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Merge pull request #1310 from SciML/fix-typos-ci
Fix typos and add exceptions to .typos.toml
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.typos.toml

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[default.extend-words]
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# Catalyst specific
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systemes = "systemes"
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Hass = "Hass"
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# Julia-specific functions
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indexin = "indexin"
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discretized = "discretized"
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vectorized = "vectorized"
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# Biochemical terms
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Pase = "Pase"
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Ba = "Ba"
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# Common variable patterns in Julia/SciML
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ists = "ists"
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ispcs = "ispcs"

docs/src/faqs.md

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```
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We can now try to change just `Γ` and implicitly the observed variable that was
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removed will be assumed to have changed its initial value to compensate for it.
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Let's confirm this. First we find the observed variable that was elminated.
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Let's confirm this. First we find the observed variable that was eliminated.
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```@example faq_remake
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obs_unknown = only(observed(nlsys)).lhs
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```

docs/src/inverse_problems/petab_ode_param_fitting.md

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---
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## References
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[^1]: [Schmiester, L et al. *PEtab—Interoperable specification of parameter estimation problems in systems biology*, PLOS Computational Biology (2021).](https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1008646)
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[^2]: [Hass, H et al. *PBenchmark problems for dynamic modeling of intracellular processes*, Bioinformatics (2019).](https://academic.oup.com/bioinformatics/article/35/17/3073/5280731?login=false)
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[^2]: [Hass, H et al. *Benchmark problems for dynamic modeling of intracellular processes*, Bioinformatics (2019).](https://academic.oup.com/bioinformatics/article/35/17/3073/5280731?login=false)

docs/src/model_creation/examples/noise_modelling_approaches.md

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```
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Next, we can use the `EnsembleSummary` interface to plot each ensemble's mean activity (as well as 5% and 95% quantiles) over time:
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```@example noise_modelling_approaches
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e_sumary_intrinsic = EnsembleAnalysis.EnsembleSummary(sol_intrinsic, 0.0:1.0:tend)
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e_sumary_extrinsic = EnsembleAnalysis.EnsembleSummary(sol_extrinsic, 0.0:1.0:tend)
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plot(e_sumary_intrinsic; label = "Intrinsic noise", idxs = 1)
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plot!(e_sumary_extrinsic; label = "Extrinsic noise", idxs = 1)
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e_summary_intrinsic = EnsembleAnalysis.EnsembleSummary(sol_intrinsic, 0.0:1.0:tend)
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e_summary_extrinsic = EnsembleAnalysis.EnsembleSummary(sol_extrinsic, 0.0:1.0:tend)
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plot(e_summary_intrinsic; label = "Intrinsic noise", idxs = 1)
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plot!(e_summary_extrinsic; label = "Extrinsic noise", idxs = 1)
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```
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Here we can see that, over time, the systems' mean $X$ activity reaches a constant level around $30$.
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docs/src/model_simulation/ensemble_simulations.md

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Various convenience functions are available for analysing and plotting ensemble simulations (a full list can be found [here](https://docs.sciml.ai/DiffEqDocs/dev/features/ensemble/#Analyzing-an-Ensemble-Experiment)). Here, we use these to first create an `EnsembleSummary` (retrieving each simulation's value at time points `0.0, 1.0, 2.0, ... 1000.0`). Next, we use this as an input to the `plot` command, which automatically plots the mean $X$ activity across the ensemble, while also displaying the 5% and 95% quantiles as the shaded area:
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```@example ensemble
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e_sumary = EnsembleAnalysis.EnsembleSummary(sols, 0.0:1.0:1000.0)
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plot(e_sumary)
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e_summary = EnsembleAnalysis.EnsembleSummary(sols, 0.0:1.0:1000.0)
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plot(e_summary)
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```
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## [Ensemble simulations using varying simulation conditions](@id ensemble_simulations_varying_conditions)

docs/src/model_simulation/examples/interactive_brusselator_simulation.md

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You can further extend this visualization by:
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- Adding other interactive elements, such as [buttons](https://docs.makie.org/stable/reference/blocks/button) or [dropdown menus](https://docs.makie.org/stable/reference/blocks/menu) to control different aspects of the simulation or visualization.
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- Adding additonal axes to the plot, such as plotting the derivatives of the species.
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- Adding additional axes to the plot, such as plotting the derivatives of the species.
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- Color coding the slider and slider labels to match the plot colors.

