consistent capitalisation in page titles

TorkelE · TorkelE · commit 46c9cdb3cfe2 · 2025-03-19T17:57:20.000Z
diff --git a/docs/src/inverse_problems/behaviour_optimisation.md b/docs/src/inverse_problems/behaviour_optimisation.md
@@ -1,4 +1,4 @@
-# [Optimization for non-data fitting purposes](@id behaviour_optimisation)
+# [Optimization for Non-data Fitting Purposes](@id behaviour_optimisation)
 In previous tutorials we have described how to use [PEtab.jl](@ref petab_parameter_fitting) and [Optimization.jl](@ref optimization_parameter_fitting) for parameter fitting. This involves solving an optimisation problem (to find the parameter set yielding the best model-to-data fit). There are, however, other situations that require solving optimisation problems. Typically, these involve the creation of a custom objective function, which minimizer can then be found using Optimization.jl. In this tutorial we will describe this process, demonstrating how parameter space can be searched to find values that achieve a desired system behaviour. Many options used here are described in more detail in [the tutorial on using Optimization.jl for parameter fitting](@ref optimization_parameter_fitting). A more throughout description of how to solve these problems is provided by [Optimization.jl's documentation](https://docs.sciml.ai/Optimization/stable/) and the literature[^1].
 
 ## [Maximising the pulse amplitude of an incoherent feed forward loop](@id behaviour_optimisation_IFFL_example)
diff --git a/docs/src/model_creation/chemistry_related_functionality.md b/docs/src/model_creation/chemistry_related_functionality.md
@@ -1,4 +1,4 @@
-# [Chemistry-related functionality](@id chemistry_functionality)
+# [Chemistry-related Functionality](@id chemistry_functionality)
 
 While Catalyst has primarily been designed around the modelling of biological systems, reaction network models are also common in chemistry. This section describes two types of functionality, that while of general interest, should be especially useful in the modelling of chemical systems.
 - The `@compound` option, which enables the user to designate that a specific species is composed of certain subspecies.
diff --git a/docs/src/model_creation/conservation_laws.md b/docs/src/model_creation/conservation_laws.md
@@ -1,4 +1,4 @@
-# [Working with conservation laws](@id conservation_laws)
+# [Working with Conservation Laws](@id conservation_laws)
 Catalyst can detect, and eliminate for differential-equation based models, *conserved quantities*, i.e. linear combinations of species which are conserved via the chemistry. This functionality is both automatically utilised by Catalyst (e.g. to [remove singular Jacobians during steady state computations](@ref homotopy_continuation_conservation_laws)), but is also available for users to utilise directly (e.g. to potentially [improve simulation performance](@ref ode_simulation_performance_conservation_laws)).
 
 To illustrate conserved quantities, let us consider the following [two-state](@ref basic_CRN_library_two_states) model:
diff --git a/docs/src/model_creation/examples/programmatic_generative_linear_pathway.md b/docs/src/model_creation/examples/programmatic_generative_linear_pathway.md
@@ -1,4 +1,4 @@
-# [Programmatic, generative, modelling of a linear pathway](@id programmatic_generative_linear_pathway)
+# [Programmatic, Generative, Modelling of a Linear Pathway](@id programmatic_generative_linear_pathway)
 This example will show how to use programmatic, generative, modelling to model a system implicitly. I.e. rather than listing all system reactions explicitly, the reactions are implicitly generated from a simple set of rules. This example is specifically designed to show how [programmatic modelling](@ref programmatic_CRN_construction) enables *generative workflows* (demonstrating one of its advantages as compared to [DSL-based modelling](@ref dsl_description)). In our example, we will model linear pathways, so we will first introduce these. Next, we will model them first using the DSL, and then using a generative programmatic workflow.
 
