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This article aims to understand the behavior of the curvature operator of the second kind under the Ricci flow in dimension three. First, we express the eigenvalues of the curvature operator of the second kind explicitly in terms of that of the curvature operator (of the first kind). Second, we prove that$$\alpha $$$\alpha$-positive/$$\alpha $$$\alpha$-nonnegative curvature operator of the second kind is preserved by the Ricci flow in dimension three for all$$\alpha \in [1,5]$$$\alpha \in [1,5]$.

 

We prove matrix Li–Yau–Hamilton estimates for positive solutions to the heat equation and the backward conjugate heat equation, both coupled with the Ricci flow. We then apply these estimates to establish the monotonicity of parabolic frequencies up to correction factors. As applications, we obtain some unique continuation results under the nonnegativity of sectional or complex sectional curvature.

 

Light echoes (LEs) are the reflections of astrophysical transients off of interstellar dust. They are fascinating astronomical phenomena that enable studies of the scattering dust as well as of the original transients. LEs, however, are rare and extremely difficult to detect as they appear as faint, diffuse, time-evolving features. The detection of LEs still largely relies on human inspection of images, a method unfeasible in the era of large synoptic surveys. The Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) will generate an unprecedented amount of astronomical imaging data at high spatial resolution, exquisite image quality, and over tens of thousands of square degrees of sky: an ideal survey for LEs. However, the Rubin data processing pipelines are optimized for the detection of point sources and will entirely miss LEs. Over the past several years, artificial intelligence (AI) object-detection frameworks have achieved and surpassed real-time, human-level performance. In this work, we leverage a data set from the Asteroid Terrestrial-impact Last Alert System telescope to test a popular AI object-detection framework, You Only Look Once, or YOLO, developed by the computer-vision community, to demonstrate the potential of AI for the detection of LEs in astronomical images. We find that an AI framework can reach human-level performance even with a size- and quality-limited data set. We explore and highlight challenges, including class imbalance and label incompleteness, and road map the work required to build an end-to-end pipeline for the automated detection and study of LEs in high-throughput astronomical surveys.

 

Abstract Pear is a major fruit tree crop distributed worldwide, yet its breeding is a very time-consuming process. To facilitate molecular breeding and gene identification, here we have performed genome-wide association studies (GWAS) on eleven fruit traits. We identify 37 loci associated with eight fruit quality traits and five loci associated with three fruit phenological traits. Scans for selective sweeps indicate that traits including fruit stone cell content, organic acid and sugar contents might have been under continuous selection during breeding improvement. One candidate gene, PbrSTONE , identified in GWAS, has been functionally verified to be involved in the regulation of stone cell formation, one of the most important fruit quality traits in pear. Our study provides insights into the complex fruit related biology and identifies genes controlling important traits in pear through GWAS, which extends the genetic resources and basis for facilitating molecular breeding in perennial trees. 

Current and future optical and near-infrared wide-field surveys have the potential to find kilonovae, the optical and infrared counterparts to neutron star mergers, independently of gravitational-wave or high-energy gamma-ray burst triggers. The ability to discover fast and faint transients such as kilonovae largely depends on the area observed, the depth of those observations, the number of revisits per field in a given time frame, and the filters adopted by the survey; it also depends on the ability to perform rapid follow-up observations to confirm the nature of the transients. In this work, we assess kilonova detectability in existing simulations of the Legacy Survey of Space and Time strategy for the Vera C. Rubin Wide Fast Deep survey, with focus on comparing rolling to baseline cadences. Although currently available cadences can enable the detection of >300 kilonovae out to ∼1400 Mpc over the 10 year survey, we can expect only 3–32 kilonovae similar to GW170817 to be recognizable as fast-evolving transients. We also explore the detectability of kilonovae over the plausible parameter space, focusing on viewing angle and ejecta masses. We find that observations in redderizybands are crucial for identification of nearby (within 300 Mpc) kilonovae that could be spectroscopically classified more easily than more distant sources. Rubin’s potential for serendipitous kilonova discovery could be increased by gain of efficiency with the employment of individual 30 s exposures (as opposed to 2 × 15 s snap pairs), with the addition of red-band observations coupled with same-night observations ingorrbands, and possibly with further development of a new rolling-cadence strategy.

 

Self-discrimination, a critical but ill-defined molecular process programmed during thymocyte development, requires myriad pre–T cell receptors (preTCRs) and αβTCRs. Using x-ray crystallography, we show how a preTCR applies the concave β-sheet surface of its single variable domain (Vβ) to “horizontally” grab the protruding MHC α2-helix. By contrast, αβTCRs purpose all six complementarity-determining region (CDR) loops of their paired VαVβ module to recognize peptides bound to major histocompatibility complex molecules (pMHCs) in “vertical” head-to-head binding. The preTCR topological fit ensures that CDR3β reaches the peptide’s featured C-terminal segment for pMHC sampling, establishing the subsequent αβTCR canonical docking mode. “Horizontal” docking precludes germline CDR1β- and CDR2β-MHC binding to broaden β-chain repertoire diversification before αβTCR-mediated selection refinement. Thus, one subunit successively attunes the recognition logic of related multicomponent receptors.