revert back to original format, giving up fix MD025...

paper.md

@@ -31,9 +31,7 @@ bibliography: paper.bib
 
 ---
 
-# `xspline`: A Python Package for Flexible Spline Modeling
-
-## Summary
+# Summary
 
 Splines are a fundamental tool for describing and estimating nonlinear relationships [@de1978practical]. They allow nonlinear functions to be represented as linear combinations of spline basis elements. Researchers in physical, biological, and health sciences rely on spline models in conjunction with statistical software packages to fit and describe a vast range of nonlinear relationships.
 
@@ -48,7 +46,7 @@ These tools include
 Several important gaps remain in python packages for spline modeling.  `xspline` is not a comprehensive tool that generalizes existing software. Instead, it provides key functionality that undergirds flexible interpolation and fitting, closing existing gaps in the available tools.  `xspline` is currently widely used in global health applications [@murray2020global], undergidring the majority of spline modeling at the Institute of Health metrics and Evaluation (IHME).
 
 
-## Statement of Need
+# Statement of Need
 
 Current spline packages offer broad functionality in spline fitting, including:
 - Manipulating and estimating curves (scipy, splines), surfaces and volumes (splipy, pySpline)
@@ -62,7 +60,7 @@ From this list, its apparent that `scipy` offers the most comprehensive features
 This functionality is essential to risk modeling. For example, data reported by all studies focusing on risk-outcome pairs are ratios of definite integrals across different exposure intervals. Prior packages do not offer a direct way to fit spline functions to these nonlinear data, because they do not provide definite integrals of splines as spline objects. Spline derivatives are also needed to impose shape constraints on risk curves of interest. Finally, extrapolations are often required to areas with little to no data, while maintaining high-fidelity fits for regions with dense data. Theoretically, it is straightforward to extrapolate any fit of degree less than or equal to the degree of the ultimate segments (for example, using slope matching for first order, slope and curvature for second order, etc.) However, this functinoality is not available in other packages.
 
 
-## Core idea and structure of `xspline`
+# Core idea and structure of `xspline`
 
 The main idea of `xspline` is to provide a python class that allows user to
 interact with basis splines, their derivatives and integrals and extrapolation
@@ -89,8 +87,8 @@ More information about the structure of the library can be found in [documentati
 while the mathematical use cases are extensively discussed in [@zheng2021trimmed] and [@zheng2022burden] in the context of fitting risks.
 
 
-## Ongoing Research and Dissemination
+# Ongoing Research and Dissemination
 
 The `xspline` package is widely used in all spline modeling done at IHME. In paricular, the new functionality described above enabled a new set of dose-response analyses recently published by the institue, including analyses of chewing tobacco [@gil2024health], education [@balaj2024effects], second-hand smoke [@flor2024health], intimate partner violence [@spencer2023health], smoking [@dai2022health], blood pressure [@razo2022effects], vegetable consumption [@stanaway2022health], and red meat consumption [@lescinsky2022health]. The results of all of these analyses are now publicly available at https://vizhub.healthdata.org/burden-of-proof/.
 
-## References
+# References