(N, u; α = .5, β = .5)
		p = quantile(Beta(α, β), u[1])
		A = erdosrenyi(N, p, u[2:end])
	end
end

# ╔═╡ 59e1e7cb-febf-4bf9-879d-1b88d7b3adc3
"""Plot the adjacency matrix `A` as a undirected graph"""
function plotadj(A)
	set_default_graphic_size(5cm, 5cm)
	g = Graph(A)
	gplot(g, nodelabel=1:nv(g), EDGELINEWIDTH=.5)
end

# ╔═╡ 048fcc34-ec59-4e07-8c54-6726822b1518
plotadj.([prior(5) for _ in 1:3])

# ╔═╡ 5bbfbffe-4af3-4a21-b95c-49e4a1d22a31
begin
	frequencies(a) = [nᵢ/length(a) for nᵢ in values(counter(a))]

	function convergence(N, inventory)
		p = frequencies(inventory)
		H = entropy(p)
		c = 1. - H/log(N)
	end
end

# ╔═╡ cb821cc2-ef48-42c1-9558-8bdd287defd1
# Define the ABM according to Dall’Asta+ (2006)
begin
	mutable struct Agent <: AbstractAgent
	    id::Int
	    lexicon::Vector{Int}
	end
	
	function initialize(A)
		graph = SimpleGraph(A)
		N = nv(graph)

		properties = Dict(
			:N => N,  # Number of agents
			:c => 0., # Convergence measure
			:graph => graph # Underlying undirected graph
		)

		# This maps each agent to an Int in 1:N
		model = ABM(Agent, nothing; properties)

		init_lexicon!(agent) = add_agent!(model, [rand(model.rng, Int)])
		init_lexicon!.(1:N)

		return model
	end

	function agent_step!(speaker, model)
		# This relies on the fact that both agents and nodes are
		# mapped to Ints on 1:N (no agents or nodes are removed)
		neighbors = all_neighbors(model.graph, speaker.id)
		isempty(neighbors) && return
		listener = model[rand(model.rng, neighbors)]

		message = rand(model.rng, speaker.lexicon)

		if message in listener.lexicon
			speaker.lexicon = [message]
			listener.lexicon = [message]
		else
			push!(listener.lexicon, message)
		end
	end

	function model_step!(model)
		inventory = vcat([speaker.lexicon for speaker in allagents(model)]...)
		model.c = convergence(nagents(model), inventory)
	end
end;

# ╔═╡ 0839b2e3-1590-4cde-8769-edb078093fe3
begin
	"""
	Estimate the marginal likelihood by Monte Carlo integration using `M` samples of the naming game convergence played on network `A` at time step `T`
	"""
	function monte_carlo_logl(M, T, λ, A)
		function sampleconvergence()
			model = initialize(A)
			adf, mdf, = run!(
				model, agent_step!, model_step!, T;
				mdata = [:c]
			)
			c = last(mdf.c)
		end
		cs = [sampleconvergence() for _ in 1:M]
		logl = logsumexp(λ*cs) - log(M)
	end

	sampleposterior(N, chain, state) = reshape(Array(sample(chain, 1), [:parameters]), N, N)

	"""
	Calculate the posterior `p(A|λ) = Z(λ)⁻¹ π(A) exp(λ⋅f(A))` using the nested sampling algorithm. This yields an MCMC `chain`  with weighted posterior samples and a `state` with the estimate for `log Z(λ)`.
	"""
	function posterior(N, M, T, λ; α=.5, β=.5, nlive=3ndim(N))
		adj(v) = reshape(v, N, N)
		vec(A) = reshape(A, N^2)
		
		ptform(u) = vec(prior(N, u; α=α, β=β))
		logl(v) = monte_carlo_logl(M, T, λ, adj(v))
	
		model = NestedModel(logl, ptform)
		sampler = Nested(ndim(N), nlive)
		chain, state = sample(model, sampler; dlogz=0.1)
		𝑃 = N, chain, state
	end
end

# ╔═╡ a8917e6d-0e67-4651-b93d-0360cb2df4b7
𝑃₁ = let
	N = 10
	M = 200
	T = 5
	λ = 1000.
	
	posterior(N, M, T, λ)
end

# ╔═╡ 83cbf6d1-1e8f-4ef2-9f99-6f2efcb71744
plotadj.([sampleposterior(𝑃₁...) for _ in 1:3])

# ╔═╡ 3536a4b6-46dc-41f4-ae98-945a2ec97986
𝑃 = let
	N = 15
	M = 200
	T = 10
	λ = 1000.
	
	posterior(N, M, T, λ)
end

# ╔═╡ c4b82af8-a10b-4ff5-8576-09f851ab8ab8
plotadj.([sampleposterior(𝑃...) for _ in 1:3])

# ╔═╡ 5f6f59e3-94b8-4238-bfeb-0f6f3bd75a66
md"""
## Conclusion

There appear to be two strategies which favor convergence: sparse and stringy-like vs. dense (more succesful).
"""

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[[Distributions]]
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[[Downloads]]
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[[DualNumbers]]
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[[Expat_jll]]
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[[Fontconfig_jll]]
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[[FreeType2_jll]]
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[[FriBidi_jll]]
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[[Gettext_jll]]
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[[Graphite2_jll]]
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[[Grisu]]
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[[HTTP]]
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[[Hyperscript]]
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[[HypertextLiteral]]
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[[IOCapture]]
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[[IntelOpenMP_jll]]
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[[Interpolations]]
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[[IntervalSets]]
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[[IrrationalConstants]]
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[[JLD2]]
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[[JSON]]
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[[JpegTurbo_jll]]
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[[KernelDensity]]
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[[LAME_jll]]
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[[LERC_jll]]
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[[LZO_jll]]
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[[LaTeXStrings]]
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[[Latexify]]
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[[LazyArtifacts]]
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[[LeftChildRightSiblingTrees]]
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[[LibCURL]]
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[[LibCURL_jll]]
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[[LibGit2]]
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[[LibSSH2_jll]]
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[[Libdl]]
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[[Libffi_jll]]
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[[Libgcrypt_jll]]
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[[Libglvnd_jll]]
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[[Libgpg_error_jll]]
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[[Libiconv_jll]]
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[[Libmount_jll]]
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[[Libtiff_jll]]
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[[Libuuid_jll]]
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[[LightOSM]]
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[[LightXML]]
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[[LogExpFunctions]]
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[[Logging]]
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[[LoggingExtras]]
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[[MCMCChains]]
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[[MbedTLS]]
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[[MbedTLS_jll]]
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[[Measures]]
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[[MetaGraphs]]
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[[MicroCollections]]
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[[Missings]]
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[[Mmap]]
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[[MozillaCACerts_jll]]
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[[MultivariateStats]]
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[[NearestNeighbors]]
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[[NestedSamplers]]
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[[NetworkOptions]]
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[[Observables]]
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[[Ogg_jll]]
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[[OpenLibm_jll]]
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[[OpenSSL_jll]]
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[[OpenSpecFun_jll]]
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[[Opus_jll]]
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[[PCRE_jll]]
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[[PDMats]]
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[[Pixman_jll]]
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[[PlotThemes]]
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[[PlotUtils]]
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[[Plots]]
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[[PlutoUI]]
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[[PooledArrays]]
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[[ProgressLogging]]
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[[Qt5Base_jll]]
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[[QuadGK]]
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[[Random]]
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[[Ratios]]
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[[RecipesBase]]
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[[RecipesPipeline]]
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[[RelocatableFolders]]
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[[Rmath_jll]]
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[[SHA]]
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[[Showoff]]
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[[SortingAlgorithms]]
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[[SpecialFunctions]]
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[[SplittablesBase]]
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[[StatisticalTraits]]
deps = ["ScientificTypesBase"]
git-tree-sha1 = "271a7fea12d319f23d55b785c51f6876aadb9ac0"
uuid = "64bff920-2084-43da-a3e6-9bb72801c0c9"
version = "3.0.0"

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

[[StatsAPI]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "c82aaa13b44ea00134f8c9c89819477bd3986ecd"
uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
version = "1.3.0"

[[StatsBase]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "8977b17906b0a1cc74ab2e3a05faa16cf08a8291"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.33.16"

[[StatsFuns]]
deps = ["ChainRulesCore", "HypergeometricFunctions", "InverseFunctions", "IrrationalConstants", "LogExpFunctions", "Reexport", "Rmath", "SpecialFunctions"]
git-tree-sha1 = "5783b877201a82fc0014cbf381e7e6eb130473a4"
uuid = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
version = "1.0.1"

[[StatsPlots]]
deps = ["AbstractFFTs", "Clustering", "DataStructures", "DataValues", "Distributions", "Interpolations", "KernelDensity", "LinearAlgebra", "MultivariateStats", "Observables", "Plots", "RecipesBase", "RecipesPipeline", "Reexport", "StatsBase", "TableOperations", "Tables", "Widgets"]
git-tree-sha1 = "43a316e07ae612c461fd874740aeef396c60f5f8"
uuid = "f3b207a7-027a-5e70-b257-86293d7955fd"
version = "0.14.34"

[[StructArrays]]
deps = ["Adapt", "DataAPI", "StaticArrays", "Tables"]
git-tree-sha1 = "9abba8f8fb8458e9adf07c8a2377a070674a24f1"
uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
version = "0.6.8"

