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Abstract Let Γ be a finite graph and let$$A(\Gamma)$$be the corresponding right-angled Artin group. From an arbitrary basis$$\mathcal B$$of$$H^1(A(\Gamma),\mathbb F)$$over an arbitrary field, we construct a natural graph$$\Gamma_{\mathcal B}$$from the cup product, called thecohomology basis graph. We show that$$\Gamma_{\mathcal B}$$always contains Γ as a subgraph. This provides an effective way to reconstruct the defining graph Γ from the cohomology of$$A(\Gamma)$$, to characterize the planarity of the defining graph from the algebra of$$A(\Gamma)$$and to recover many other natural graph-theoretic invariants. We also investigate the behaviour of the cohomology basis graph under passage to elementary subminors and show that it is not well-behaved under edge contraction.
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This content will become publicly available on January 1, 2027
Probing the firn refractive index profile using antenna response
Abstract The Radio Neutrino Observatory-Greenland (RNO-G, at Summit Station) experiment comprises an extensive fat-dipole antenna array deployed into ice boreholes over an eventual area of approximately 35 km2. Since the RNO-G experimental sensitivity depends on the radio-frequency properties of the firn, which are known to vary laterally on sub-km distance scales and vertically on sub-meter distance scales, a technique for quickly extracting information on firn ice properties with depth ($$n(z)$$) during drilling and deployment is desirable. Given that a dipole’s resonant wavelength is fixed by geometry, the resonant frequency$$f_{res}$$(measured as an S-parameter reflection coefficient [‘$$S_{11}$$’] minimum) scales inversely with the local refractive index, allowing a translation of a depth-dependent$$S_{11}$$(z) profile into$$n(z)$$.$$S_{11}$$(z) data were initially taken in August 2024 using a dipole lowered into a newly drilled 98 ± 1 mm diameter, 350 m deep borehole at Summit Station, Greenland, approximately 1 km from the site of the original GISP-2 core; improved measurements were subsequently made in May 2025. We conclude that$$S_{11}$$(z) data can be used to estimate$$n(z)$$, on 50 cm vertical scales, at the per cent level of accuracy required by experiments such as RN0-G.
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- PAR ID:
- 10704662
- Author(s) / Creator(s):
- ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
- Publisher / Repository:
- AGU
- Date Published:
- Journal Name:
- Journal of Glaciology
- Volume:
- 72
- ISSN:
- 0022-1430
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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