Hodge numbers are not derived invariants in positive characteristic

We study a pair of Calabi-Yau threefolds X and M, fibered in non-principally polarized Abelian surfaces and their duals, and an equivalence D^b(X) = D^b(M), building on work of Gross, Popescu, Bak, and Schnell. Over the complex numbers, X is simply connected while pi_1(M) = (Z/3)^2. In characteristic 3, we find that X and M have different Hodge numbers, which would be impossible in characteristic 0. In an appendix, we give a streamlined proof of Abuaf's result that the ring H^*(O) is a derived invariant of complex threefolds and fourfolds. A second appendix by Alexander Petrov gives a family of higher-dimensional examples to show that h^{0,3} is not a derived invariant in any positive characteristic

Annotation and comparative analysis of the glycoside hydrolase genes in Brachypodium distachyon

Abstract Background Glycoside hydrolases cleave the bond between a carbohydrate and another carbohydrate, a protein, lipid or other moiety. Genes encoding glycoside hydrolases are found in a wide range of organisms, from archea to animals, and are relatively abundant in plant genomes. In plants, these enzymes are involved in diverse processes, including starch metabolism, defense, and cell-wall remodeling. Glycoside hydrolase genes have been previously cataloged for Oryza sativa (rice), the model dicotyledonous plant Arabidopsis thaliana, and the fast-growing tree Populus trichocarpa (poplar). To improve our understanding of glycoside hydrolases in plants generally and in grasses specifically, we annotated the glycoside hydrolase genes in the grasses Brachypodium distachyon (an emerging monocotyledonous model) and Sorghum bicolor (sorghum). We then compared the glycoside hydrolases across species, at the levels of the whole genome and individual glycoside hydrolase families. Results We identified 356 glycoside hydrolase genes in Brachypodium and 404 in sorghum. The corresponding proteins fell into the same 34 families that are represented in rice, Arabidopsis, and poplar, helping to define a glycoside hydrolase family profile which may be common to flowering plants. For several glycoside hydrolase familes (GH5, GH13, GH18, GH19, GH28, and GH51), we present a detailed literature review together with an examination of the family structures. This analysis of individual families revealed both similarities and distinctions between monocots and eudicots, as well as between species. Shared evolutionary histories appear to be modified by lineage-specific expansions or deletions. Within GH families, the Brachypodium and sorghum proteins generally cluster with those from other monocots. Conclusions This work provides the foundation for further comparative and functional analyses of plant glycoside hydrolases. Defining the Brachypodium glycoside hydrolases sets the stage for Brachypodium to be a grass model for investigations of these enzymes and their diverse roles in planta. Insights gained from Brachypodium will inform translational research studies, with applications for the improvement of cereal crops and bioenergy grasses

Electronic structure and optical properties of ZnX (X=O, S, Se, Te)

Electronic band structure and optical properties of zinc monochalcogenides with zinc-blende- and wurtzite-type structures were studied using the ab initio density functional method within the LDA, GGA, and LDA+U approaches. Calculations of the optical spectra have been performed for the energy range 0-20 eV, with and without including spin-orbit coupling. Reflectivity, absorption and extinction coefficients, and refractive index have been computed from the imaginary part of the dielectric function using the Kramers--Kronig transformations. A rigid shift of the calculated optical spectra is found to provide a good first approximation to reproduce experimental observations for almost all the zinc monochalcogenide phases considered. By inspection of the calculated and experimentally determined band-gap values for the zinc monochalcogenide series, the band gap of ZnO with zinc-blende structure has been estimated.Comment: 17 pages, 10 figure

The RKKY interactions and the Mott Transition

A two-site cluster generalization of the Hubbard model in large dimensions is examined in order to study the role of short-range spin correlations near the metal-insulator transition (MIT). The model is mapped to a two-impurity Kondo-Anderson model in a self-consistently determined bath, making it possible to directly address the competition between the Kondo effect and RKKY interactions in a lattice context. Our results indicate that the RKKY interactions lead to qualitative modifications of the MIT scenario even in the absence of long range antiferromagnetic ordering.Comment: 10 pages, 10 figures; to appear in Phys. Rev. B (1999

