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+### A Pluto.jl notebook ###
+# v0.20.1
+
+using Markdown
+using InteractiveUtils
+
+# ╔═╡ 1575b3cc-b786-11ef-34ef-dd6f58044fcc
+using DrWatson
+
+# ╔═╡ 0306d9f3-c210-4236-b9db-9ecb29787f08
+@quickactivate
+
+# ╔═╡ 8579e700-ef01-4ab9-a117-21bbf559d3dd
+using GraphRecipes, Plots, DataFrames, Random, GraphDynamicalSystems, Graphs, MetaGraphsNext
+
+# ╔═╡ 63b200cc-ae46-468e-ab25-e6d6ab58874b
+using DynamicalSystems: Attractors, trajectory, StateSpaceSets
+
+# ╔═╡ 90852030-deae-43d3-a573-124749d19d44
+md"""
+# Synthesizing Graph Dynamical Systems
+
+PONY Lab Group Meeting, 11/12/2024
+"""
+
+# ╔═╡ 04361d06-11c1-468a-a97d-04a41b5d606a
+md"""
+## What's a GDS?
+
+A model represented by
+
+- A graph
+- Each vertex in the graph has a function
+- Edges in the graph denote which vertices are inputs to others
+- Each vertex has a state
+- Dynamics of the system depend on
+  - Vertices' functions
+  - The order you update them (_schedule_)
+"""
+
+# ╔═╡ 4a95f701-cf79-4800-aa5a-72c6ee4c2e13
+md"""
+## Example GDS: Boolean Network
+"""
+
+# ╔═╡ e59b989c-2e88-4063-88d0-a2a4e3aae567
+md"""
+## Why do we care about them?
+
+- Executable models for bio, for example
+- Can use to study the effect of a drug on a biological system
+
+![BMA](https://github.com/user-attachments/assets/486bd9a9-a2a9-4dd3-8b55-00f7c8f1462a)
+"""
+
+# ╔═╡ c01be032-ec3f-4b7b-9698-90c7555cac50
+md"""
+## Why synthesize?
+
+- Constructing by hand is time consuming
+- Basically amounts to guess-and-check
+
+To understand how we synthesize, let's return to our example network. What kind of information can we extract from it?
+"""
+
+# ╔═╡ 2092c9f8-515e-4674-ad76-fdb2f22c0439
+md"""
+## Data from our BN
+
+State space/single cell measurements
+"""
+
+# ╔═╡ 9d09bc34-043c-4793-96f6-c7db927fed42
+md"""
+Steady state/mutation experiments
+"""
+
+# ╔═╡ 124b39da-e8a7-45d0-9a67-82dd08d16672
+md"""
+## Types of Schedules
+
+- **Asynchronous**
+  - Choose a vertex at random from the network
+  - Run its function to update its value
+- Synchronous
+  - Run all vertices' functions to update their values
+- Bounded Asynchrony
+  - Run subsets of the vertices at the same time
+  - Tricky case, probably will ignore this for today
+"""
+
+# ╔═╡ b608b534-4753-4529-8852-089aff34fab9
+md"""
+## Async BN
+
+The `dynamic rule` is the asynchronous schedule mentioned before.
+"""
+
+# ╔═╡ aab65a05-e256-4140-ae83-6547985e01a2
+md"""
+## State Space
+"""
+
+# ╔═╡ 04ed17cb-69bd-48eb-b294-af120fe26b19
+mg = MetaGraph(SimpleDiGraph(), label_type = String)
+
+# ╔═╡ 8955d1d1-3cd0-4691-9c7f-f6179cc6e048
+md"""
+## Steady State(s)
+"""
+
+# ╔═╡ bf0a7add-f668-4fcc-87d4-ad535bf93b12
+md"""
+## Synthesizing
+
+From the two types of data, two kinds of specifications:
+- State space specifies how a specific vertex's function should transform the state
+- Steady state specifies how a collection of vertex functions should behave
+
+Refering to these as _local_ and _global_ constraints.
