When is a Schubert variety Gorenstein?

A (normal) variety is Gorenstein if it is Cohen-Macualay and its canonical sheaf is a line bundle. This property, which measures the ``pathology'' of the singularities of a variety, is thus stronger than Cohen-Macualayness, but is also weaker than smoothness. We determine which Schubert varieties are Gorenstein in terms of a combinatorial characterization using generalized pattern avoidance conditions. We also give an explicit description as a line bundle of the canonical sheaf of a Gorenstein Schubert variety.Comment: 15 pages, geometric characterization of Gorensteinness added; final version to appear in Adv. Mat

Dietary variations in three co-occurring rockfish species off the Pacific Northwest during anomalous oceanographic events in 1998 and 1999

Stomach samples from three rockfish species, yellowtail (Sebastes f lavidus), widow (S. entomelas), and canary (S. pinniger) rockfish, seasonally collected off the Pacific Northwest in 1998 and 1999, provided quantitative information on the food habits of these species during and after the 1997–98 El Niño event. Although euphausiids were the most common major prey of all three predators, gelatinous zooplankton and fishes were the most commonly consumed prey items during some seasonal quarters. The influence of the El Niño event was evident in the diets. Anomalous prey items, including the southern euphausiid species Nyctiphanes simplex and juveniles of Pacific whiting (Merluccius productus) frequently appeared in the diets in the spring and summer of 1998. The results of stomach contents analyses, based on 905 stomach samples from 49 trawl hauls during seven commercial fishing trips and from 56 stations during research surveys, were consistent with the timing of occurrence and the magnitude of change in biomass of some zooplankton species reported from zooplankton studies in the northern California Current during the 1997–98 El Niño. Our findings indicate that the observed variations of prey groups in some rockfish diets may be a function of prey variability related to climate and environment changes

Balance between information gain and reversibility in weak measurement

We derive a tight bound between the quality of estimating a quantum state by measurement and the success probability of undoing the measurement in arbitrary dimensional systems, which completely describes the tradeoff relation between the information gain and reversibility. In this formulation, it is clearly shown that the information extracted from a weak measurement is erased through the reversing process. Our result broadens the information-theoretic perspective on quantum measurement as well as provides a standard tool to characterize weak measurements and reversals.Comment: 5 pages, final versio

Observation of Topologically Stable 2D Skyrmions in an Antiferromagnetic Spinor Bose-Einstein Condensate

We present the creation and time evolution of two-dimensional Skyrmion excitations in an antiferromagnetic spinor Bose-Einstein condensate. Using a spin rotation method, the Skyrmion spin textures were imprinted on a sodium condensate in a polar phase, where the two-dimensional Skyrmion is topologically protected. The Skyrmion was observed to be stable on a short time scale of a few tens of ms but to have dynamical instability to deform its shape and eventually decay to a uniform spin texture. The deformed spin textures reveal that the decay dynamics involves breaking the polar phase inside the condensate without having topological charge density flow through the boundary of the finite-sized sample. We discuss the possible formation of half-quantum vortices in the deformation process.Comment: 5 pages, 5 figure