fixing links, docs

Author: MartinuzziFrancesco

README.md

@@ -1,6 +1,7 @@
 <p align="center">
     <img width="400px" src="docs/src/assets/logo.png"/>
 </p>
+
 <div align="center">
 
 [![Join the chat at https://julialang.zulipchat.com #sciml-bridged](https://img.shields.io/static/v1?label=Zulip&message=chat&color=9558b2&labelColor=389826)](https://julialang.zulipchat.com/#narrow/stream/279055-sciml-bridged)
@@ -11,9 +12,11 @@
 [![Build status](https://badge.buildkite.com/db8f91b89a10ad79bbd1d9fdb1340e6f6602a1c0ed9496d4d0.svg)](https://buildkite.com/julialang/reservoircomputing-dot-jl)
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+
 </div>
 
 # ReservoirComputing.jl
+
 ReservoirComputing.jl provides an efficient, modular and easy to use implementation of Reservoir Computing models such as Echo State Networks (ESNs). For information on using this package please refer to the [stable documentation](https://docs.sciml.ai/ReservoirComputing/stable/). Use the [in-development documentation](https://docs.sciml.ai/ReservoirComputing/dev/) to take a look at at not yet released features.
 
 ## Quick Example

docs/make.jl

@@ -1,7 +1,7 @@
 using Documenter, ReservoirComputing
 
-cp("./docs/Manifest.toml", "./docs/src/assets/Manifest.toml", force = true)
-cp("./docs/Project.toml", "./docs/src/assets/Project.toml", force = true)
+cp("./docs/Manifest.toml", "./docs/src/assets/Manifest.toml"; force=true)
+cp("./docs/Project.toml", "./docs/src/assets/Project.toml"; force=true)
 
 ENV["PLOTS_TEST"] = "true"
 ENV["GKSwstype"] = "100"

docs/src/api/esn_variations.md

@@ -11,4 +11,4 @@
 ```@docs
     HybridESN
     KnowledgeModel
-```
+```

docs/src/api/inits.md

@@ -1,4 +1,5 @@
 # Echo State Networks Initializers
+
 ## Input layers
 
 ```@docs
@@ -17,4 +18,4 @@
     cycle_jumps
     simple_cycle
     pseudo_svd
-```
+```

docs/src/api/states.md

@@ -22,4 +22,4 @@
 
 ```@docs
     ReservoirComputing.create_states
-```
+```

docs/src/esn_tutorials/deep_esn.md

@@ -2,7 +2,7 @@
 
 Deep Echo State Network architectures started to gain some traction recently. In this guide, we illustrate how it is possible to use ReservoirComputing.jl to build a deep ESN.
 
-The network implemented in this library is taken from [^1]. It works by stacking reservoirs on top of each other, feeding the output from one into the next. The states are obtained by merging all the inner states of the stacked reservoirs. For a more in-depth explanation, refer to the paper linked above. 
+The network implemented in this library is taken from [^1]. It works by stacking reservoirs on top of each other, feeding the output from one into the next. The states are obtained by merging all the inner states of the stacked reservoirs. For a more in-depth explanation, refer to the paper linked above.
 
 ## Lorenz Example
 

docs/src/general/states_variation.md

@@ -6,11 +6,11 @@ In ReservoirComputing models, it's possible to perform alterations on the reserv
 
 ### Extending States
 
-Extending the states involves appending the corresponding input values to the reservoir states. If \(\textbf{x}(t)\) represents the reservoir state at time \(t\) corresponding to the input \(\textbf{u}(t)\), the extended state is represented as \([\textbf{x}(t); \textbf{u}(t)]\), where \([;]\) denotes vertical concatenation. This procedure is commonly used in Echo State Networks and is described in [Jaeger's Scholarpedia](http://www.scholarpedia.org/article/Echo_state_network). You can extend the states in every ReservoirComputing.jl model by using the `states_type` keyword argument and calling the `ExtendedStates()` method. No additional arguments are needed.
+Extending the states involves appending the corresponding input values to the reservoir states. If $\textbf{x}(t)$ represents the reservoir state at time $t$ corresponding to the input $\textbf{u}(t)$, the extended state is represented as $[\textbf{x}(t); \textbf{u}(t)]$, where $[;]$ denotes vertical concatenation. This procedure is commonly used in Echo State Networks and is described in [Jaeger's Scholarpedia](http://www.scholarpedia.org/article/Echo_state_network). You can extend the states in every ReservoirComputing.jl model by using the `states_type` keyword argument and calling the `ExtendedStates()` method. No additional arguments are needed.
 
 ### Padding States
 
-Padding the states involves appending a constant value, such as 1.0, to each state. In the notation introduced earlier, padded states can be represented as \([\textbf{x}(t); 1.0]\). This approach is detailed in the [seminal guide](https://mantas.info/get-publication/?f=Practical_ESN.pdf) to Echo State Networks by Mantas Lukoševičius. To pad the states, you can use the `states_type` keyword argument and call the `PaddedStates(padding)` method, where `padding` represents the value to be concatenated to the states. By default, the padding value is set to 1.0, so most of the time, calling `PaddedStates()` will suffice.
+Padding the states involves appending a constant value, such as 1.0, to each state. In the notation introduced earlier, padded states can be represented as $[\textbf{x}(t); 1.0]$. This approach is detailed in "A practical guide to applying echo state networks." by Lukoševičius, Mantas. To pad the states, you can use the `states_type` keyword argument and call the `PaddedStates(padding)` method, where `padding` represents the value to be concatenated to the states. By default, the padding value is set to 1.0, so most of the time, calling `PaddedStates()` will suffice.
 
 Additionally, you can pad the extended states by using the `PaddedExtendedStates(padding)` method, which also has a default padding value of 1.0.