Toric degenerations of Gelfand-Cetlin systems and potential functions

We define a toric degeneration of an integrable system on a projective manifold, and prove the existence of a toric degeneration of the Gelfand-Cetlin system on the flag manifold of type A. As an application, we calculate the potential function for a Lagrangian torus fiber of the Gelfand-Cetlin system.Comment: 54 pages, 8 figures. v2: added section 4, revised section 9, and minor changes here and ther

Homological mirror symmetry for the quintic 3-fold

We prove homological mirror symmetry for the quintic Calabi-Yau 3-fold. The proof follows that for the quartic surface by Seidel (arXiv:math/0310414) closely, and uses a result of Sheridan (arXiv:1012.3238). In contrast to Sheridan's approach (arXiv:1111.0632), our proof gives the compatibility of homological mirror symmetry for the projective space and its Calabi-Yau hypersurface.Comment: 29 pages, 6 figures. v2: revised following the suggestions of the referee

Alteration of Dissimilatory Nitrate Reduction Pathways in the Intertidal Sediment during Macroalgae Blooms

To elucidate the effect of macroalgae blooms on dissimilatory nitrate reduction pathways (denitrification, anammox, and DNRA) in sediments of the hypereutrophic Yatsu tidal flat, eastern Japan, sediment denitrification, anammox, and DNRA rates were measured using a 15N tracer technique at two sites affected and unaffected by macroalgae (Ulva) blooms and in incubation experiments with and without Ulva. Anammox was insignificant at both sites and in both experiments. The denitrification rate was consistently higher than the DNRA rate, and its contributions to the total dissimilatory nitrate reduction were 82% and 85% at sites affected and unaffected by Ulva, respectively. In a sediment incubation experiment with Ulva, the contribution of DNRA had increased to approximately 30% on day 7, which is when the sulfide concentration was the highest. Sulfide produced by sulfate reduction during macroalgae blooms inhibited denitrification and did not change the DNRA, and consequently increased the DNRA contribution. On day 21, after reaching the peak sulfide concentration during the late macroalgae collapse, the DNRA contribution decreased to 15%. These results indicated that the DNRA contribution was greater during the macroalgae blooms than at the collapse, although denitrification dominated DNRA regardless of the macroalgal status. Therefore, vigorous macroalgae cover and sulfide production under the macroalgae cover had an important impact on the nitrogen dynamics