An L2-Poincaré–Dolbeault lemma of spaces with mixed cone-cusp singular metrics

The existence of Kähler Einstein metrics with mixed cone and cusp singularity has received considerable attentions in recent years. It is believed that such kind of metric would give rise to important geometric invariants. We computed their [Formula: see text]-Hodge–Frölicher spectral sequence under the Dirichlet and Neumann boundary conditions and examine the pure Hodge structures on them. It turns out that these cohomologies agree well with the de Rham cohomology of a good compactification.

Capturing and Selecting Senescence Variation in Wheat

Senescence is a highly quantitative trait, but in wheat the genetics underpinning senescence regulation remain relatively unknown. To select senescence variation and ultimately identify novel genetic regulators, accurate characterization of senescence phenotypes is essential. When investigating senescence, phenotyping efforts often focus on, or are limited to, the visual assessment of flag leaves. However, senescence is a whole-plant process, involving remobilization and translocation of resources into the developing grain. Furthermore, the temporal progression of senescence poses challenges regarding trait quantification and description, whereupon the different models and approaches applied result in varying definitions of apparently similar metrics. To gain a holistic understanding of senescence, we phenotyped flag leaf and peduncle senescence progression, alongside grain maturation. Reviewing the literature, we identified techniques commonly applied in quantification of senescence variation and developed simple methods to calculate descriptive and discriminatory metrics. To capture senescence dynamism, we developed the idea of calculating thermal time to different flag leaf senescence scores, for which between-year Spearman’s rank correlations of r ≥ 0.59, P < 4.7 × 10–5 (TT70), identify as an accurate phenotyping method. Following our experience of senescence trait genetic mapping, we recognized the need for singular metrics capable of discriminating senescence variation, identifying thermal time to flag leaf senescence score of 70 (TT70) and mean peduncle senescence (MeanPed) scores as most informative. Moreover, grain maturity assessments confirmed a previous association between our staygreen traits and grain fill extension, illustrating trait functionality. Here we review different senescence phenotyping approaches and share our experiences of phenotyping two independent recombinant inbred line (RIL) populations segregating for staygreen traits. Together, we direct readers toward senescence phenotyping methods we found most effective, encouraging their use when investigating and discriminating senescence variation of differing genetic bases, and aid trait selection and weighting in breeding and research programs alike.

Capturing and Selecting Senescence Variation in Wheat

Senescence is a highly quantitative trait, but in wheat the genetics underpinning senescence regulation remain relatively unknown. To select senescence variation, and ultimately identify novel genetic regulators, accurate characterisation of senescence phenotypes is essential. When investigating senescence, phenotyping efforts often focus on, or are limited to, visual assessment of the flag leaves. However, senescence is a whole plant process, involving remobilisation and translocation of resources into the developing grain. Furthermore, the temporal progression of senescence poses challenges regarding trait quantification and description, whereupon the different models and approaches applied result in varying definitions of apparently similar metrics.To gain a holistic understanding of senescence we phenotyped flag leaf and peduncle senescence progression, alongside grain maturation. Reviewing the literature, we identified techniques commonly applied in quantification of senescence variation and developed simple methods to calculate descriptive and discriminatory metrics. To capture senescence dynamism, we developed the idea of calculating thermal time to different flag leaf senescence scores, for which between year Spearman’s rank correlations of r ≥ 0.59, P < 4.7 × 10−5(TT70), identify as an accurate phenotyping method. Following our experience of senescence trait genetic mapping, we recognised the need for singular metrics capable of discriminating senescence variation, identifying Thermal Time to Flag Leaf Senescence score of 70 (TT70) and Mean Peduncle senescence (MeanPed) scores as most informative. Moreover, grain maturity assessments confirmed a previous association between our staygreen traits and grain fill extension, illustrating trait functionality.Here we review different senescence phenotyping approaches and share our experiences of phenotyping two independent RIL populations segregating for staygreen traits. Together, we direct readers towards senescence phenotyping methods we found most effective, encouraging their use when investigating and discriminating senescence variation of differing genetic bases, and to aid trait selection and weighting in breeding and research programs alike.

Capacity, quasi-local mass, and singular fill-ins

We derive new inequalities between the boundary capacity of an asymptotically flat 3-manifold with nonnegative scalar curvature and boundary quantities that relate to quasi-local mass; one relates to Brown–York mass and the other is new. We argue by recasting the setup to the study of mean-convex fill-ins with nonnegative scalar curvature and, in the process, we consider fill-ins with singular metrics, which may have independent interest. Among other things, our work yields new variational characterizations of Riemannian Schwarzschild manifolds and new comparison results for surfaces in them.

Information Geometry on Groupoids: The Case of Singular Metrics

We use the general setting for contrast (potential) functions in statistical and information geometry provided by Lie groupoids and Lie algebroids. The contrast functions are defined on Lie groupoids and give rise to two-forms and three-forms on the corresponding Lie algebroid. We study the case when the two-form is degenerate and show how in sufficiently regular cases one reduces it to a pseudometric structures. Transversal Levi-Civita connections for Riemannian foliations are generalized to the Lie groupoid/Lie algebroid case.