@@ -66,36 +66,45 @@ <h2> What is a basis function expansion? </h2>
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69- < h2 > Why should I use basis function expansions?</ h2 >
70- < p > Basis function expansions (BFEs) provide a mathematical framework for interrogating and understanding
71- complex systems. Through this framework, it is possible to discover the underlying dynamics within
72- simulations that span the full gamut of complexity, ranging from idealized periodic boxes to large
73- cosmological simulations. This framework provides natural ties to analytic theory as well as new
74- supervised and unsupervised machine learning tools. One such tool is multi-channel Single Spectrum
75- Analysis (mSSA), and examples of using mSSA + BFE for dynamical discovery can be seen in
76- < a href ="https://ui.adsabs.harvard.edu/abs/2021MNRAS.501.5408W/abstract "> here</ a > and
77- < a href ="https://ui.adsabs.harvard.edu/abs/2023MNRAS.521.1757J/abstract "> here</ a > (see also the
78- < a href = "https://exp-docs.readthedocs.io/en/latest/topics/ssa.html "> EXP readthedocs</ a > ).
79- A particularly powerful use of BFE is as a universal language to succinctly summarize the relevant
80- dynamical information in galaxies for comparison across and between different simulations.</ p >
69+ < h2 > < b > Exp </ b > = Adaptive BFEs: precision and concision in the language</ h2 >
70+ < p > < b > Exp </ b > provides numerical tools that derive efficient representations of BFEs from linear combinations
71+ of an initial set of functions based on the character of the data, providing a concise description that
72+ minimizes the degrees of freedom while efficiently capturing the properties of the fields. At the same
73+ time, the description is more precise in its representation of the fields. These distillations provide
74+ opportunities to store and reuse key dynamical content in easy-to-reconstruct field form. Applications
75+ include resampling phase space at higher resolution than the original simulation, replaying the
76+ time-evolving fields to study their influence on ensembles of orbits that may represent stellar streams,
77+ star clusters, dwarf galaxies, dark matter substructure, just to name a few. </ p >
8178 </ article >
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84- < h2 > Basis Function Expansions for Cosmological Simulations</ h2 >
85- < p > Basis function expansions (BFEs) can be used as a post-processing analysis framework for cosmological simulations.
86- With BFEs, you can analyze the dark matter halo of your favorite galaxy from any cosmological
87- simulation to find wakes, dipoles, and more. You can also succinctly describe the stellar disk of
88- a galaxy, use the expansions to integrate orbits in the gravitational potential, and more. See some highlights
89- of recent cosmological analyses below</ p >
90- < p > Add a blurb of your paper here! </ p >
81+ < h2 > < b > Exp </ b > = BFE+mSSA: finding the story being told by BFE’s </ h2 >
82+ < p > < b > EXP </ b > also provides tools that correlate the morphology and time dependence of dominant features contributing
83+ to the evolution of a field from multiple sets of expansion coefficients. By adding correlations in the time
84+ domain to the correlations represented by the BFEs, the dynamical content of temporal variation becomes manifest.
85+ This automatic spatio-temporal discovery is a form of unsupervised learning and has already led to
86+ discovery of new, previously unknown, dynamics in our simulations. < b > EXP </ b > implements multivariate Singular
87+ Spectrum Analysis (SSA) – an unsupervised machine learning algorithm – tailored to basis-function expansions.
88+ SSA decomposes the BFE variation in time into interpretable components and provides for spectral estimation
89+ without specific assumptions about the time dependence of the system. We also provide some preliminary
90+ support for dynamical mode decomposition (DMD) and other Koopman-related techniques. </ p >
9191 </ article >
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94- < h2 > Basis Function Expansions for Analytic Theorists</ h2 >
95- < p > Basis function expansions allow us to seamlessly connect analytic theory, such as linear response, to more complex N-body simulations. Basis function
96- expansions enable the study of coupled modes, for example, such as those from a baryonic disk and a dark matter halo. </ p >
97- < p > not sure what to say here</ p >
98- < p > your paper blurb here! </ p >
94+ < h2 > < b > EXP </ b > : applications to cosmology</ h2 >
95+ < p > < b > EXP </ b > can be used to analyze structure in cosmological simulations. Members of the < b > EXP </ b > Collaboration are applying
96+ these tools to snapshots from simulations of galaxy formation to:
97+ < ul >
98+ < li > Compare and contrast the signatures of filamentary accretion from halo deformation in the FIRE simulation suite
99+ (< a “https: //ui.adsabs.harvard.edu/abs/2025ApJ...988..190A/abstract” Arora et al, 2025 </ a> ); </ li >
100+ < li > Describe the deformation of dark matter halos as they respond to infalling satellites in the MWest simulation suite
101+ (Darragh-Ford et al 2025, in prep)</ li >
102+ < li > Characterise the effect of deforming dark matter halos on the structural properties of disks in the Auriga simulation
103+ suite (Lavin et al 2025, in prep); </ li >
