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Abstract We present a new method based on information theory to find the optimal number of bands required to measure the physical properties of galaxies with desired accuracy. As a proof of concept, using the recently updated COSMOS catalog (COSMOS2020), we identify the most relevant wave bands for measuring the physical properties of galaxies in a Hawaii Two-0- (H20) and UVISTA-like survey for a sample ofi< 25 AB mag galaxies. We find that with the availablei-band fluxes,r,u, IRAC/ch2, andzbands provide most of the information regarding the redshift with importance decreasing fromrband tozband. We also find that for the same sample, IRAC/ch2,Y,r, andubands are the most relevant bands in stellar-mass measurements with decreasing order of importance. Investigating the intercorrelation between the bands, we train a model to predict UVISTA observations in near-IR from H20-like observations. We find that magnitudes in theYJHbands can be simulated/predicted with an accuracy of 1σmag scatter ≲0.2 for galaxies brighter than 24 AB mag in near-IR bands. One should note that these conclusions depend on the selection criteria of the sample. For any new sample of galaxies with a different selection, these results should be remeasured. Our results suggest that in the presence of a limited number of bands, a machine-learning model trained over the population of observed galaxies with extensive spectral coverage outperforms template fitting. Such a machine-learning model maximally comprises the information acquired over available extensive surveys and breaks degeneracies in the parameter space of template fitting inevitable in the presence of a few bands.
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New building blocks for F1${\mathbb {F}}_1$‐geometry: Bands and band schemes
Abstract We develop and study a generalization of commutative rings calledbands, along with the corresponding geometric theory ofband schemes. Bands generalize both hyperrings, in the sense of Krasner, and partial fields in the sense of Semple and Whittle. They form a ring‐like counterpart to the field‐like category ofidyllsintroduced by the first and third authors in the previous work. The first part of the paper is dedicated to establishing fundamental properties of bands analogous to basic facts in commutative algebra. In particular, we introduce various kinds of ideals in a band and explore their properties, and we study localization, quotients, limits, and colimits. The second part of the paper studies band schemes. After giving the definition, we present some examples of band schemes, along with basic properties of band schemes and morphisms thereof, and we describe functors into some other scheme theories. In the third part, we discuss some “visualizations” of band schemes, which are different topological spaces that one can functorially associate to a band scheme .
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- Award ID(s):
- 2154224
- PAR ID:
- 10627226
- Publisher / Repository:
- eScholarship
- Date Published:
- Journal Name:
- Journal of the London Mathematical Society
- Volume:
- 111
- Issue:
- 4
- ISSN:
- 0024-6107
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript
- Journal Article:
- https://doi.org/10.1112/jlms.70125