 ## [Linear pathways](@id programmatic_generative_linear_pathway_intro)
diff --git a/docs/src/model_creation/parametric_stoichiometry.md b/docs/src/model_creation/parametric_stoichiometry.md
@@ -1,4 +1,4 @@
-# [Symbolic Stochiometries](@id parametric_stoichiometry)
+# [Symbolic Stoichiometries](@id parametric_stoichiometry)
 Catalyst supports stoichiometric coefficients that involve parameters, species,
 or even general expressions. In this tutorial we show several examples of how to
 use symbolic stoichiometries, and discuss several caveats to be aware of.
diff --git a/docs/src/model_creation/reactionsystem_content_accessing.md b/docs/src/model_creation/reactionsystem_content_accessing.md
@@ -1,4 +1,4 @@
-# [Accessing model properties](@id model_accessing)
+# [Accessing Model Properties](@id model_accessing)
 Catalyst is based around the creation, analysis, and simulation of chemical reaction network models. Catalyst stores these models in [`ReactionSystem`](@ref) structures. This page describes some basic functions for accessing the content of these structures. This includes retrieving lists of species, parameters, or reactions that a model consists of. An extensive list of relevant functions for working with `ReactionSystem` models can be found in Catalyst's [API](@ref api).
 
 !!! warning
diff --git a/docs/src/model_simulation/examples/periodic_events_simulation.md b/docs/src/model_simulation/examples/periodic_events_simulation.md
@@ -1,4 +1,4 @@
-# [Modelling a periodic event during ODE and jump simulations](@id periodic_event_simulation_example)
+# [Modelling a Periodic Event During ODE and Jump Simulations](@id periodic_event_simulation_example)
 This tutorial will describe how to simulate systems with periodic events in ODEs and jump simulations (SDEs use identical syntax). We will consider a model with a [circadian rhythm](https://en.wikipedia.org/wiki/Circadian_rhythm), where a parameter represents the level of light. While outdoor light varies smoothly, in experimental settings a lamp is often simply turned on/off every 12 hours. Here we will model this toggling of the light using a periodic event that is triggered every 12 hours.
 
 ## [Modelling a circadian periodic event in an ODE simulation](@id periodic_event_simulation_example_ode)
diff --git a/docs/src/model_simulation/ode_simulation_performance.md b/docs/src/model_simulation/ode_simulation_performance.md
@@ -1,4 +1,4 @@
-# [Advice for performant ODE simulations](@id ode_simulation_performance)
+# [Advice for Performant ODE Simulations](@id ode_simulation_performance)
 We have previously described how to perform ODE simulations of *chemical reaction network* (CRN) models. These simulations are typically fast and require little additional consideration. However, when a model is simulated many times (e.g. as a part of solving an inverse problem), or is very large, simulation run
 times may become noticeable. Here we will give some advice on how to improve performance for these cases [^1].
 
diff --git a/docs/src/model_simulation/sde_simulation_performance.md b/docs/src/model_simulation/sde_simulation_performance.md
@@ -1,4 +1,4 @@
-# [Advice for performant SDE simulations](@id sde_simulation_performance)
+# [Advice for Performant SDE Simulations](@id sde_simulation_performance)
 While there exist relatively straightforward approaches to manage performance for [ODE](@ref ode_simulation_performance) and jump simulations, this is generally not the case for SDE simulations. Below, we briefly describe some options. However, as one starts to investigate these, one quickly reaches what is (or could be) active areas of research.
 
 ## [SDE solver selection](@id sde_simulation_performance_solvers)
diff --git a/docs/src/model_simulation/simulation_plotting.md b/docs/src/model_simulation/simulation_plotting.md
@@ -1,4 +1,4 @@
-# [Simulation plotting](@id simulation_plotting)
+# [Simulation Plotting](@id simulation_plotting)
 Catalyst uses the [Plots.jl](https://github.com/JuliaPlots/Plots.jl) package for performing all plots. This section provides a brief summary of some useful plotting options, while [Plots.jl's documentation](https://docs.juliaplots.org/stable/) provides a more throughout description of how to tune your plots.
 
