Full C-Set implementation (#17)

* [WIP] implementation of whole-grained Petri nets (#12)

* implementation of whole-grained Petri nets

* ENH: Some cleanup of basic Petri net implementation

Co-authored-by: Owen Lynch <root@owenlynch.org>

* Updated reaction network definition

* Catch up petset to master (#16)

* Updated catlab interface (#14)

* Updated catlab interface

* patch version bump to fix broken catlab

* Don't dev catlab for docs

* Updated petri to fix graphing

* Update examples to match new interface

* Change test versions

* Added code coverage (#15)

* Added code coverage

* Fix documentation dependency incorrect resolution

* Use newest version of catlab

* Updated Catlab API

* Working on CSet implementation of Petri nets

* Added better constructor for building petri nets

* Updated to newer cset type definitions

* Improve interface to work with both Petri and ReactionNets

* Added labelled petri nets

* Added more nice constructors for building petri nets

* Finished constructors and cleaned up duplicate code a little

* Updated comment of example code

* Added interface for Petri.jl

* Added chime toy model

* Removed unnecessary comments

* Separated time span to variable for clearer definition

* Added JSON generation

* Added final json form and cleaned up

* Added executable CHIME model using CSet implementation as well as JSON generation with code

* Cleaned up code some more

* Final code clean up for this example

* Fix typo

* Added chime model folder

* Updated README

* Updated documentation for CHIME models

* Updated README

* Updated README

* Updated types with new patch in Catlab

* Update to catlab 0.8 and petri 1.2.1

* Added looser codecov rules

* Moved open petri nets to use the cset implementation

* Updated examples

* Updated chime-cset imports

* Updated examples

* Added more testing

* Fix julia v1.0 support

* Simplified each row iterator

* Fix dimensionality mismatch in rate_eq

* Added support for labelled petri net vector field generation

* Split out vectorfield generation using multiple dispatch

* Removed duplicate function

* Moved to LabelledArrays to fix diffeq bug with dictionaries

* Fix typo and update tests

Co-authored-by: olynch <oclynch888@gmail.com>
Co-authored-by: Owen Lynch <root@owenlynch.org>

Project.toml

@@ -7,11 +7,13 @@ version = "0.3.2"
 [deps]
 AutoHashEquals = "15f4f7f2-30c1-5605-9d31-71845cf9641f"
 Catlab = "134e5e36-593f-5add-ad60-77f754baafbe"
+LabelledArrays = "2ee39098-c373-598a-b85f-a56591580800"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Petri = "4259d249-1051-49fa-8328-3f8ab9391c33"
 
 [compat]
 AutoHashEquals = "^0.2.0"
-Catlab = "0.7.4"
+Catlab = "^0.8"
 Petri = "^1.1.0"
 julia = "1.0"
 

codecov.yml

@@ -0,0 +1,13 @@
+comment: false
+
+coverage:
+  precision: 2
+  status:
+    patch:
+      default:
+        target: 0%
+        threshold: 100%
+    project:
+      default:
+        target: 0%
+        threshold: 100%

docs/Project.toml

@@ -2,6 +2,7 @@
 AlgebraicPetri = "4f99eebe-17bf-4e98-b6a1-2c4f205a959b"
 Catlab = "134e5e36-593f-5add-ad60-77f754baafbe"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
+JSON = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
 Literate = "98b081ad-f1c9-55d3-8b20-4c87d4299306"
 OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
 Petri = "4259d249-1051-49fa-8328-3f8ab9391c33"

examples/covid/Project.toml

@@ -1,6 +1,8 @@
 [deps]
 AlgebraicPetri = "4f99eebe-17bf-4e98-b6a1-2c4f205a959b"
 Catlab = "134e5e36-593f-5add-ad60-77f754baafbe"
+JSON = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
+LabelledArrays = "2ee39098-c373-598a-b85f-a56591580800"
 OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
 Petri = "4259d249-1051-49fa-8328-3f8ab9391c33"
 Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"

examples/covid/_generate_figs.jl

@@ -78,13 +78,13 @@ splot(sol, "seird_soln.svg")
 
 include("covid.jl")
 
-[save_graph(Graph(decoration(p)), pname) for (p,pname) in [(spontaneous_petri, "spont.svg"),
+[save_graph(Graph(Petri.Model(decoration(p))), pname) for (p,pname) in [(spontaneous_petri, "spont.svg"),
                                                (transmission_petri, "transmission.svg"),
                                                (exposure_petri, "exposure.svg"),
                                                (travel_petri, "travel.svg")]]
 
 save_wd(seird_city, "seird_city.svg")
-save_graph(Graph(decoration(F(seird_city))), "seird_graph.svg")
+save_graph(Graph(Petri.Model(decoration(F(seird_city)))), "seird_graph.svg")
 
 save_wd(seird_3, "seird_3.svg")
 save_graph(Graph(p_seird_3), "seird_3_graph.svg")

examples/covid/chime/Manifest.toml

@@ -0,0 +1,922 @@
+# This file is machine-generated - editing it directly is not advised
+
+[[AbstractTrees]]
+deps = ["Markdown"]
+git-tree-sha1 = "33e450545eaf7699da1a6e755f9ea65f14077a45"
+uuid = "1520ce14-60c1-5f80-bbc7-55ef81b5835c"
+version = "0.3.3"
+
+[[Adapt]]
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+git-tree-sha1 = "95f8bda0555209f122bc796b0382ea4a3a121720"
+uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
+version = "2.1.0"
+
+[[AlgebraicPetri]]
+deps = ["AutoHashEquals", "Catlab", "LabelledArrays", "LinearAlgebra", "Petri"]
+path = "../../.."
+uuid = "4f99eebe-17bf-4e98-b6a1-2c4f205a959b"
+version = "0.3.2"
+
+[[ArnoldiMethod]]
+deps = ["DelimitedFiles", "LinearAlgebra", "Random", "SparseArrays", "StaticArrays", "Test"]
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+version = "2.12.0"
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+[[Base64]]
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+
+[[Statistics]]
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+
+[[StatsBase]]
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+
+[[SteadyStateDiffEq]]
+deps = ["DiffEqBase", "DiffEqCallbacks", "LinearAlgebra", "NLsolve", "Reexport"]
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+[[StochasticDiffEq]]
+deps = ["ArrayInterface", "DataStructures", "DiffEqBase", "DiffEqJump", "DiffEqNoiseProcess", "FillArrays", "FiniteDiff", "ForwardDiff", "LinearAlgebra", "Logging", "MuladdMacro", "NLsolve", "OrdinaryDiffEq", "Random", "RandomNumbers", "RecursiveArrayTools", "Reexport", "SparseArrays", "SparseDiffTools", "StaticArrays", "UnPack"]
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+[[StructArrays]]
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+[[SuiteSparse]]
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+
+[[TableTraits]]
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+[[Tables]]
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+[[TerminalLoggers]]
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+[[TranscodingStreams]]
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+[[UUIDs]]
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+
+[[UnPack]]
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+[[Unicode]]
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+
+[[VectorizationBase]]
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+[[VertexSafeGraphs]]
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+
+[[XML2_jll]]
+deps = ["Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"]
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+
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+
+[[ZygoteRules]]
+deps = ["MacroTools"]
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+uuid = "700de1a5-db45-46bc-99cf-38207098b444"
+version = "0.2.0"
+
+[[libass_jll]]
+deps = ["Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "Libdl", "Pkg", "Zlib_jll"]
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+uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
+version = "0.14.0+3"
+
+[[libfdk_aac_jll]]
+deps = ["Libdl", "Pkg"]
+git-tree-sha1 = "e17b4513993b4413d31cffd1b36a63625ebbc3d3"
+uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
+version = "0.1.6+3"
+
+[[libvorbis_jll]]
+deps = ["Libdl", "Ogg_jll", "Pkg"]
+git-tree-sha1 = "8014e1c1033009edcfe820ec25877a9f1862ba4c"
+uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
+version = "1.3.6+5"
+
+[[x264_jll]]
+deps = ["Libdl", "Pkg"]
+git-tree-sha1 = "e496625b900df1b02ab0e02fad316b77446616ef"
+uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
+version = "2020.7.14+1"
+
+[[x265_jll]]
+deps = ["Libdl", "Pkg"]
+git-tree-sha1 = "ac7d44fa1639a780d0ae79ca1a5a7f4181131825"
+uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
+version = "3.0.0+2"

