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We prove a one-to-one correspondence between the operadic ideals of the operad uAss and T-ideals. As a consequence, we show that uAss is noetherian and that every proper operadic ideal of uAss is generated by a single element. 

Abstract Alfalfa (Medicago sativaL.) is a critical forage crop whose improvement depends on resolving the complex genetic architecture of agronomic traits. While genome-wide association studies (GWAS) effectively identify statistically associated markers, they often fail to distinguish direct genetic effectors from indirect or pleiotropic signals arising from linkage disequilibrium and population structure. Here, we present a causal graph based genomic discovery framework that integrates de-confounded feature screening with causal graph learning to infer directional dependency structures from observational genomic data. Using Double Machine Learning to control for confounding and the PC algorithm for structural learning, we construct directed acyclic graphs that distinguishDirect Parent SNPs (DPSs), representing local effectors within the Markov Blanket of a trait, fromUpstream Hub SNPs (UHSs), representing pleiotropic regulators with broad network connectivity. Applied to four stem-related traits in alfalfa, the framework reduces genome-wide associations to compact, interpretable causal-consistent networks. Predictive validation demonstrates that DPSs consistently outperform both upstream UHSs and random controls, confirming their role as precise trait-specific biomarkers, while UHSs exhibit limited direct predictive power consistent with signal dilution along causal pathways. Together, these results demonstrate that causal graph learning can act as a biologically grounded regularizer for GWAS in polyploid crops, enabling principled marker prioritization and providing a structural foundation for future multi-omics integration. 

We study several classes of operadic ideals of the unital associative algebra operad uAss. As an application, we classify quotient operads of uAss of GK-dimension no more than 6. This corresponds to a classification of all T-ideals of codimension growth no more than 5 (or equivalently, varieties of grade no more than 5). 

Abstract Automatic segmentation of breast tumors in ultrasound images can assist physicians in making accurate and effective decisions. However, fully supervised learning methods typically require large amounts of pixel-level annotations, which are often difficult to obtain. Weakly supervised segmentation using image-level labels offers a promising alternative, but generating high-quality pseudo-segmentation labels remains a major challenge. In this study, we propose DRSeg, a weakly supervised segmentation framework for breast ultrasound (BUS) images that explicitly addresses the variability of pseudo-label quality. DRSeg augments a standard CAM-based pipeline with four components: (1) Class Activation Map (CAM) generation and refinement; (2) a Dual-ROI selection algorithm that identifies images with stable CAM localizations for reliable pseudo-label generation; (3) pseudo-label generation using the Segment Anything Model; and (4) training a segmentation model with the Mean Teacher strategy, leveraging both pseudo-labeled and non-pseudo-labeled images. Extensive experiments on two public BUS datasets, BUSI and BLU, demonstrate the effectiveness of the proposed DRSeg framework and its individual components. Using Swin Transformer V2 as the backbone, DRSeg achieves an IoU of 59.35% and an F1 score of 69.27% on BUSI. Using ResNet-50 as the backbone, DRSeg achieves an IoU of 51.79% and an F1 score of 60.00% on BLU, outperforming six existing weakly supervised methods. Overall, DRSeg reduces reliance on pixel-wise annotations while achieving competitive segmentation performance across two public BUS datasets and two backbones. 

Abstract Calcium is a key component in the shell and skeleton structure, serving as a second messenger for regulating biomineralization across many species. Ocean acidification (OA) is well-studied for causing shell dissolution in marine bivalve species by disordering calcium deposition. However, the regulatory pathway of calcification affected by OA remains unclear. This study assessed eastern oyster (Crassostrea virginica) to determine how calcium signaling responds to elevatedpCO₂and influences shell formation. Under elevatedpCO₂, increased calcium influx was found in mantle epithelial cells, followed by the upregulation of calmodulin, a primary sensor of intracellular calcium. Expression levels of shell matrix proteins (SMPs), representing shell construction conditions, were significantly upregulated in the CO₂-induced mantle cells. LarvalC. virginicaexhibited developmental stage-dependent alterations in calcium signaling and SMPs disarrangement stimulated bypCO₂. Pharmaceutical blockage of the calcium binding on calmodulin induced abnormal expression of downstream genes and shell matrix changes consistent with those caused by elevatedpCO₂. Restored SMPs expressions in CO₂-treated mantle cells were achieved by rescuing the level of calcineurin, a downstream effector of calmodulin. These findings suggest that shell deformities under OA are primarily caused by the disruption of the calcium-calmodulin signaling pathway in mantle epithelial cells. 

Abstract Solar-thermal interfacial desalination is a sustainable solution to meet the ever-increasing global freshwater demand. However, when treating actual ocean water, salt accumulation on the evaporator surfaces and brine discharge are major issues limiting the performance and posing environmental concerns. By utilizing a femtosecond laser surface processing technique, we create a multi-functional superwicking black metal (SWBM) panel that can pull a thin water film uphill across its surface, absorb nearly all solar radiation, and most importantly, automatically move the crystalized salts from the active regions to the passive regions for self-cleaning and salt collection. This SWBM serves as an energy-efficient, self-maintained, and additive-free and brine-discharge-free solar-thermal interfacial crystallizer (ABF-STIC) that simultaneously produces fresh water and harnesses nearly all salts directly from ocean water. This self-cleaning effect is attributed to the coffee ring effect and salt creeping, which can be enhanced by deeper and wider grooves, enabling self-cleaning even when treating real ocean water. Our ABF-STIC tracks the sun and operates continuously for a week to purify actual ocean water, achieving an average evaporation rate of 1.76±0.04 kg m⁻²h⁻¹and salt harvesting rate of 61.74 ± 2.46 g m⁻²h⁻¹under one sun, corresponding to ~ 74% solar to vapor conversion efficiency and nearly 100% salt extraction.