Flag varieties and interpretations of Young tableau algorithms

The conjugacy classes of nilpotent $n\times n$ matrices can be parametrised by partitions $\lambda$ of $n$, and for a nilpotent $\eta$ in the class parametrised by $\lambda$, the variety $F_\eta$ of $\eta$-stable flags has its irreducible components parametrised by the standard Young tableaux of shape $\lambda$. We indicate how several algorithmic constructions defined for Young tableaux have significance in this context, thus extending Steinberg's result that the relative position of flags generically chosen in the irreducible components of $F_\eta$ parametrised by tableaux $P$ and $Q$, is the permutation associated to $(P,Q)$ under the Robinson-Schensted correspondence. Other constructions for which we give interpretations are Sch\"utzenberger's involution of the set of Young tableaux, jeu de taquin (leading also to an interpretation of Littlewood-Richardson coefficients), and the transpose Robinson-Schensted correspondence (defined using column insertion). In each case we use a doubly indexed family of partitions, defined in terms of the flag (or pair of flags) determined by a point chosen in the variety under consideration. We show that for generic choices, the family satisfies certain combinatorial relations, whence the family describes the computation of the algorithmic operation being interpreted, as we described in a previous publication.Comment: 16 page

The Littlewood-Richardson Rule, Theory and Implementation

ABSTRACT We present the implementation of the Littlewood-Richardson rule in L ı E. We describe the mathematical problem it applies to, formulate the rule, and indicate a proof. In a brief historical sketch we indicate some early formulations and partial proofs. We derive a formulation of the rule that can be implemented very efficiently

Assessing the Carbon Footprint of Telemedicine:A Systematic Review

Background: Healthcare is responsible for 4% to 10% of carbon emissions worldwide, of which 22% is related to transport. Telemedicine emerged as a potential solution to reduce the footprint, for example, by reducing travel. However, a need to understand which variables to include in carbon footprint estimations in telemedicine limits our understanding of the beneficial impact telemedicine might have on our environment. This paper aims to systematically assess the reported carbon footprint and include variables assessed by the literature, comparing telemedicine with usual care. Methods: The systematic review followed the PRISMA guidelines in PubMed, Medline, Embase and Scopus. A quality assessment was performed using a transparency checklist for carbon footprint calculators. Carbon emissions were evaluated based on four categories, including patient travel, and streamlined life cycle assessment (LCA) for assessing included variables relevant to telemedicine. Results: We included 33 articles from 1117 records for analysis. The average transparency score was 38% (range 18%-68%). The median roundtrip travel distance for each patient was 131 km (interquartile range [IQR]: 60.8-351), or 25.6 kgCO2 (IQR: 10.6-105.6) emissions. There is high variance among included variables. Saved emissions are structurally underestimated by not including external factors such as a streamlined LCA.Conclusions: Telemedicine aids in reducing emissions, with travel distance being the most significant contributor. Additionally, we recommend accounting for the LCA since it highlights important nuances. This review furthers the debate on assessing carbon footprint savings due to telemedicine.</p

The Distances to Open Clusters from Main-Sequence Fitting. I. New Models and a Comparison to the Properties of the Hyades Eclipsing Binary vB 22

In the first of a new series of papers on open cluster distances, we use updated stellar evolution models to construct an isochrone appropriate for the Hyades, and compare it with the Hyades eclipsing binary system vB 22. We find that the absolute and relative luminosities of the two stars are in good agreement with the model, but the radii do not match the values inferred from eclipse data. We present evidence that there is a consistency problem with the flux ratios and the inferred radii, and discuss possible theoretical effects that could be responsible for the mismatch in the radii. We derive a helium abundance for the Hyades of Y = 0.271 \pm 0.006, which is equal within the errors to the Sun's initial helium abundance even though the Hyades is considerably more metal-rich.Comment: Accepted for publication in Astrophysical Journa

Why are the K dwarfs in the Pleiades so Blue?

The K dwarfs in the Pleiades fall nearly one half magnitude below a main sequence isochrone when plotted in a color-magnitude diagram utilizing V magnitude as the luminosity index and B-V as the color index. This peculiarity has been known for forty years but has gone unexplained and mostly ignored. When compared to Praesepe members, the Pleiades K dwarfs again are subluminous (or blue) in a color-magnitude diagram using B-V as the color index. However, using V-I as the color index, stars in the two clusters are coincident to M_V ~ 10; using V-K as the color index, Pleiades late K and M stars fall above the main sequence locus defined by Praesepe members. We believe that the anomalous spectral energy distributions for the Pleiades K dwarfs, as compared to older clusters, are a consequence of rapid stellar rotation and may be primarily due to spottedness. If so, the required areal filling factor for the cool component has to be very large (=> 50%). Weak-lined T Tauri stars have similar color anomalies, and we suspect this is a common feature of all very young K dwarfs (sp. type > K3). The peculiar spectral energy distribution needs to be considered in deriving accurate pre-main sequence isochrone-fitting ages for clusters like the Pleiades since the age derived will depend on the temperature index used.Comment: 41 pages, 15 figures, AASTeX5.0. Accepted 05 May 2003; Scheduled for publication in the Astronomical Journal (August 2003