examples/covid/chime/Project.toml

@@ -0,0 +1,8 @@
+[deps]
+AlgebraicPetri = "4f99eebe-17bf-4e98-b6a1-2c4f205a959b"
+Catlab = "134e5e36-593f-5add-ad60-77f754baafbe"
+JSON = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
+OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
+Petri = "4259d249-1051-49fa-8328-3f8ab9391c33"
+Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
+StochasticDiffEq = "789caeaf-c7a9-5a7d-9973-96adeb23e2a0"

examples/covid/chime/README.md

@@ -0,0 +1,54 @@
+# CHIME Model
+
+The folder contains implementations of the [CHIME COVID-19
+Model](https://github.com/CodeForPhilly/chime). This model is an SIR
+epidemiological model where the rate of infection changes over time to represent
+policy changes such as shelter in place orders or masking requirements.
+
+Both
+[`chime.jl`](https://github.com/AlgebraicJulia/AlgebraicPetri.jl/blob/petset/examples/covid/chime/chime.jl)
+and
+[`chime-cset.jl`](https://github.com/AlgebraicJulia/AlgebraicPetri.jl/blob/petset/examples/covid/chime/chime-cset.jl)
+implement the same model. Here
+[`chime.jl`](https://github.com/AlgebraicJulia/AlgebraicPetri.jl/blob/petset/examples/covid/chime/chime.jl)
+represents building the model out of the composition of open systems using
+AlgebraicJulia's Epidemiology module, and
+[`chime-cset.jl`](https://github.com/AlgebraicJulia/AlgebraicPetri.jl/blob/petset/examples/covid/chime/chime-cset.jl)
+uses the new C-Set implementation of Petri Nets that keeps track of initial
+conditions and rates automatically. This is a new notation and has not yet been
+built to support the open systems of decorated cospans, but this is on the way!
+
+## Running the Models
+
+To initialize the project in Julia, `cd` into this directory and run `julia
+--project -e 'pkg"instantiate"'`
+
+Once the project has been instantiated, both of these models can be run easily
+from within this folder with `julia --project chime.jl` or `julia --project
+chime-cset.jl`.
+
+These models can be represented as a JSON format for interoperability purposes
+which can be found in
+[`chime.json`](https://github.com/AlgebraicJulia/AlgebraicPetri.jl/blob/petset/examples/covid/chime/chime.json).
+An explanation on how to read this schema can be found in
+[`cset-json-schema.pdf`](https://github.com/AlgebraicJulia/AlgebraicPetri.jl/blob/petset/examples/covid/chime/cset-json-schema.pdf).
+
+## Example Solutions
+
+When running these models,
+[`Petri.jl`](https://mehalter.github.io/Petri.jl/stable/) supports solvers using
+ODEs, SDEs, and Gillespie discrete simulations. Some example outputs are shown
+below with the following initial conditions and parameters:
+
+- Enacted policy changing after 20, 40, and then 60 days
+- A relative contact rate of 0.05
+- an infectious day length of 14
+- And initial conditions of 990 susceptible, 10 infected, and 0 recovered
+
+### ODE Solution
+
+![ODE Solution of the CHIME Model](ode-chime.png)
+
+### SDE Solution
+
+![SDE Solution of the CHIME Model](sde-chime.png)

examples/covid/chime/chime-cset.jl

@@ -0,0 +1,38 @@
+using AlgebraicPetri
+using Petri: Model, Graph
+using OrdinaryDiffEq
+using Plots
+using Catlab.Meta
+using JSON
+
+import OrdinaryDiffEq: ODEProblem
+ODEProblem(p::LabelledReactionNet, t) = ODEProblem(vectorfield(p), concentrations(p), t, rates(p))
+
+# help capture JSON of defined functions
+macro capture(funcname, exname, ex)
+    quote
+        $(esc(exname)) = $(repr(strip_lines(ex, recurse=true)))
+        $(esc(funcname)) = $ex
+    end
+end
+
+@capture γ γ_text 1/14
+@capture β β_text t->begin
+    policy_days = [20,60,120] .+ 17
+    contact_rate = 0.05
+    pol = findfirst(x->t<=x, policy_days) # array of days when policy changes
+    growth_rate = pol == 1 ? 0.0 : (2^(1/((pol-1)*5)) - 1) # growth rate depending on policy
+    return (growth_rate + γ) / 990 * (1-contact_rate) # calculate rate of infection
+end
+
+sir_cset= LabelledReactionNet{Function, Float64}((:S=>990, :I=>10, :R=>0), (:inf, β)=>((:S, :I)=>(:I,:I)), (:rec, t->γ)=>(:I=>:R))
+
+Graph(Model(sir_cset))
+
+prob = ODEProblem(sir_cset, (17.0, 120.0))
+sol = OrdinaryDiffEq.solve(prob,Tsit5())
+plot(sol)
+
+## Getting Sharable JSON
+sir_cset_string = LabelledReactionNet{String, Int}((:S=>990, :I=>10, :R=>0), (:inf, β_text)=>((:S, :I)=>(:I,:I)), (:rec, γ_text)=>(:I=>:R))
+JSON.print(sir_cset_string.tables, 2)

