Search for: All records

Abstract The Gromov–Wasserstein distance—a generalization of the usual Wasserstein distance—permits comparing probability measures defined on possibly different metric spaces. Recently, this notion of distance has found several applications in Data Science and in Machine Learning. With the goal of aiding both the interpretability of dissimilarity measures computed through the Gromov–Wasserstein distance and the assessment of the approximation quality of computational techniques designed to estimate the Gromov–Wasserstein distance, we determine the precise value of a certain variant of the Gromov–Wasserstein distance between unit spheres of different dimensions. Indeed, we consider a two-parameter family$$\{d_{{{\text {GW}}}p,q}\}_{p,q=1}^{\infty }$$ ${\left\{d_{\text{GW}p,q}\right\}}_{p,q=1}^{\infty }$of Gromov–Wasserstein distances between metric measure spaces. By exploiting a suitable interaction between specific values of the parameterspandqand the metric of the underlying spaces, we are able to determine the exact value of the distance$$d_{{{\text {GW}}}4,2}$$ $d_{\text{GW}4,2}$between all pairs of unit spheres of different dimensions endowed with their Euclidean distance and their uniform measure. 

Quinoa ( Chenopodium quinoa Willd.), a pseudocereal with high protein quality originating from the Andean region of South America, has broad genetic variation and adaptability to diverse agroecological conditions, contributing to the potential to serve as a global keystone protein crop in a changing climate. However, the germplasm resources currently available to facilitate quinoa expansion worldwide are restricted to a small portion of quinoa’s total genetic diversity, in part because of day-length sensitivity and issues related to seed sovereignty. This study aimed to characterize phenotypic relationships and variation within a quinoa world core collection. The 360 accessions were planted in a randomized complete block design with four replicates in each of two greenhouses in Pullman, WA during the summer of 2018. Phenological stages, plant height, and inflorescence characteristics were recorded. Seed yield, composition, thousand seed weight, nutritional composition, shape, size, and color were measured using a high-throughput phenotyping pipeline. Considerable variation existed among the germplasm. Crude protein content ranged from 11.24% to 17.81% (fixed at 14% moisture). We found that protein content was negatively correlated with yield and positively correlated with total amino acid content and days to harvest. Mean essential amino acids values met adult daily requirements but not leucine and lysine infant requirements. Yield was positively correlated with thousand seed weight and seed area, and negatively correlated with ash content and days to harvest. The accessions clustered into four groups, with one-group representing useful accessions for long-day breeding programs. The results of this study establish a practical resource for plant breeders to leverage as they strategically develop germplasm in support of the global expansion of quinoa.