 !!! note
diff --git a/docs/src/model_simulation/simulation_structure_interfacing.md b/docs/src/model_simulation/simulation_structure_interfacing.md
@@ -1,4 +1,4 @@
-# [Interfacing problems, integrators, and solutions](@id simulation_structure_interfacing)
+# [Interfacing Problems, Integrators, and Solutions](@id simulation_structure_interfacing)
 When simulating a model, one begins with creating a [problem](https://docs.sciml.ai/DiffEqDocs/stable/basics/problem/). Next, a simulation is performed on the problem, during which the simulation's state is recorded through an [integrator](https://docs.sciml.ai/DiffEqDocs/stable/basics/integrator/). Finally, the simulation output is returned as a [solution](https://docs.sciml.ai/DiffEqDocs/stable/basics/solution/). This tutorial describes how to access (or modify) the state (or parameter) values of problem, integrator, and solution structures.
 
 Generally, when we have a structure `simulation_struct` and want to interface with the unknown (or parameter) `x`, we use `simulation_struct[:x]` to access the value. For situations where a value is accessed (or changed) a large number of times, it can *improve performance* to first create a [specialised getter/setter function](@ref simulation_structure_interfacing_functions).
diff --git a/docs/src/spatial_modelling/spatial_jump_simulations.md b/docs/src/spatial_modelling/spatial_jump_simulations.md
@@ -1,4 +1,4 @@
-# [Spatial jump simulations](@id spatial_lattice_jump_simulations)
+# [Spatial Jump Simulations](@id spatial_lattice_jump_simulations)
 Our [introduction to spatial lattice simulations](@ref spatial_lattice_modelling_intro) has already described how to simulate [`LatticeReactionSystem`](@ref)s using ODEs. Jump simulations of [`LatticeReactionSystem`](@ref) are carried out using an almost identical approach. However, just like for non-spatial models, we must first create a `DiscreteProblem`, which is then used as input to our `JumpProblem`. Furthermore, a spatial [jump aggregator](@ref simulation_intro_jumps_solver_designation) (like `NSM`) can be used. Spatial jump simulations in Catalyst are built on top of JumpProcesses.jl's spatial jump simulators, more details on which can be found [here](https://docs.sciml.ai/JumpProcesses/stable/tutorials/spatial/).
 
 Below we perform a spatial jump simulation of a simple [birth-death process](@ref basic_CRN_library_bd). Note that we use our [`LatticeReactionSystem`](@ref) as input to both our `DiscreteProblem` and `JumpProblem`, and that we [provide](@ref simulation_intro_jumps_solver_designation) the spatial `NSM` jump aggregator to `JumpProblem`.
diff --git a/docs/src/steady_state_functionality/dynamical_systems.md b/docs/src/steady_state_functionality/dynamical_systems.md
@@ -1,4 +1,4 @@
-# [Analysing model steady state properties with DynamicalSystems.jl](@id dynamical_systems)
+# [Analysing Model Steady State Properties with DynamicalSystems.jl](@id dynamical_systems)
 The [DynamicalSystems.jl package](https://github.com/JuliaDynamics/DynamicalSystems.jl) implements a wide range of methods for analysing dynamical systems[^1][^2]. This includes both continuous-time systems (i.e. ODEs) and discrete-times ones (difference equations, however, these are not relevant to chemical reaction network modelling). Here we give two examples of how DynamicalSystems.jl can be used, with the package's [documentation describing many more features](https://juliadynamics.github.io/DynamicalSystemsDocs.jl/dynamicalsystems/dev/tutorial/). Finally, it should also be noted that DynamicalSystems.jl contain several tools for [analysing data measured from dynamical systems](https://juliadynamics.github.io/DynamicalSystemsDocs.jl/dynamicalsystems/dev/contents/#Exported-submodules).
 
