A Note on Doubly Warped Product Contact CR-Submanifolds in trans-Sasakian Manifolds

Warped product CR-submanifolds in Kaehlerian manifolds were intensively studied only since 2001 after the impulse given by B.Y. Chen. Immediately after, another line of research, similar to that concerning Sasakian geometry as the odd dimensional version of Kaehlerian geometry, was developed, namely warped product contact CR-submanifolds in Sasakian manifolds. In this note we proved that there exists no proper doubly warped product contact CR-submanifolds in trans-Sasakian manifolds.Comment: 5 Latex page

Bioavailability of Iron, Zinc, Phytate and Phytase Activity during Soaking and Germination of White Sorghum Varieties

The changes in phytate, phytase activity and in vitro bioavailability of iron and zinc during soaking and germination of three white sorghum varieties (Sorghum bicolor L. Moench), named Dorado, Shandweel-6, and Giza-15 were investigated. Sorghum varieties were soaked for 20 h and germinated for 72 h after soaking for 20 h to reduce phytate content and increase iron and zinc in vitro bioavailability. The results revealed that iron and zinc content was significantly reduced from 28.16 to 32.16% and 13.78 to 26.69% for soaking treatment and 38.43 to 39.18% and 21.80 to 31.27% for germination treatments, respectively. Phytate content was significantly reduced from 23.59 to 32.40% for soaking treatment and 24.92 to 35.27% for germination treatments, respectively. Phytase enzymes will be activated during drying in equal form in all varieties. The results proved that the main distinct point is the change of phytase activity as well as specific activity during different treatment which showed no significant differences between the varieties used. The in vitro bioavailability of iron and zinc were significantly improved as a result of soaking and germination treatments

Impact of instrument and data characteristics in the interferometric reconstruction of the 21 cm power spectrum

Combining the visibilities measured by an interferometer to form a cosmological power spectrum is a complicated process. In a delay-based analysis, the mapping between instrumental and cosmological space is not a one-to-one relation. Instead, neighbouring modes contribute to the power measured at one point, with their respective contributions encoded in the window functions. To better understand the power measured by an interferometer, we assess the impact of instrument characteristics and analysis choices on these window functions. Focusing on the Hydrogen Epoch of Reionization Array (HERA) as a case study, we find that long-baseline observations correspond to enhanced low-k tails of the window functions, which facilitate foreground leakage, whilst an informed choice of bandwidth and frequency taper can reduce said tails. With simple test cases and realistic simulations, we show that, apart from tracing mode mixing, the window functions help accurately reconstruct the power spectrum estimator of simulated visibilities. The window functions depend strongly on the beam chromaticity and less on its spatial structure – a Gaussian approximation, ignoring side lobes, is sufficient. Finally, we investigate the potential of asymmetric window functions, down-weighting the contribution of low-k power to avoid foreground leakage. The window functions presented here correspond to the latest HERA upper limits for the full Phase I data. They allow an accurate reconstruction of the power spectrum measured by the instrument and will be used in future analyses to confront theoretical models and data directly in cylindrical space

Improved Constraints on the 21 cm EoR Power Spectrum and the X-Ray Heating of the IGM with HERA Phase I Observations

We report the most sensitive upper limits to date on the 21 cm epoch of reionization power spectrum using 94 nights of observing with Phase I of the Hydrogen Epoch of Reionization Array (HERA). Using similar analysis techniques as in previously reported limits, we find at 95% confidence that Δ2(k = 0.34 h Mpc−1) ≤ 457 mK2 at z = 7.9 and that Δ2(k = 0.36 h Mpc−1) ≤ 3496 mK2 at z = 10.4, an improvement by a factor of 2.1 and 2.6, respectively. These limits are mostly consistent with thermal noise over a wide range of k after our data quality cuts, despite performing a relatively conservative analysis designed to minimize signal loss. Our results are validated with both statistical tests on the data and end-to-end pipeline simulations. We also report updated constraints on the astrophysics of reionization and the cosmic dawn. Using multiple independent modeling and inference techniques previously employed by HERA Collaboration, we find that the intergalactic medium must have been heated above the adiabatic cooling limit at least as early as z = 10.4, ruling out a broad set of so-called “cold reionization” scenarios. If this heating is due to high-mass X-ray binaries during the cosmic dawn, as is generally believed, our result’s 99% credible interval excludes the local relationship between soft X-ray luminosity and star formation and thus requires heating driven by evolved low-metallicity stars

Characterization of inpaint residuals in interferometric measurements of the epoch of reionization

To mitigate the effects of Radio Frequency Interference (RFI) on the data analysis pipelines of 21 cm interferometric instruments, numerous inpaint techniques have been developed. In this paper, we examine the qualitative and quantitative errors introduced into the visibilities and power spectrum due to inpainting. We perform our analysis on simulated data as well as real data from the Hydrogen Epoch of Reionization Array (HERA) Phase 1 upper limits. We also introduce a convolutional neural network that is capable of inpainting RFI corrupted data. We train our network on simulated data and show that our network is capable of inpainting real data without requiring to be retrained. We find that techniques that incorporate high wavenumbers in delay space in their modelling are best suited for inpainting over narrowband RFI. We show that with our fiducial parameters discrete prolate spheroidal sequences (DPSS) and CLEAN provide the best performance for intermittent RFI while Gaussian progress regression (GPR) and least squares spectral analysis (LSSA) provide the best performance for larger RFI gaps. However, we caution that these qualitative conclusions are sensitive to the chosen hyperparameters of each inpainting technique. We show that all inpainting techniques reliably reproduce foreground dominated modes in the power spectrum. Since the inpainting techniques should not be capable of reproducing noise realizations, we find that the largest errors occur in the noise dominated delay modes. We show that as the noise level of the data comes down, CLEAN and DPSS are most capable of reproducing the fine frequency structure in the visibilities

Improved Constraints on the 21 cm EoR Power Spectrum and the X-Ray Heating of the IGM with HERA Phase I Observations

We report the most sensitive upper limits to date on the 21 cm epoch of reionization power spectrum using 94 nights of observing with Phase I of the Hydrogen Epoch of Reionization Array (HERA). Using similar analysis techniques as in previously reported limits (HERA Collaboration 2022a), we find at 95% confidence that $\Delta^2(k = 0.34$ $h$ Mpc$^{-1}$) $\leq 457$ mK$^2$ at $z = 7.9$ and that $\Delta^2 (k = 0.36$ $h$ Mpc$^{-1}) \leq 3,496$ mK$^2$ at $z = 10.4$, an improvement by a factor of 2.1 and 2.6 respectively. These limits are mostly consistent with thermal noise over a wide range of $k$ after our data quality cuts, despite performing a relatively conservative analysis designed to minimize signal loss. Our results are validated with both statistical tests on the data and end-to-end pipeline simulations. We also report updated constraints on the astrophysics of reionization and the cosmic dawn. Using multiple independent modeling and inference techniques previously employed by HERA Collaboration (2022b), we find that the intergalactic medium must have been heated above the adiabatic cooling limit at least as early as $z = 10.4$, ruling out a broad set of so-called "cold reionization" scenarios. If this heating is due to high-mass X-ray binaries during the cosmic dawn, as is generally believed, our result's 99% credible interval excludes the local relationship between soft X-ray luminosity and star formation and thus requires heating driven by evolved low-metallicity stars.Comment: 57 pages, 37 figures. Updated to match the accepted ApJ version. Corresponding author: Joshua S. Dillo