+"""
+
+# ╔═╡ 80136458-da57-4ea9-943c-bd6692fad780
+md"""
+## "Global" Constraint
+
+> The steady state of the model is `[1, 0, 0, 1, 1]`
+
+This is a constraint on the steady state of the model when combining synthesized functions for all vertices.
+"""
+
+# ╔═╡ 606d1e0e-ee79-4b12-964a-c5d597508761
+md"""
+## Discussion Question #1
+
+If an incorrect steady-state is reached, which vertex is to blame?
+"""
+
+# ╔═╡ 1f02a380-2f17-44d2-a0a7-e4f7f3974c4c
+begin
+    mg2 = deepcopy(mg)
+    bad_v = string([1, 0, 1, 1, 1])
+    add_vertex!(mg2, bad_v)
+    add_edge!(mg2, string([1, 0, 0, 1, 1]), bad_v)
+    plot(
+        mg2.graph;
+        names = mg2.vertex_labels,
+        nodesize = 0.06,
+        nodecolor = [:lightblue, :lightblue, :lightblue, :red],
+    )
+end
+
+# ╔═╡ a1759c77-2ff3-4722-a65c-25ecf50ac279
+md"""
+## Discussion Question #2
+
+Assuming a synchronous schedule, how can we reconstruct the state space like we saw before?
+"""
+
+# ╔═╡ 8a243870-3d53-4312-b4d5-056f2372eb68
+md"""
+## Extras
+"""
+
+# ╔═╡ 5879d4f1-6bba-4675-b34b-9a1fcc023441
+seed = 42
+
+# ╔═╡ a217cd51-8c4b-4e74-90d3-b8d22daa6d62
+Random.seed!(seed)
+
+# ╔═╡ 964fca0e-b28d-4ebd-a2ad-3daf2ba2d4cd
+network = BooleanNetworks.sample_boolean_network(5, 3, seed)
+
+# ╔═╡ 452fda7d-e2f7-4162-a3d3-eef13ff3bdfc
+plot(network.graph; names = network.vertex_labels, nodesize = 0.2)
+
+# ╔═╡ 230f34b5-c160-4f06-b560-8306ae62e51e
+[(k => v[2]) for (k, v) in network.vertex_properties]
+
+# ╔═╡ d207a020-97e1-40ab-8f9b-8503cca9acf3
+plot(network.graph; names = network.vertex_labels, nodesize = 0.2)
+
+# ╔═╡ 51c331eb-77ef-4fcb-afff-c62fbf77d398
+async_bn = BooleanNetworks.abn(network)
+
+# ╔═╡ 6811c128-1aff-48e6-8af6-6946ebf7e6c1
+trjs = [trajectory(async_bn, 100) for _ = 1:1000]
+
+# ╔═╡ a52b6f33-bd36-4dae-9e90-4201e30bab78
+trjs[1][1][1:5]
+
+# ╔═╡ 8aeb938e-8cd2-4f0c-9bfc-9b35457b4e5d
+trjs[1]
+
+# ╔═╡ a16f15fe-491d-43a4-b41f-5e3b82c0ec85
+ssp = begin
+    for t in trjs
+        for (f, s) in zip(t[1][1:end-1], t[1][2:end])
+            add_vertex!(mg, string(f))
+            add_vertex!(mg, string(s))
+            add_edge!(mg, string(f), string(s))
+        end
+    end
+    plot(mg.graph; names = mg.vertex_labels, nodesize = 0.05)
+end
+
+# ╔═╡ d7a3067a-5b81-4409-bcf7-0254bcd591fb
+ssp
+
+# ╔═╡ 8d39c39f-0897-43e8-942a-9a7884eb1dd4
+ssp
+
+# ╔═╡ 320ce9dc-5390-42eb-9b09-3e73f1bdd28b
+attr = begin
+    grid = Tuple(range(0, 1) for _ = 1:5)
+    mapper = Attractors.AttractorsViaRecurrences(async_bn, grid)
+    for _ = 1:1000
+        mapper(rand(0:1, 5))
+    end
+    Attractors.extract_attractors(mapper)
+end
+
+# ╔═╡ e99505e5-6697-42c5-b763-77e5ee3d0158
+attr[1]
+
+# ╔═╡ 743cb689-469e-48f1-82cc-f7e2abeadf9a
+md"""
+## Local Constraint
+
+> In: `[1, 0, 0, 1, 1]`, out: `[1, 0, 0, 0, 1]`
+
+This is a constraint on vertex `4`'s update function.
