Lagrangian Floer superpotentials and crepant resolutions for toric orbifolds

We investigate the relationship between the Lagrangian Floer superpotentials for a toric orbifold and its toric crepant resolutions. More specifically, we study an open string version of the crepant resolution conjecture (CRC) which states that the Lagrangian Floer superpotential of a Gorenstein toric orbifold $\mathcal{X}$ and that of its toric crepant resolution $Y$ coincide after analytic continuation of quantum parameters and a change of variables. Relating this conjecture with the closed CRC, we find that the change of variable formula which appears in closed CRC can be explained by relations between open (orbifold) Gromov-Witten invariants. We also discover a geometric explanation (in terms of virtual counting of stable orbi-discs) for the specialization of quantum parameters to roots of unity which appears in Y. Ruan's original CRC ["The cohomology ring of crepant resolutions of orbifolds", Gromov-Witten theory of spin curves and orbifolds, 117-126, Contemp. Math., 403, Amer. Math. Soc., Providence, RI, 2006]. We prove the open CRC for the weighted projective spaces $\mathcal{X}=\mathbb{P}(1,\ldots,1,n)$ using an equality between open and closed orbifold Gromov-Witten invariants. Along the way, we also prove an open mirror theorem for these toric orbifolds.Comment: 48 pages, 1 figure; v2: references added and updated, final version, to appear in CM

Phosphorus nutrition and management – overcoming constraints to wider adoption

The importance of phosphorus nutrition for cattle grazing northern Australian rangelands has been well documented and demonstrated. Phosphorus is clearly one of the most important nutritional deficiencies, within the limitations of potential metabolizable energy intakes, of grazing cattle in the seasonally dry tropics. Nevertheless it appears that only a small proportion of cattle grazing phosphorus deficient pastures are supplemented or otherwise managed to alleviate phosphorus deficiency. Estimated requirements for dietary phosphorus by various classes of cattle grazing tropical pastures have recently been revised (CSIRO 2007). The development of faecal near infrared spectroscopy (F.NIRS) allows the routine estimation of metabolizable energy and nitrogen concentrations in the diet, and thus the potential productivity, of cattle grazing northern rangelands. The concentration of phosphorus in the diet of grazing cattle can be estimated from the concentration of phosphorus in the faeces, at least in cattle not fed phosphorus supplements. Combining estimates of diet metabolizable energy, nitrogen and phosphorus allows estimation whether current needs of the animal are supplied by the diet. Phosphorus-replete cattle have substantial body reserves of phosphorus which can be mobilized, especially in late pregnancy and lactation, to alleviate a dietary deficiency. However, these body reserves need to be replenished in late lactation or post-lactation if mobilization occurs each year. Diagnosis of subclinical phosphorus deficiency in grazing cattle, and prediction of animal responses to phosphorus supplements is difficult. In growing cattle the concentration of inorganic phosphorus in blood (Pi), in the late wet or early dry season, combined with information on diet metabolizable energy and nitrogen concentrations obtained by F.NIRS, provides the most reliable test. In pregnant or lactating cows measurements of faecal phosphorus concentration and F.NIRS provide the best estimate of whether phosphorus intake meets the current needs of the animal. However, estimates of adequacy of phosphorus supply need to also consider possible mobilization of body phosphorus reserves. Indicative responses to provision of phosphorus supplements by cattle grazing pastures ranging from marginal to acute deficiency are summarized. Economic evaluation of benchmark enterprises where cattle are expected to be phosphorus deficient indicate that phosphorus supplementation is highly cost-effective. Major obstacles to more widespread adoption of phosphorus supplementation appear to be lack of knowledge and appreciation by managers of the phosphorus status of their cattle, lack of appreciation of the cost-effectiveness of a phosphorus supplementation particularly for some classes of cattle, and the practical difficulties in implementing phosphorus supplementation during the wet season

On the Crepant Resolution Conjecture in the Local Case

In this paper we analyze four examples of birational transformations between local Calabi-Yau 3-folds: two crepant resolutions, a crepant partial resolution, and a flop. We study the effect of these transformations on genus-zero Gromov-Witten invariants, proving the Coates-Corti-Iritani-Tseng/Ruan form of the Crepant Resolution Conjecture in each case. Our results suggest that this form of the Crepant Resolution Conjecture may also hold for more general crepant birational transformations. They also suggest that Ruan's original Crepant Resolution Conjecture should be modified, by including appropriate "quantum corrections", and that there is no straightforward generalization of either Ruan's original Conjecture or the Cohomological Crepant Resolution Conjecture to the case of crepant partial resolutions. Our methods are based on mirror symmetry for toric orbifolds.Comment: 27 pages. This is a substantially revised and shortened version of my preprint "Wall-Crossings in Toric Gromov-Witten Theory II: Local Examples"; all results contained here are also proved there. To appear in Communications in Mathematical Physic