examples/covid/chime/chime.jl

@@ -0,0 +1,41 @@
+using AlgebraicPetri
+using AlgebraicPetri.Epidemiology
+using Petri: Model, Graph
+using OrdinaryDiffEq
+using StochasticDiffEq
+using Plots
+using Catlab.Theories
+using Catlab.CategoricalAlgebra.FreeDiagrams
+using Catlab.Graphics
+
+display_wd(ex) = to_graphviz(ex, orientation=LeftToRight, labels=true);
+
+sir = transmission ⋅ recovery
+
+p_sir = decoration(F_epi(sir));
+display_wd(sir)
+#-
+Graph(Model(p_sir))
+
+u0 = [990.0, 10, 0];
+t_span = (17.0,120.0)
+
+γ = 1/14
+β = t->begin
+    policy_days = [20,60,120] .+ 17
+    contact_rate = 0.05
+    pol = findfirst(x->t<=x, policy_days) # array of days when policy changes
+    growth_rate = pol == 1 ? 0.0 : (2^(1/((pol-1)*5)) - 1) # growth rate depending on policy
+    return (growth_rate + γ) / 990 * (1-contact_rate) # calculate rate of infection
+end
+p = [β, γ];
+
+prob = ODEProblem(vectorfield(p_sir),u0,t_span,p)
+sol = OrdinaryDiffEq.solve(prob,Tsit5())
+plot(sol)
+png("ode-chime.png")
+
+prob,cb = SDEProblem(Model(p_sir),u0,t_span,p);
+sol = solve(prob,SRA1(),callback=cb)
+plot(sol)
+png("sde-chime.png")

examples/covid/chime/chime.json

@@ -0,0 +1,27 @@
+{
+  "T": [
+    {
+      "rate": ":(t->begin\n          policy_days = [20, 60, 120] .+ 17\n          contact_rate = 0.05\n          pol = findfirst((x->begin\n                          t <= x\n                      end), policy_days)\n          growth_rate = if pol == 1\n                  0.0\n              else\n                  2 ^ (1 / ((pol - 1) * 5)) - 1\n              end\n          return ((growth_rate + γ) / 990) * (1 - contact_rate)\n      end)",
+      "tname": "inf"
+    },
+    {
+      "rate": ":(1 / 14)",
+      "tname": "rec"
+    }
+  ],
+  "S": [
+    { "concentration": 990, "sname": "S" },
+    { "concentration": 10, "sname": "I" },
+    { "concentration": 0, "sname": "R" }
+  ],
+  "I": [
+    { "it": 1, "is": 1 },
+    { "it": 1, "is": 2 },
+    { "it": 2, "is": 2 }
+  ],
+  "O": [
+    { "ot": 1, "os": 2 },
+    { "ot": 1, "os": 2 },
+    { "ot": 2, "os": 3 }
+  ]
+}

