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88 changes: 37 additions & 51 deletions paper.bib
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@@ -1,59 +1,45 @@
@article{Pearson:2017,
url = {http://adsabs.harvard.edu/abs/2017arXiv170304627P},
Archiveprefix = {arXiv},
Author = {{Pearson}, S. and {Price-Whelan}, A.~M. and {Johnston}, K.~V.},
Eprint = {1703.04627},
Journal = {ArXiv e-prints},
Keywords = {Astrophysics - Astrophysics of Galaxies},
Month = mar,
Title = {{Gaps in Globular Cluster Streams: Pal 5 and the Galactic Bar}},
Year = 2017
@article{scheffer2009early,
title={Early-warning signals for critical transitions},
author={Scheffer, Marten and Bascompte, Jordi and Brock, William A and Brovkin, Victor and Carpenter, Stephen R and Dakos, Vasilis and Held, Hermann and Van Nes, Egbert H and Rietkerk, Max and Sugihara, George},
journal={Nature},
volume={461},
number={7260},
pages={53--59},
year={2009},
publisher={Nature Publishing Group}
}

@book{Binney:2008,
url = {http://adsabs.harvard.edu/abs/2008gady.book.....B},
Author = {{Binney}, J. and {Tremaine}, S.},
Booktitle = {Galactic Dynamics: Second Edition, by James Binney and Scott Tremaine.~ISBN 978-0-691-13026-2 (HB).~Published by Princeton University Press, Princeton, NJ USA, 2008.},
Publisher = {Princeton University Press},
Title = {{Galactic Dynamics: Second Edition}},
Year = 2008
@article{clements2018indicators,
title={Indicators of transitions in biological systems},
author={Clements, Christopher F and Ozgul, Arpat},
journal={Ecology letters},
volume={21},
number={6},
pages={905--919},
year={2018},
publisher={Wiley Online Library}
}

@article{gaia,
author = {{Gaia Collaboration}},
title = "{The Gaia mission}",
journal = {Astronomy and Astrophysics},
archivePrefix = "arXiv",
eprint = {1609.04153},
primaryClass = "astro-ph.IM",
keywords = {space vehicles: instruments, Galaxy: structure, astrometry, parallaxes, proper motions, telescopes},
year = 2016,
month = nov,
volume = 595,
doi = {10.1051/0004-6361/201629272},
url = {http://adsabs.harvard.edu/abs/2016A%26A...595A...1G},
@article{bury2020detecting,
title={Detecting and distinguishing tipping points using spectral early warning signals},
author={Bury, Thomas M and Bauch, Chris T and Anand, Madhur},
journal={Journal of the Royal Society Interface},
volume={17},
number={170},
pages={20200482},
year={2020},
publisher={The Royal Society}
}

@article{astropy,
author = {{Astropy Collaboration}},
title = "{Astropy: A community Python package for astronomy}",
journal = {Astronomy and Astrophysics},
archivePrefix = "arXiv",
eprint = {1307.6212},
primaryClass = "astro-ph.IM",
keywords = {methods: data analysis, methods: miscellaneous, virtual observatory tools},
year = 2013,
month = oct,
volume = 558,
doi = {10.1051/0004-6361/201322068},
url = {http://adsabs.harvard.edu/abs/2013A%26A...558A..33A}
@article{bury2021deep,
title={Deep learning for early warning signals of tipping points},
author={Bury, Thomas M and Sujith, RI and Pavithran, Induja and Scheffer, Marten and Lenton, Timothy M and Anand, Madhur and Bauch, Chris T},
journal={Proceedings of the National Academy of Sciences},
volume={118},
number={39},
pages={e2106140118},
year={2021},
publisher={National Acad Sciences}
}

@misc{fidgit,
author = {A. M. Smith and K. Thaney and M. Hahnel},
title = {Fidgit: An ungodly union of GitHub and Figshare},
year = {2020},
publisher = {GitHub},
journal = {GitHub repository},
url = {https://github.com/arfon/fidgit}
}

122 changes: 31 additions & 91 deletions paper.md
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@@ -1,115 +1,55 @@
---
title: 'Gala: A Python package for galactic dynamics'
title: 'ewstools: A Python package for early warning signals of bifurcations in time series data.'
tags:
- Python
- astronomy
- dynamics
- galactic dynamics
- milky way
- time series
- early warning signal
- tipping point
- dynamical system
- bifurcation

authors:
- name: Adrian M. Price-Whelan
orcid: 0000-0000-0000-0000
equal-contrib: true
- name: Thomas M. Bury
orcid: 0000-0003-1595-9444
affiliation: "1, 2" # (Multiple affiliations must be quoted)
- name: Author Without ORCID
equal-contrib: true # (This is how you can denote equal contributions between multiple authors)
affiliation: 2
- name: Author with no affiliation
corresponding: true # (This is how to denote the corresponding author)
affiliation: 3
affiliations:
- name: Lyman Spitzer, Jr. Fellow, Princeton University, USA
- name: Department of Physiology, McGill University, Montréal, Canada
index: 1
- name: Institution Name, Country
- name: Department of Applied Mathematics, University of Waterloo, Waterloo, Canada
index: 2
- name: Independent Researcher, Country
index: 3
date: 13 August 2017
date: 17 August 2022
bibliography: paper.bib