 ## [Finding basins of attraction](@id dynamical_systems_basins_of_attraction)

Original file line number	Diff line number	Diff line change
`@@ -1,4 +1,4 @@`
`1`		`-# [Optimization for non-data fitting purposes](@id behaviour_optimisation)`
	`1`	`+# [Optimization for Non-data Fitting Purposes](@id behaviour_optimisation)`
`2`	`2`	In previous tutorials we have described how to use [PEtab.jl](@ref petab_parameter_fitting) and [Optimization.jl](@ref optimization_parameter_fitting) for parameter fitting. This involves solving an optimisation problem (to find the parameter set yielding the best model-to-data fit). There are, however, other situations that require solving optimisation problems. Typically, these involve the creation of a custom objective function, which minimizer can then be found using Optimization.jl. In this tutorial we will describe this process, demonstrating how parameter space can be searched to find values that achieve a desired system behaviour. Many options used here are described in more detail in [the tutorial on using Optimization.jl for parameter fitting](@ref optimization_parameter_fitting). A more throughout description of how to solve these problems is provided by [Optimization.jl's documentation](https://docs.sciml.ai/Optimization/stable/) and the literature[^1].
`3`	`3`
`4`	`4`	`## [Maximising the pulse amplitude of an incoherent feed forward loop](@id behaviour_optimisation_IFFL_example)`
Original file line number	Diff line number	Diff line change
`@@ -1,4 +1,4 @@`
`1`		`-# [Chemistry-related functionality](@id chemistry_functionality)`
	`1`	`+# [Chemistry-related Functionality](@id chemistry_functionality)`
`2`	`2`
`3`	`3`	`While Catalyst has primarily been designed around the modelling of biological systems, reaction network models are also common in chemistry. This section describes two types of functionality, that while of general interest, should be especially useful in the modelling of chemical systems.`
`4`	`4`	- The `@compound` option, which enables the user to designate that a specific species is composed of certain subspecies.
Original file line number	Diff line number	Diff line change
`@@ -1,4 +1,4 @@`
`1`		`-# [Working with conservation laws](@id conservation_laws)`
	`1`	`+# [Working with Conservation Laws](@id conservation_laws)`
`2`	`2`	Catalyst can detect, and eliminate for differential-equation based models, conserved quantities, i.e. linear combinations of species which are conserved via the chemistry. This functionality is both automatically utilised by Catalyst (e.g. to [remove singular Jacobians during steady state computations](@ref homotopy_continuation_conservation_laws)), but is also available for users to utilise directly (e.g. to potentially [improve simulation performance](@ref ode_simulation_performance_conservation_laws)).
`3`	`3`
`4`	`4`	`To illustrate conserved quantities, let us consider the following [two-state](@ref basic_CRN_library_two_states) model:`
Original file line number	Diff line number	Diff line change
`@@ -1,4 +1,4 @@`
`1`		`-# [Programmatic, generative, modelling of a linear pathway](@id programmatic_generative_linear_pathway)`
	`1`	`+# [Programmatic, Generative, Modelling of a Linear Pathway](@id programmatic_generative_linear_pathway)`
`2`	`2`	This example will show how to use programmatic, generative, modelling to model a system implicitly. I.e. rather than listing all system reactions explicitly, the reactions are implicitly generated from a simple set of rules. This example is specifically designed to show how [programmatic modelling](@ref programmatic_CRN_construction) enables generative workflows (demonstrating one of its advantages as compared to [DSL-based modelling](@ref dsl_description)). In our example, we will model linear pathways, so we will first introduce these. Next, we will model them first using the DSL, and then using a generative programmatic workflow.
`3`	`3`
`4`	`4`	`## [Linear pathways](@id programmatic_generative_linear_pathway_intro)`