The sphere-in-contact model of carbon materials

A sphere-in-contact model is presented that is used to build physical models of carbon materials such as graphite, graphene, carbon nanotubes and fullerene. Unlike other molecular models, these models have correct scale and proportions because the carbon atoms are represented by their atomic radius, in contrast to the more commonly used space-fill models, where carbon atoms are represented by their van der Waals radii. Based on a survey taken among 65 undergraduate chemistry students and 28 PhD/postdoctoral students with a background in molecular modeling, we found misconceptions arising from incorrect visualization of the size and location of the electron density located in carbon materials. Based on analysis of the survey and on a conceptual basis we show that the sphere-in-contact model provides an improved molecular representation of the electron density of carbon materials compared to other molecular models commonly used in science textbooks (i.e., wire-frame, ball-and-stick, space-fill). We therefore suggest that its use in chemistry textbooks along with the ball-and-stick model would significantly enhance the visualization of molecular structures according to their electron density

A 4% Geometric Distance to the Galaxy NGC4258 from Orbital Motions in a Nuclear Gas Disk

The water maser in the mildly active nucleus in the nearby galaxy NGC4258 traces a thin, nearly edge-on, subparsec-scale Keplerian disk. Using the technique of very long baseline interferometry, we have detected the proper motions of these masers as they sweep in front of the central black hole at an orbital velocity of about 1100 km/s. The average maser proper motion of 31.5 microarcseconds per year is used in conjunction with the observed acceleration of the masers to derive a purely geometric distance to the galaxy of 7.2 +- 0.3 Mpc. This is the most precise extragalactic distance measured to date, and, being independent of all other distance indicators, is likely to play an important role in calibrating the extragalactic distance scale.Comment: 11 pages, 3 figures. Accepted for publication in Natur

A randomized, controlled, double-blind crossover study on the effects of isoeffective and isovolumetric intravenous crystalloid and gelatin on blood volume, and renal and cardiac hemodynamics

Background & aimsBlood volume expanding properties of colloids are superior to crystalloids. In addition to oncotic/osmotic properties, the electrolyte composition of infusions may have important effects on visceral perfusion, with infusions containing supraphysiological chloride causing hyperchloremic acidosis and decreased renal blood flow. In this non-inferiority study, a validated healthy human subject model was used to compare effects of colloid (4% succinylated gelatin) and crystalloid fluid regimens on blood volume, renal function, and cardiac output.MethodsHealthy male participants were given infusions over 60 min > 7 days apart in a randomized, crossover manner. Reference arm (A): 1.5 L of Sterofundin ISO, isoeffective arm (B): 0.5 L of 4% Gelaspan®, isovolumetric arm (C): 0.5 L of 4% Gelaspan® and 1 L of Sterofundin ISO (all B. Braun, Melsungen, Germany). Participants were studied over 240 min. Changes in blood volume were calculated from changes in weight and hematocrit. Renal volume, renal artery blood flow (RABF), renal cortex perfusion and diffusion, and cardiac index were measured with magnetic resonance imaging.ResultsTen of 12 males [mean (SE) age 23.9 (0.8) years] recruited, completed the study. Increase in body weight and extracellular fluid volume were significantly less after infusion B than infusions A and C, but changes in blood volume did not significantly differ between infusions. All infusions increased renal volume, with no significant differences between infusions. There was no significant difference in RABF across the infusion time course or between infusion types. Renal cortex perfusion decreased during the infusion (mean 18% decrease from baseline), with no significant difference between infusions. There was a trend for increased renal cortex diffusion (4.2% increase from baseline) for the crystalloid infusion. All infusions led to significant increases in cardiac index.ConclusionsA smaller volume of colloid (4% succinylated gelatin) was as effective as a larger volume of crystalloid at expanding blood volume, increasing cardiac output and changing renal function. Significantly less interstitial space expansion occurred with the colloid