examples/covid/chime/cset-json-schema.rmd

@@ -0,0 +1,89 @@
+---
+title: Petri Net JSON Schema
+date: September 10, 2020
+author: Micah Halter
+output: pdf_document
+header-includes:
+    - \usepackage{tikz-cd}
+---
+
+# Formulation
+
+We can define a Petri net to be the following diagram of finite sets
+
+$$
+\begin{tikzcd}[row sep=large, column sep=large]
+Str & \arrow[l, "sname" swap] S \arrow[r, "conc."] & \mathbb{R}^+ \\
+I \arrow[ru, "is" swap] \arrow[rd, "it"] & & O \arrow[lu, "os"] \arrow[ld, "ot" swap] \\
+Str &\arrow[l, "tname"] T \arrow[r, "rate" swap] & \mathbb{R}^+
+\end{tikzcd}
+$$
+
+Here, $T$ is the set of transitions, $S$ is the set of states, $I$ is the set of input edges from some state $s$ to some transition $t$, and $O$ is the set of output edges from some transition $t$ to some state $s$ where $s \in S$ and $t \in T$. Along with these definitions for transitions, we also have maps from $S \rightarrow \mathbb{R}^+$ that map states to their initial concentrations and $S \rightarrow Str$ that map states to labels. Similarly, we have maps from $T \rightarrow \mathbb{R}^+$ that map transitions to their transition rates and $T \rightarrow Str$ that map transitions to labels.
+
+With this formulation, we can naturally convert the resulting structure into JSON schema:
+
+```json
+{
+  "T": [
+    { "rate": 0.0003, "tname": "inf" },
+    { "rate": 0.2, "tname": "rec" }
+  ],
+  "S": [
+    { "concentration": 990, "sname": "S" },
+    { "concentration": 10, "sname": "I" },
+    { "concentration": 0, "sname": "R" }
+  ],
+  "I": [
+    { "it": 1, "is": 1 },
+    { "it": 1, "is": 2 },
+    { "it": 2, "is": 2 }
+  ],
+  "O": [
+    { "ot": 1, "os": 2 },
+    { "ot": 1, "os": 2 },
+    { "ot": 2, "os": 3 }
+  ]
+}
+```
+
+**Fields:**
+
+- `T`: an array of transitions each with both a `rate` and `tname` specified to represent the transition rate and the label of the transition respectively
+- `S`: an array of states each with both a `concentration` and `sname` specified to represent the initial concentration and the label of the state respectively
+- `I`: an array of input edges each with an input transition (`it`) and input state (`is`) whose values are indexes into the `T` and `S` arrays respectively. These represent an edge from state `is` to transition `it`.
+- `O`: an array of output edges each with an output transition (`it`) and output state (`is`) whose values are indexes into the `T` and `S` arrays respectively. These represent an edge from transition `it` to state `is`.
+
+### Dynamic Transition Rates
+
+In order to support dynamic transition rates, we will be providing raw Julia code blocks that defines a function as either a function of time (`t->begin ... end`) or both time and current state (`(u,t)->begin ... end`). This will allow us to provide the math the defines the change of the rate in regards to different parts of the system while maintaining the structure of the original model. For interoperability, these rates can either be transpiled between languages or you can focus on just extracting the model structure from the `json` file and write your own definitions for the rates. An example of this would be `{ "rate": ":((u,t)->((3/sum(u))/(t+1)))", "tname": "inf" }`. Here the rate of the transition `inf` changes as a function of the current state of the system (total population) and time, where infection rate decreases over time to represent a virus weakening over time. Another example can be found in the [`chime.json`](https://github.com/AlgebraicJulia/AlgebraicPetri.jl/blob/petset/examples/covid/chime/chime.json) where the rate of infection is dependent on time to model changes in intervention policies.
+
+*Note:* While this is how we plan to represent dynamic rates currently, we are investigating using a dataflow graph in the future to represent the math that defines dynamic rates in a more programming language/implementation agnostic way.
+
+## SIR Example
+
+```json
+{
+  "T": [
+    { "rate": 0.0003, "tname": "inf" },
+    { "rate": 0.2, "tname": "rec" }
+  ],
+  "S": [
+    { "concentration": 990, "sname": "S" },
+    { "concentration": 10, "sname": "I" },
+    { "concentration": 0, "sname": "R" }
+  ],
+  "I": [
+    { "it": 1, "is": 1 },
+    { "it": 1, "is": 2 },
+    { "it": 2, "is": 2 }
+  ],
+  "O": [
+    { "ot": 1, "os": 2 },
+    { "ot": 1, "os": 2 },
+    { "ot": 2, "os": 3 }
+  ]
+}
+```
+
+![Resulting SIR Petri Net](sir.png)

examples/covid/covid.jl

@@ -5,14 +5,14 @@
 using AlgebraicPetri
 using AlgebraicPetri.Epidemiology
 
-using Petri
+using Petri: Model, Graph
 using OrdinaryDiffEq
 using Plots
 
 using Catlab
 using Catlab.Theories
 using Catlab.Programs
-using Catlab.CategoricalAlgebra.ShapeDiagrams
+using Catlab.CategoricalAlgebra.FreeDiagrams
 using Catlab.WiringDiagrams
 using Catlab.Graphics
 