Original file line number	Diff line number	Diff line change
`@@ -1,4 +1,4 @@`
`1`		`-# [Symbolic Stochiometries](@id parametric_stoichiometry)`
	`1`	`+# [Symbolic Stoichiometries](@id parametric_stoichiometry)`
`2`	`2`	`Catalyst supports stoichiometric coefficients that involve parameters, species,`
`3`	`3`	`or even general expressions. In this tutorial we show several examples of how to`
`4`	`4`	`use symbolic stoichiometries, and discuss several caveats to be aware of.`
Original file line number	Diff line number	Diff line change
`@@ -1,4 +1,4 @@`
`1`		`-# [Accessing model properties](@id model_accessing)`
	`1`	`+# [Accessing Model Properties](@id model_accessing)`
`2`	`2`	Catalyst is based around the creation, analysis, and simulation of chemical reaction network models. Catalyst stores these models in [`ReactionSystem`](@ref) structures. This page describes some basic functions for accessing the content of these structures. This includes retrieving lists of species, parameters, or reactions that a model consists of. An extensive list of relevant functions for working with `ReactionSystem` models can be found in Catalyst's [API](@ref api).
`3`	`3`
`4`	`4`	`!!! warning`
Original file line number	Diff line number	Diff line change
`@@ -1,4 +1,4 @@`
`1`		`-# [Modelling a periodic event during ODE and jump simulations](@id periodic_event_simulation_example)`
	`1`	`+# [Modelling a Periodic Event During ODE and Jump Simulations](@id periodic_event_simulation_example)`
`2`	`2`	`This tutorial will describe how to simulate systems with periodic events in ODEs and jump simulations (SDEs use identical syntax). We will consider a model with a [circadian rhythm](https://en.wikipedia.org/wiki/Circadian_rhythm), where a parameter represents the level of light. While outdoor light varies smoothly, in experimental settings a lamp is often simply turned on/off every 12 hours. Here we will model this toggling of the light using a periodic event that is triggered every 12 hours.`
`3`	`3`
`4`	`4`	`## [Modelling a circadian periodic event in an ODE simulation](@id periodic_event_simulation_example_ode)`
Original file line number	Diff line number	Diff line change
`@@ -1,4 +1,4 @@`
`1`		`-# [Advice for performant ODE simulations](@id ode_simulation_performance)`
	`1`	`+# [Advice for Performant ODE Simulations](@id ode_simulation_performance)`
`2`	`2`	`We have previously described how to perform ODE simulations of chemical reaction network (CRN) models. These simulations are typically fast and require little additional consideration. However, when a model is simulated many times (e.g. as a part of solving an inverse problem), or is very large, simulation run`
`3`	`3`	`times may become noticeable. Here we will give some advice on how to improve performance for these cases [^1].`
`4`	`4`
Original file line number	Diff line number	Diff line change
`@@ -1,4 +1,4 @@`
`1`		`-# [Advice for performant SDE simulations](@id sde_simulation_performance)`
	`1`	`+# [Advice for Performant SDE Simulations](@id sde_simulation_performance)`
`2`	`2`	`While there exist relatively straightforward approaches to manage performance for [ODE](@ref ode_simulation_performance) and jump simulations, this is generally not the case for SDE simulations. Below, we briefly describe some options. However, as one starts to investigate these, one quickly reaches what is (or could be) active areas of research.`
`3`	`3`
`4`	`4`	`## [SDE solver selection](@id sde_simulation_performance_solvers)`
Original file line number	Diff line number	Diff line change
`@@ -1,4 +1,4 @@`
`1`		`-# [Simulation plotting](@id simulation_plotting)`
	`1`	`+# [Simulation Plotting](@id simulation_plotting)`
`2`	`2`	`Catalyst uses the [Plots.jl](https://github.com/JuliaPlots/Plots.jl) package for performing all plots. This section provides a brief summary of some useful plotting options, while [Plots.jl's documentation](https://docs.juliaplots.org/stable/) provides a more throughout description of how to tune your plots.`
`3`	`3`
`4`	`4`	`!!! note`