# Optional fields if submitting to a AAS journal too, see this blog post:
# https://blog.joss.theoj.org/2018/12/a-new-collaboration-with-aas-publishing
aas-doi: 10.3847/xxxxx <- update this with the DOI from AAS once you know it.
aas-journal: Astrophysical Journal <- The name of the AAS journal.
---

# Summary

The forces on stars, galaxies, and dark matter under external gravitational
fields lead to the dynamical evolution of structures in the universe. The orbits
of these bodies are therefore key to understanding the formation, history, and
future state of galaxies. The field of "galactic dynamics," which aims to model
the gravitating components of galaxies to study their structure and evolution,
is now well-established, commonly taught, and frequently used in astronomy.
Aside from toy problems and demonstrations, the majority of problems require
efficient numerical tools, many of which require the same base code (e.g., for
performing numerical orbit integration).

# Statement of need

`Gala` is an Astropy-affiliated Python package for galactic dynamics. Python
enables wrapping low-level languages (e.g., C) for speed without losing
flexibility or ease-of-use in the user-interface. The API for `Gala` was
designed to provide a class-based and user-friendly interface to fast (C or
Cython-optimized) implementations of common operations such as gravitational
potential and force evaluation, orbit integration, dynamical transformations,
and chaos indicators for nonlinear dynamics. `Gala` also relies heavily on and
interfaces well with the implementations of physical units and astronomical
coordinate systems in the `Astropy` package [@astropy] (`astropy.units` and
`astropy.coordinates`).

`Gala` was designed to be used by both astronomical researchers and by
students in courses on gravitational dynamics or astronomy. It has already been
used in a number of scientific publications [@Pearson:2017] and has also been
used in graduate courses on Galactic dynamics to, e.g., provide interactive
visualizations of textbook material [@Binney:2008]. The combination of speed,
design, and support for Astropy functionality in `Gala` will enable exciting
scientific explorations of forthcoming data releases from the *Gaia* mission
[@gaia] by students and experts alike.

# Mathematics

Single dollars ($) are required for inline mathematics e.g. $f(x) = e^{\pi/x}$
Many systems across nature and society have the capacity to undergo an abrupt and
profound change in their dynamics. From a dynamical systemes perspective, these events
are often associated with the crossing of a bifurcation. Early warning signals (EWS)
for bifurcations are therefore in high demand. Two commonly used EWS for bifurcations
are variance and lag-1 autocorrelation, that are expected to increase prior to many
bifurcations due to critical slowing down [@scheffer2009early]. There now exist a
wealth of other EWS based on changes in time series dynamics that are expected to occur
prior to bifurcations [@clements2018indicators]. More recently, deep learning
classifiers have been trained and applied to detect bifurcations, with promising
results [@bury2021deep]

Double dollars make self-standing equations:

$$\Theta(x) = \left\{\begin{array}{l}
0\textrm{ if } x < 0\cr
1\textrm{ else}
\end{array}\right.$$

You can also use plain \LaTeX for equations
\begin{equation}\label{eq:fourier}
\hat f(\omega) = \int_{-\infty}^{\infty} f(x) e^{i\omega x} dx
\end{equation}
and refer to \autoref{eq:fourier} from text.

# Citations

Citations to entries in paper.bib should be in
[rMarkdown](http://rmarkdown.rstudio.com/authoring_bibliographies_and_citations.html)
format.

If you want to cite a software repository URL (e.g. something on GitHub without a preferred
citation) then you can do it with the example BibTeX entry below for @fidgit.

For a quick reference, the following citation commands can be used:
- `@author:2001` -> "Author et al. (2001)"
- `[@author:2001]` -> "(Author et al., 2001)"
- `[@author1:2001; @author2:2001]` -> "(Author1 et al., 2001; Author2 et al., 2002)"
# Statement of need

# Figures
`ewstools` is a Python package for computing, analysing, and visualising
early warning signals in time series data.

Figures can be included like this:
![Caption for example figure.\label{fig:example}](figure.png)
and referenced from text using \autoref{fig:example}.

Figure sizes can be customized by adding an optional second parameter:
![Caption for example figure.](figure.png){ width=20% }

# Acknowledgements

We acknowledge contributions from Brigitta Sipocz, Syrtis Major, and Semyeong
Oh, and support from Kathryn Johnston during the genesis of this project.
TB acknowledge contributions from Chris Bauch on code for training deep learning
classifiers. This project is currently supported by the
Fonds de recherche du Québec (FRQ),
and has received funding in the past from the
Natural Sciences and Engineering Research Council of Canada (NSERC).


# References

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