@@ -25,7 +25,7 @@ id(args...) = foldl((x,y)->id(x) ⊗ id(y), args);
 
 travel_petri = PetriCospan(
         [1,2,3],
-        Petri.Model(1:6, [(Dict(1=>1), Dict(4=>1)), (Dict(2=>1), Dict(5=>1)), (Dict(3=>1), Dict(6=>1))]),
+        PetriNet(6, (1,4), (2,5), (3,6)),
         [4,5,6]);
 
 # #### Step 2: Extend the Infectious Disease presentation,
@@ -62,7 +62,7 @@ seird_city = to_hom_expr(FreeBiproductCategory, seird_city)
 
 display_wd(seird_city)
 # -
-Graph(decoration(F(seird_city)))
+Graph(Model(decoration(F(seird_city))))
 
 # create a multi-city SEIRD models
 
@@ -73,7 +73,7 @@ pc_seird_3 = F(seird_3)
 p_seird_3 = decoration(pc_seird_3)
 display_wd(seird_3)
 # -
-Graph(p_seird_3)
+Graph(Model(p_seird_3))
 
 # Define time frame and initial parameters
 
@@ -94,7 +94,7 @@ params = seirdparams(3, 5);
 
 # Generate, solve, and visualize resulting ODE
 
-prob = ODEProblem(p_seird_3,u0,tspan,params);
+prob = ODEProblem(vectorfield(p_seird_3),u0,tspan,params);
 sol = solve(prob,Tsit5());
 
 plot(sol)
@@ -125,7 +125,7 @@ a,b,p = 10, 1, 1/6
 
 dynparams = waveparams(asymptotic, a/sum(u0), b/sum(u0),p)
 
-prob = ODEProblem(p_seird_3,u0,tspan, dynparams)
+prob = ODEProblem(vectorfield(p_seird_3),u0,tspan, dynparams)
 sol = solve(prob,Tsit5(), saveat=1:1:tspan[2])
 
 plot(sol)

examples/covid/epidemiology.jl

@@ -2,14 +2,16 @@
 #
 #md # [![](https://img.shields.io/badge/show-nbviewer-579ACA.svg)](@__NBVIEWER_ROOT_URL__/examples/covid/epidemiology.ipynb)
 
+using AlgebraicPetri
 using AlgebraicPetri.Epidemiology
 
-using Petri
+using Petri: Model, Graph
+using OrdinaryDiffEq
 using StochasticDiffEq
 using Plots
 
 using Catlab.Theories
-using Catlab.CategoricalAlgebra.ShapeDiagrams
+using Catlab.CategoricalAlgebra.FreeDiagrams
 using Catlab.Graphics
 
 display_wd(ex) = to_graphviz(ex, orientation=LeftToRight, labels=true);
@@ -20,12 +22,15 @@ display_wd(ex) = to_graphviz(ex, orientation=LeftToRight, labels=true);
 
 sir = transmission ⋅ recovery
 
-# get resulting petri net and visualize model
+# get resulting petri net as a C-Set
 
-p_sir = decoration(F_epi(sir));
+cset_sir = decoration(F_epi(sir));
 display_wd(sir)
 #-
-Graph(p_sir)
+
+# Use Petri.jl to visualize the C-Set
+
+Graph(Model(cset_sir))
 
 # define initial states and transition rates, then
 # create, solve, and visualize ODE problem
@@ -33,8 +38,10 @@ Graph(p_sir)
 u0 = [10.0, 1, 0];
 p = [0.4, 0.4];
 
-prob,cb = SDEProblem(p_sir,u0,(0.0,7.5),p);
-sol = solve(prob,SRA1(),callback=cb)
+# The C-Set representation has direct support for generating a DiffEq vector field
+
+prob = ODEProblem(vectorfield(cset_sir),u0,(0.0,7.5),p);
+sol = solve(prob,Tsit5())
 
 plot(sol)
 
@@ -46,9 +53,10 @@ sei = exposure ⋅ (illness ⊗ id(I)) ⋅ ∇(I)
 
 seir = sei ⋅ recovery
 
-# get resulting petri net and visualize model
+# here we convert the C-Set decoration to a Petri.jl model
+# to use its StochasticDifferentialEquations support
 
-p_seir = decoration(F_epi(seir));
+