Polar motion and UT1: Comparison of VLBI, lunar laser, satellite laser, satellite Doppler, and conventional astrometric determinations

Very long baseline interferometry observations made with a 3900 km baseline interferometer (Haystack Observatory in Massachusetts to Owens Valley Observation in California) were used to estimate changes in the X-component of the position of the Earth's pole and in UT1. These estimates are compared with corresponding ones from lunar laser ranging, satellite laser ranging, satellite Doppler, and stellar observations

Cassini observations of ion and electron beams at Saturn and their relationship to infrared auroral arcs

We present Cassini Visual and Infrared Mapping Spectrometer observations of infrared auroral emissions from the noon sector of Saturn's ionosphere revealing multiple intense auroral arcs separated by dark regions poleward of the main oval. The arcs are interpreted as the ionospheric signatures of bursts of reconnection occurring at the dayside magnetopause. The auroral arcs were associated with upward field-aligned currents, the magnetic signatures of which were detected by Cassini at high planetary latitudes. Magnetic field and particle observations in the adjacent downward current regions showed upward bursts of 100–360 keV light ions in addition to energetic (hundreds of keV) electrons, which may have been scattered from upward accelerated beams carrying the downward currents. Broadband, upward propagating whistler waves were detected simultaneously with the ion beams. The acceleration of the light ions from low altitudes is attributed to wave-particle interactions in the downward current regions. Energetic (600 keV) oxygen ions were also detected, suggesting the presence of ambient oxygen at altitudes within the acceleration region. These simultaneous in situ and remote observations reveal the highly energetic magnetospheric dynamics driving some of Saturn's unusual auroral features. This is the first in situ identification of transient reconnection events at regions magnetically conjugate to Saturn's magnetopause

Precision surveying using very long baseline interferometry

Radio interferometry measurements were used to measure the vector baselines between large microwave radio antennas. A 1.24 km baseline in Massachusetts between the 36 meter Haystack Observatory antenna and the 18 meter Westford antenna of Lincoln Laboratory was measured with 5 mm repeatability in 12 separate experiments. Preliminary results from measurements of the 3,928 km baseline between the Haystack antenna and the 40 meter antenna at the Owens Valley Radio Observatory in California are presented

Structural plasticity of the selectivity filter in a nonselective ion channel

The sodium potassium ion channel (NaK) is a nonselective ion channel that conducts both sodium and potassium across the cellular membrane. A new crystallographic structure of NaK reveals conformational differences in the residues that make up the selectivity filter between the four subunits that form the ion channel and the inner helix of the ion channel. The crystallographic structure also identifies a side-entry, ion-conduction pathway for Na+ permeation that is unique to NaK. NMR studies and molecular dynamics simulations confirmed the dynamical nature of the top part of the selectivity filter and the inner helix in NaK as also observed in the crystal structure. Taken together, these results indicate that the structural plasticity of the selectivity filter combined with the dynamics of the inner helix of NaK are vital for the efficient conduction of different ions through the non-selective ion channel of NaK

Neutrons for Catalysis: A Workshop on Neutron Scattering Techniques for Studies in Catalysis

This report summarizes the Workshop on Neutron Scattering Techniques for Studies in Catalysis, held at the Spallation Neutron Source (SNS) at Oak Ridge National Laboratory (ORNL) on September 16 and 17, 2010. The goal of the Workshop was to bring experts in heterogeneous catalysis and biocatalysis together with neutron scattering experimenters to identify ways to attack new problems, especially Grand Challenge problems in catalysis, using neutron scattering. The Workshop locale was motivated by the neutron capabilities at ORNL, including the High Flux Isotope Reactor (HFIR) and the new and developing instrumentation at the SNS. Approximately 90 researchers met for 1 1/2 days with oral presentations and breakout sessions. Oral presentations were divided into five topical sessions aimed at a discussion of Grand Challenge problems in catalysis, dynamics studies, structure characterization, biocatalysis, and computational methods. Eleven internationally known invited experts spoke in these sessions. The Workshop was intended both to educate catalyst experts about the methods and possibilities of neutron methods and to educate the neutron community about the methods and scientific challenges in catalysis. Above all, it was intended to inspire new research ideas among the attendees. All attendees were asked to participate in one or more of three breakout sessions to share ideas and propose new experiments that could be performed using the ORNL neutron facilities. The Workshop was expected to lead to proposals for beam time at either the HFIR or the SNS; therefore, it was expected that each breakout session would identify a few experiments or proof-of-principle experiments and a leader who would pursue a proposal after the Workshop. Also, a refereed review article will be submitted to a prominent journal to present research and ideas illustrating the benefits and possibilities of neutron methods for catalysis research