104+ < li > Investigate the interplay between dynamical structure formation, dark matter physics, and feedback mechanisms in the
105+ < a “https: //dreams-project.readthedocs.io/en/latest/index.html” DREAMS< a/> suite of cosmological simulations
106+ (Filion et al 2025, in prep) </ li >
107+ </ ul >
99108 </ article >
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@@ -107,30 +116,35 @@ <h2></h2>
107116 < h2 > Basis Function Expansions for N-body Dynamical Simulations</ h2 >
108117 < p > Basis function expansions (BFEs) can be used to both run and analyze dynamical N-body simulations. The EXP
109118 collaboration - spearheaded by Martin Weinberg - has developed eponymous code to perform both of these
110- functions. EXP uses BFEs to represent the potential and mass distributions of the star and dark
119+ functions. < b > Exp </ b > uses BFEs to represent the potential and mass distributions of the star and dark
111120 matter particles of a galaxy to run simulations significantly faster than alternate techniques. The
112121 theory underpinning BFE simulations and the implementation are discussed in
113122 more detail in the < a href ="https://exp-docs.readthedocs.io/en/latest/topics/multistep.html "readthedocs > </ a > ,
114123 as well as these papers (< a href ="https://ui.adsabs.harvard.edu/abs/1999AJ....117..629W/abstract "1 > </ a > ,
115124 < a href ="https://ui.adsabs.harvard.edu/abs/2022MNRAS.510.6201P/abstract "2 > </ a > ).</ p >
116125 < p > The resulting simulations have both particle-based snapshot data and basis function information, including
117126 the basis and time-evolving coefficients. These data can be used together to provide unique insight into
118- the underlying dynamics. EXP can also be run on simulations that were produced with different software,
127+ the underlying dynamics. < b > Exp </ b > can also be run on simulations that were produced with different software,
119128 including cosmological simulations, to provide BFEs at each time step. See below for
120- examples that use either or both of these functionalities of EXP .</ p >
129+ examples that use either or both of these functionalities of < b > Exp </ b > .</ p >
121130 < p > Your paper links and blurbs here!</ p >
122131 </ article >
123132 < article class ="thumb ">
124133 < a href ="images/fulls/plain.png " class ="image "> < img src ="images/thumbs/8.png " alt ="" /> </ a >
125- < h2 > Basis Function Expansions for Observational Insight</ h2 >
126- < p > Two dimensional basis function expansions can also be performed on observational data. Such 2D expansions
127- on image data describe the light (stellar) distribution in a galaxy, and provide a language for succinctly,
128- quantitatively summarizing the morphological features. We adopt a Fourier-Laguerre basis for image data,
129- which captures both the angular (Fourier) and radial (Laguerre) information. These expansions are also
130- how we map an image of a galaxy to a sound via sonification. We are currently developing a framework for
131- expansions of integral field spectrograph data, which will allow for analyses of both velocity and chemical
132- information.</ p >
133- < p > Your paper links and blurbs here! </ p >
134+ < h2 > < b > EXP</ b > : applications to observations</ h2 >
135+ < p > Two dimensional basis function expansions can also be performed on observational data. As shown in
136+ < a href =”https://ui.adsabs.harvard.edu/abs/2025MNRAS.539..661G/abstract” > Ganapathy et al 2025</ a > , 2D
137+ expansions on image data can be used to describe the light (stellar) distribution in a galaxy, and
138+ provide a language for succinctly, quantitatively summarizing the morphological features. A
139+ Fourier-Laguerre basis is a natural choice for expanding imaging data, capturing both the angular
140+ (Fourier) and radial (Laguerre) information. Expansions using this basis can be used to quantify
141+ lopsidedness in galaxies
142+ (e.g. < a href =”https://ui.adsabs.harvard.edu/abs/2025MNRAS.539..661G/abstract” > Ganapathy et al 2025</ a > ),
143+ measure galaxy inclination (e.g. Martinez et al, in prep), and identify morphological features like bars.
144+ These expansions are also how we map an image of a
145+ (< a href =”https://carriefilion.github.io/#Sonification” > into a sound </ a > ) via sonification. Similarly,
146+ we can perform expansions of integral field spectrograph data, which allow for analyses of both velocity
147+ and chemical information. </ p >
134148 </ article >
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@@ -150,7 +164,7 @@ <h2>Basis Function Expansions for Sonification</h2>
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152166 < h2 > How to get started</ h2 >
153- < p > We have built and compiled a variety of resources to help you get started with EXP and basis function expansions!</ p >
167+ < p > We have built and compiled a variety of resources to help you get started with < b > Exp </ b > and basis function expansions!</ p >
154168 < p > Check out our < a href ="https://github.com/EXP-code "> GitHub page</ a > and accompanying
155169 < a href ="https://exp-docs.readthedocs.io/en/latest/topics/multistep.html "readthedocs > </ a > for how to install EXP.</ p >
156170 < p > If you want to experiment with EXP, try out the < a href ="https://github.com/EXP-code/EXP-container "> Docker image</ a > and
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