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In conventional statistical and machine learning methods, it is typically assumed that the test data are identically distributed with the training data. However, this assumption does not always hold, especially in applications where the target population are not well-represented in the training data. This is a notable issue in health-related studies, where specific ethnic populations may be underrepresented, posing a significant challenge for researchers aiming to make statistical inferences about these minority groups. In this work, we present a novel approach to addressing this challenge in linear regression models. We organize the model parameters for all the sub-populations into a tensor. By studying a structured tensor completion problem, we can achieve robust domain generalization, that is, learning about sub-populations with limited or no available data. Our method novelly leverages the structure of group labels and it can produce more reliable and interpretable generalization results. We establish rigorous theoretical guarantees for the proposed method and demonstrate its minimax optimality. To validate the effectiveness of our approach, we conduct extensive numerical experiments and a real data study focused on diabetes prediction for multiple subgroups, comparing our results with those obtained using other existing methods. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work. 

We conducted an exhaustive analysis combining optical photometry and spectroscopy of the type Ia supernova designated SN 2023xqm. Our observational period spanned from the two weeks preceding to 88 days after theB-band peak luminosity time. We determined the peak brightness in theB-band to be −18.90 ± 0.50 mag, and it is accompanied by a moderately slow decay rate of 0.90 ± 0.07 mag. The maximum quasi-bolometric luminosity was estimated to be 1.52 × 10⁴³erg s⁻¹and correlated with a calculated⁵⁶Ni mass of 0.74 ± 0.05M_⊙, aligning with the modestly reduced rate of light curve decay. A plateau that can be observed in ther − icolor curve might correlate with the minor elevation noted between the principal and secondary peaks of thei-band light curve. An initial spectral analysis of SN 2023xqm revealed distinct high-velocity features (HVFs) in Ca IIthat contrast with the subdued HVFs observed in Si II. Such attributes may stem from variations in ionization or temperature or from scenarios involving enhanced element abundance, suggesting a naturally lower photospheric temperature for SN 2023xqm, which could be indicative of incomplete burning during the white dwarf’s detonation. The observed traits in the light curve and the spectral features offer significant insights into the variability among type Ia supernovae and their explosion dynamics. 

Abstract SN 2023ehl, a normal Type Ia supernova with a typical decline rate, was discovered in the galaxy UGC 11555 and offers valuable insights into the explosion mechanisms of white dwarfs. We present a detailed analysis of SN 2023ehl, including spectroscopic and photometric observations. The supernova exhibits high-velocity features in its ejecta, which are crucial for understanding the physical processes during the explosion. We compared the light curves of SN 2023ehl with other well-observed Type Ia supernovae, finding similarities in their evolution. The line strength ratioR(Siii) was calculated to be 0.17 ± 0.04, indicating a higher photospheric temperature compared to other supernovae. The maximum quasi-bolometric luminosity was determined to be 1.52 × 10⁴³erg s⁻¹, and the synthesized⁵⁶Ni mass was estimated at 0.77 ± 0.05M_⊙. The photospheric velocity atB-band maximum light was measured as 10,150 ± 240 km s⁻¹, classifying SN 2023ehl as a normal velocity Type Ia supernova. Our analysis suggests that SN 2023ehl aligns more with both the gravitationally confined detonation, providing a comprehensive view of the diversity and complexity of Type Ia supernovae. 

In this paper, we present an extensive analysis of SN 2021 wuf, a transition between Ia-norm and SN 1991T-like supernovae, which exploded at the periphery of the tidal bridge between the pair galaxy NGC 6500 and NGC 6501, at a redshift ofz = 0.01. Our observations, ranging from −21 to +276 days relative to theB-band maximum light, reveal that SN 2021wuf exhibits properties akin to normal SNe Ia, with a peak absolute magnitude ofM_max(B)  ∼   − 19.49  ±  0.10 mag and a post-peak decline rate of Δm₁₅(B)  ∼  1.11  ±  0.06 mag. The peak bolometric luminosity of this SN is estimated as 1.58  × 10⁴³erg s⁻¹, corresponding to a⁵⁶Ni mass ofM_Ni  ∼  0.64  ±  0.05 M_⊙. The spectral features, including high-velocity Si IIλ6355 lines, a plateau in the Si IIλ6355 velocity evolution and the nickel-to-iron ratio in the nebular phase, suggest a potential pulsating delayed detonation mechanism. The absence of intermediate-mass elements in the early phase and the high photospheric temperature, as inferred from the line-strength ratio of Si IIλ5972 to Si IIλ6355 (named asR(Si II)), further support this classification.