draft paper updates

Paper/paper/paper.bib

@@ -7,6 +7,46 @@ @book{Binney:2008
   	Year = 2008
 }
 
+@ARTICLE{Gadget4,
+       author = {{Springel}, Volker and {Pakmor}, R{\"u}diger and {Zier}, Oliver and {Reinecke}, Martin},
+        title = "{Simulating cosmic structure formation with the GADGET-4 code}",
+      journal = {\mnras},
+     keywords = {methods: numerical, galaxies: interactions, dark matter, Astrophysics - Instrumentation and Methods for Astrophysics, Astrophysics - Cosmology and Nongalactic Astrophysics},
+         year = 2021,
+        month = sep,
+       volume = {506},
+       number = {2},
+        pages = {2871-2949},
+          doi = {10.1093/mnras/stab1855},
+archivePrefix = {arXiv},
+       eprint = {2010.03567},
+ primaryClass = {astro-ph.IM},
+       adsurl = {https://ui.adsabs.harvard.edu/abs/2021MNRAS.506.2871S},
+      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
+}
+
+
+
+@ARTICLE{Wang:15,
+       author = {{Wang}, Long and {Spurzem}, Rainer and {Aarseth}, Sverre and {Nitadori}, Keigo and {Berczik}, Peter and {Kouwenhoven}, M.~B.~N. and {Naab}, Thorsten},
+        title = "{NBODY6++GPU: ready for the gravitational million-body problem}",
+      journal = {\mnras},
+     keywords = {methods: numerical, globular clusters: general, Astrophysics - Instrumentation and Methods for Astrophysics, Astrophysics - Solar and Stellar Astrophysics},
+         year = 2015,
+        month = jul,
+       volume = {450},
+       number = {4},
+        pages = {4070-4080},
+          doi = {10.1093/mnras/stv817},
+archivePrefix = {arXiv},
+       eprint = {1504.03687},
+ primaryClass = {astro-ph.IM},
+       adsurl = {https://ui.adsabs.harvard.edu/abs/2015MNRAS.450.4070W},
+      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
+}
+
+
+
 @article{gaia,
     author = {{Gaia Collaboration}},
     title = "{The Gaia mission}",

Paper/paper/paper.md

@@ -139,11 +139,21 @@ computed bases and resulting coefficient data are stored in HDF5
 
 ## N-body simulation
 
+Computing the gravitational potential and forces from a collection of
+N particles is typically an expensive endeavour. EXP reduces the cost
+by using BFE to compute the potential and forces such that computational
+effort scales with the number of particles. Other modern N-body codes
+use direct summation [@Wang:15] or tree-based solutions [@Gadget4],
+which have computational effort that scales as N$^2$ and N log N,
+respectively. The trade off for BFE solutions comes in the form of
+restricted degrees of freedom; for many problems in near-equilibrium
+galactic dynamics this is not a problem, but rather a feature.
+
 Our design includes a wide choice of run-time summary diagnostics,
 phase-space output formats, dynamically loadable user libraries, and
 easy extensibility. Stand-alone routines include the EOF and mSSA 
 methods described above, and the modular software architecture of 
-EXP enables users to easily build and maintain extensions. The `EXP` 
+`EXP` enables users to easily build and maintain extensions. The `EXP` 
 code base is described in published papers [@Petersen:22; @Weinberg:23]
 and has been used, enhanced, and rigorously tested for nearly two 
 decades.
@@ -174,12 +184,15 @@ table above as well as coefficients for an input data set.  Each of
 these tools are Python classes that accept `numpy` [@numpy] arrays for
 immediate interoperability with `matplotlib` [@matplotlib] and
 Astropy.  We include a verified set of stand-alone routines that read
-phase-space files from many major cosmological tree codes and produce
+phase-space files from many major cosmological tree codes (for example,
+@Gadget4) and produce
 BFE-based analyses.  The code suite includes adapters for reading and
 writing phase space for many of the widely used cosmology codes, with
 a base class for developing new ones.  There are multiple ways to use
 the versatile and modular tools in `pyEXP`, and we anticipate
-pipelines that we have not yet imagined.
+pipelines that we have not yet imagined. The flexibility of the basis
+sets available in `EXP` greatly enhances the number of available basis
+sets implemented in Python (see, e.g. @gala).
 
 
 ## Using pyEXP to analyze time series