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

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

[[TableOperations]]
deps = ["SentinelArrays", "Tables", "Test"]
git-tree-sha1 = "e383c87cf2a1dc41fa30c093b2a19877c83e1bc1"
uuid = "ab02a1b2-a7df-11e8-156e-fb1833f50b87"
version = "1.2.0"

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

[[Tables]]
deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "OrderedCollections", "TableTraits", "Test"]
git-tree-sha1 = "5ce79ce186cc678bbb5c5681ca3379d1ddae11a1"
uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
version = "1.7.0"

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

[[TensorCore]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "1feb45f88d133a655e001435632f019a9a1bcdb6"
uuid = "62fd8b95-f654-4bbd-a8a5-9c27f68ccd50"
version = "0.1.1"

[[TerminalLoggers]]
deps = ["LeftChildRightSiblingTrees", "Logging", "Markdown", "Printf", "ProgressLogging", "UUIDs"]
git-tree-sha1 = "62846a48a6cd70e63aa29944b8c4ef704360d72f"
uuid = "5d786b92-1e48-4d6f-9151-6b4477ca9bed"
version = "0.1.5"

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

[[TranscodingStreams]]
deps = ["Random", "Test"]
git-tree-sha1 = "216b95ea110b5972db65aa90f88d8d89dcb8851c"
uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
version = "0.9.6"

[[Transducers]]
deps = ["Adapt", "ArgCheck", "BangBang", "Baselet", "CompositionsBase", "DefineSingletons", "Distributed", "InitialValues", "Logging", "Markdown", "MicroCollections", "Requires", "Setfield", "SplittablesBase", "Tables"]
git-tree-sha1 = "c76399a3bbe6f5a88faa33c8f8a65aa631d95013"
uuid = "28d57a85-8fef-5791-bfe6-a80928e7c999"
version = "0.4.73"

[[Tricks]]
git-tree-sha1 = "6bac775f2d42a611cdfcd1fb217ee719630c4175"
uuid = "410a4b4d-49e4-4fbc-ab6d-cb71b17b3775"
version = "0.1.6"

[[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"

[[UnicodeFun]]
deps = ["REPL"]
git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
version = "0.4.1"

[[Unzip]]
git-tree-sha1 = "34db80951901073501137bdbc3d5a8e7bbd06670"
uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d"
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"]
git-tree-sha1 = "4528479aa01ee1b3b4cd0e6faef0e04cf16466da"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.25.0+0"

[[WeakRefStrings]]
deps = ["DataAPI", "InlineStrings", "Parsers"]
git-tree-sha1 = "b1be2855ed9ed8eac54e5caff2afcdb442d52c23"
uuid = "ea10d353-3f73-51f8-a26c-33c1cb351aa5"
version = "1.4.2"

[[Widgets]]
deps = ["Colors", "Dates", "Observables", "OrderedCollections"]
git-tree-sha1 = "fcdae142c1cfc7d89de2d11e08721d0f2f86c98a"
uuid = "cc8bc4a8-27d6-5769-a93b-9d913e69aa62"
version = "0.6.6"

[[WoodburyMatrices]]
deps = ["LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "de67fa59e33ad156a590055375a30b23c40299d3"
uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6"
version = "0.5.5"

[[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 = "e45044cd873ded54b6a5bac0eb5c971392cf1927"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.2+0"

[[ZygoteRules]]
deps = ["MacroTools"]
git-tree-sha1 = "8c1a8e4dfacb1fd631745552c8db35d0deb09ea0"
uuid = "700de1a5-db45-46bc-99cf-38207098b444"
version = "0.2.2"

[[libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.1+0"

[[libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.2+0"

[[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 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+1"

[[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 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"

[[x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.5.0+0"

[[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:
# ╟─9967a91d-5c6a-4642-be6d-7d5d6e129d1f
# ╟─37c410c8-f563-4c5f-a0c1-a135c7fed73a
# ╠═a9584c19-2516-4b15-b074-094e478831ae
# ╠═fd47f9b1-ad53-4aab-a53c-a0c7e11419bc
# ╠═59e1e7cb-febf-4bf9-879d-1b88d7b3adc3
# ╠═048fcc34-ec59-4e07-8c54-6726822b1518
# ╠═5bbfbffe-4af3-4a21-b95c-49e4a1d22a31
# ╠═cb821cc2-ef48-42c1-9558-8bdd287defd1
# ╠═0839b2e3-1590-4cde-8769-edb078093fe3
# ╠═a8917e6d-0e67-4651-b93d-0360cb2df4b7
# ╠═83cbf6d1-1e8f-4ef2-9f99-6f2efcb71744
# ╠═3536a4b6-46dc-41f4-ae98-945a2ec97986
# ╠═c4b82af8-a10b-4ff5-8576-09f851ab8ab8
# ╟─5f6f59e3-94b8-4238-bfeb-0f6f3bd75a66
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002