docs/src/spatial_modelling/lattice_reaction_systems.md

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If we want, it is also possible to provide the values as a [*sparse array*](https://github.com/JuliaSparse/SparseArrays.jl) with values only in the coordinates that corresponds to compartments.
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### [Non-uniform compartment values for unstructured lattices](@id spatial_lattice_modelling_intro_simulation_inputs_graphs)
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In graphs (which are used to represent unstructured lattices) each vertex (i.e. compartment) has a specific index. To set non-uniform values for unstructured lattices, provide a vector where the $i$'th value corresponds to the value in the compartment with index $i$ in the graph. E.g. for a graph with 5 vertexes, where we want $X$ to be zero in all compartments bar one (where it is $1.0$) we use:
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In graphs (which are used to represent unstructured lattices) each vertex (i.e. compartment) has a specific index. To set non-uniform values for unstructured lattices, provide a vector where the $i$'th value corresponds to the value in the compartment with index $i$ in the graph. E.g. for a graph with 5 vertices, where we want $X$ to be zero in all compartments bar one (where it is $1.0$) we use:
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```@example spatial_intro_nonuniform_vals
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[:X1 => [0.0, 0.0, 0.0, 0.0, 1.0], :X2 => 10.0]
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nothing # hide

docs/src/steady_state_functionality/bifurcation_diagrams.md

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Most of the options required by the `bifurcationdiagram` function are provided through the `ContinuationPar` structure. For full details, please read the [BifurcationKit documentation](https://bifurcationkit.github.io/BifurcationKitDocs.jl/dev/library/#BifurcationKit.ContinuationPar). However, a few common options, and how they affect the continuation computation, are described here:
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- `p_min` and `p_max`: Set the interval over which the bifurcation diagram is computed (with the continuation stopping if it reaches these bounds).
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- `dsmin` and `dsmax`: The minimum and maximum length of the continuation steps (in the bifurcation parameter's value).
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- `ds`: The initial length of the continuation steps. This is especially important when `bothside = true` *is not* used, as teh sign of `ds` determines the direction from the initial point in which the continuation will proceed.
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- `ds`: The initial length of the continuation steps. This is especially important when `bothside = true` *is not* used, as the sign of `ds` determines the direction from the initial point in which the continuation will proceed.
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- `max_steps`: The maximum number of continuation steps. If a bifurcation diagram looks incomplete, try increasing this value.
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- `newton_options`: Options for the Newton's method that BifurcationKit uses to find steady states. This can be created using `NewtonPar(tol = 1e-9, max_iterations = 100)` which here sets the tolerance (to `1e-9`) and the maximum number of newton iterations (to `100`).
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docs/src/steady_state_functionality/dynamical_systems.md

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sol = solve(oprob, Rodas5P())
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plot(sol; idxs=(:X, :Y, :Z))
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```
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Next, like when we [computed basins of attraction](@ref dynamical_systems_basins_of_attraction), we create a `CoupledODEs` corresponding to the model and state for which we wish to compute our Lyapunov spectrum. Lke previously, `tspan` must provide some small interval (at least `(0.0, 1.0)` is recommended), but else have no impact on the computed Lyapunov spectrum.
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Next, like when we [computed basins of attraction](@ref dynamical_systems_basins_of_attraction), we create a `CoupledODEs` corresponding to the model and state for which we wish to compute our Lyapunov spectrum. Like previously, `tspan` must provide some small interval (at least `(0.0, 1.0)` is recommended), but else have no impact on the computed Lyapunov spectrum.
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```@example dynamical_systems_lyapunov
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using DynamicalSystems
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ds = CoupledODEs(oprob, (alg = Rodas5P(autodiff = false),))

src/spatial_reaction_systems/lattice_jump_systems.jl

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# Currently, the resulting JumpProblem does not depend on parameters (no way to incorporate these).
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# Hence the parameters of this one do not actually matter. If at some point JumpProcess can
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# handle parameters this can be updated and improved.
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# The non-spatial DiscreteProblem have a u0 matrix with entries for all combinations of species and vertexes.
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# The non-spatial DiscreteProblem have a u0 matrix with entries for all combinations of species and vertices.
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hopping_constants = make_hopping_constants(dprob, lrs)
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sma_jumps = make_spatial_majumps(dprob, lrs)
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non_spat_dprob = DiscreteProblem(reshape(dprob.u0, num_species(lrs), num_verts(lrs)),

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