+
+A satisfying function would be $(string(network.vertex_properties[4][2])[26:end])
+"""
+
+# ╔═╡ Cell order:
+# ╟─90852030-deae-43d3-a573-124749d19d44
+# ╟─04361d06-11c1-468a-a97d-04a41b5d606a
+# ╟─4a95f701-cf79-4800-aa5a-72c6ee4c2e13
+# ╟─452fda7d-e2f7-4162-a3d3-eef13ff3bdfc
+# ╟─230f34b5-c160-4f06-b560-8306ae62e51e
+# ╟─e59b989c-2e88-4063-88d0-a2a4e3aae567
+# ╟─c01be032-ec3f-4b7b-9698-90c7555cac50
+# ╟─d207a020-97e1-40ab-8f9b-8503cca9acf3
+# ╟─2092c9f8-515e-4674-ad76-fdb2f22c0439
+# ╟─a52b6f33-bd36-4dae-9e90-4201e30bab78
+# ╟─9d09bc34-043c-4793-96f6-c7db927fed42
+# ╟─e99505e5-6697-42c5-b763-77e5ee3d0158
+# ╟─124b39da-e8a7-45d0-9a67-82dd08d16672
+# ╟─b608b534-4753-4529-8852-089aff34fab9
+# ╠═51c331eb-77ef-4fcb-afff-c62fbf77d398
+# ╟─aab65a05-e256-4140-ae83-6547985e01a2
+# ╟─6811c128-1aff-48e6-8af6-6946ebf7e6c1
+# ╠═8aeb938e-8cd2-4f0c-9bfc-9b35457b4e5d
+# ╠═04ed17cb-69bd-48eb-b294-af120fe26b19
+# ╟─a16f15fe-491d-43a4-b41f-5e3b82c0ec85
+# ╟─8955d1d1-3cd0-4691-9c7f-f6179cc6e048
+# ╟─320ce9dc-5390-42eb-9b09-3e73f1bdd28b
+# ╟─d7a3067a-5b81-4409-bcf7-0254bcd591fb
+# ╟─bf0a7add-f668-4fcc-87d4-ad535bf93b12
+# ╟─743cb689-469e-48f1-82cc-f7e2abeadf9a
+# ╟─80136458-da57-4ea9-943c-bd6692fad780
+# ╟─606d1e0e-ee79-4b12-964a-c5d597508761
+# ╟─1f02a380-2f17-44d2-a0a7-e4f7f3974c4c
+# ╟─a1759c77-2ff3-4722-a65c-25ecf50ac279
+# ╟─8d39c39f-0897-43e8-942a-9a7884eb1dd4
+# ╟─8a243870-3d53-4312-b4d5-056f2372eb68
+# ╠═1575b3cc-b786-11ef-34ef-dd6f58044fcc
+# ╠═0306d9f3-c210-4236-b9db-9ecb29787f08
+# ╠═a217cd51-8c4b-4e74-90d3-b8d22daa6d62
+# ╠═5879d4f1-6bba-4675-b34b-9a1fcc023441
+# ╠═964fca0e-b28d-4ebd-a2ad-3daf2ba2d4cd
+# ╠═8579e700-ef01-4ab9-a117-21bbf559d3dd
+# ╠═63b200cc-ae46-468e-ab25-e6d6ab58874b