docs: fix references, spacing and language in the example section

joss/paper.md

@@ -31,12 +31,12 @@ bibliography: paper.bib
 
 # Summary
 
-Interpolations are used to estimate values between known data points using an approximate continuous function.DataInterpolations.jl is a Julia [@Bezanson2017] package containing 1D implementations of some of the most commonly used interpolation functions. These include:
+Interpolations are used to estimate values between known data points using an approximate continuous function. DataInterpolations.jl is a Julia [@Bezanson2017] package containing 1D implementations of some of the most commonly used interpolation functions. These include:
 
   - Constant Interpolation
   - Linear Interpolation
   - Quadratic Interpolation
-  - Lagrange Interpolation [@lagrange]
+  - Lagrange Interpolation [@lagrange1898lectures]
   - Quadratic Splines
   - Cubic Splines [@Schoenberg1988]
   - Akima Splines [@10.1145/321607.321609]
@@ -46,15 +46,19 @@ Interpolations are used to estimate values between known data points using an ap
   - B-Splines [@Curry1988] [@DEBOOR197250]
   - Regression based B-Splines
 
-and a continually growing list. Along with these, the package also has methods to fit parameterized curves with the data points and Tikhonov regularization [@Tikhonov1943OnTS] [@amt-14-7909-2021] for obtaining smooth curves. The package also provides functionality to compute integrals and derivatives upto second order for those interpolations methods. It is also automatic differentiation friendly. It can also be used symbolically with Symbolics.jl [@gowda2021high] and plugged into models defined using ModelingToolkit.jl [@ma2021modelingtoolkit].
+and a continually growing list. Along with these, the package also has methods to fit parameterized curves with the data points and Tikhonov regularization [@Tikhonov1943OnTS] [@amt-14-7909-2021] for obtaining smooth curves. The package also provides functionality to compute integrals and derivatives upto second order for those interpolations methods. It is also automatic differentiation friendly. It can also be used symbolically with Symbolics.jl [@10.1145/3511528.3511535] and plugged into models defined using ModelingToolkit.jl [@ma2021modelingtoolkit].
 
 # Statement of need
 
 Interpolations are a very important component of many modeling workflows. Often, sampled or measured inputs need to be transformed into continuous functions or smooth curves for simulation purposes. In many scientific machine learning workflows, interpolating data is essential to learn continuous models. DataInterpolations.jl can be used for facilitating these types of workflows. Several interpolation packages already exist in Julia, such as [Interpolations.jl](https://juliamath.github.io/Interpolations.jl/stable/), which primarily specializes in B-Splines and uniformly spaced data with some support for irregularly spaced data. In contrast, DataInterpolations.jl does not assume any specific structure in the data, offering greater flexibility for diverse datasets. [Interpolations.jl](https://juliamath.github.io/Interpolations.jl/stable/) also doesn't offer methods like Quadratic Interpolation, Lagrange Interpolation, Hermite Splines etc. [BasicInterpolators.jl](https://github.com/markmbaum/BasicInterpolators.jl) is more similar to DataInterpolations.jl, although it doesn't offer methods like B-Splines. Rest of the interpolation packages focus on particular methods like [BSplineKit.jl](https://github.com/jipolanco/BSplineKit.jl) for B-Splines, [FastChebInterp.jl](https://github.com/JuliaMath/FastChebInterp.jl) for Chebyshev interpolation, [PCHIPInterpolation](https://github.com/gerlero/PCHIPInterpolation.jl) for PCHIP interpolation etc. Additionally, DataInterpolations.jl includes many novel techniques for accelerating the interpolation searches with specialized caching, quasi-linear guessing, and more to improve the performance algorithmically, beyond the simple computational optimizations. In summary, DataInterpolations.jl is more generic from other packages and offers many fast interpolation methods for arbitrarily spaced 1D data, all within a consistent and simple interface.
 
 # Example
 
-The following tutorials in the documentation [1](https://docs.sciml.ai/DataInterpolations/stable/methods/) provides how to define each of the interpolation methods and compute the value at any point. [2](https://docs.sciml.ai/DataInterpolations/stable/interface/) provides explanation for using the interface and interpolated objects for evaluating at any point, computing the derivative at any point and computing the integral between any two points. [3](https://docs.sciml.ai/DataInterpolations/stable/symbolics/) provides how to use interpolation objects with Symbolics.jl and ModelingToolkit.jl.
+The following tutorials are provided in the documentation:
+
+  - [Tutorial 1](https://docs.sciml.ai/DataInterpolations/stable/methods/) provides how to define each of the interpolation methods and compute the value at any point.
+  - [Tutorial 2](https://docs.sciml.ai/DataInterpolations/stable/interface/) provides explanation for using the interface and interpolated objects for evaluating at any point, computing the derivative at any point and computing the integral between any two points.
+  - [Tutorial 3](https://docs.sciml.ai/DataInterpolations/stable/symbolics/) provides how to use interpolation objects with Symbolics.jl and ModelingToolkit.jl.
 
 A simple demonstration here: