Extending Johnson's and Morita's homomorphisms to the mapping class group

We extend certain homomorphisms defined on the higher Torelli subgroups of the mapping class group to crossed homomorphisms defined on the entire mapping class group. In particular, for every $k\geq 2$, we construct a crossed homomorphism $\epsilon_k$ which extends Morita's homomorphism $\tilde \tau_k$ to the entire mapping class group. From this crossed homomorphism we also obtain a crossed homomorphism extending the $k$th Johnson homomorphism $\tau_k$ to the mapping class group. D. Johnson and S. Morita obtained their respective homomorphisms by considering the action of the mapping class group on the nilpotent truncations of the surface group; our approach is to mimic Morita's construction topologically by using nilmanifolds associated to these truncations. This allows us to take the ranges of these crossed homomorphisms to be certain finite-dimensional real vector spaces associated to these nilmanifolds.Comment: 32 pages; cleaned up and minor corrections to proofs; updated to agree with version published by Alg. & Geom. Top at: http://msp.warwick.ac.uk/agt/2007/07/p050.xhtm

Assimilation of GPM-Retrieved Marine Surface Meteorology Variables for Two Winter Storms

No abstract availabl

Land Surface Modeling and Evaporative Stress Products for Increased Situational Awareness

No abstract availabl

Towards an integrated soil moisture drought monitor for East Africa

Drought in East Africa is a recurring phenomenon with significant humanitarian impacts. Given the steep climatic gradients, topographic contrasts, general data scarcity, and, in places, political instability that characterize the region, there is a need for spatially distributed, remotely derived monitoring systems to inform national and international drought response. At the same time, the very diversity and data scarcity that necessitate remote monitoring also make it difficult to evaluate the reliability of these systems. Here we apply a suite of remote monitoring techniques to characterize the temporal and spatial evolution of the 2010–2011 Horn of Africa drought. Diverse satellite observations allow for evaluation of meteorological, agricultural, and hydrological aspects of drought, each of which is of interest to different stakeholders. Focusing on soil moisture, we apply triple collocation analysis (TCA) to three independent methods for estimating soil moisture anomalies to characterize relative error between products and to provide a basis for objective data merging. The three soil moisture methods evaluated include microwave remote sensing using the Advanced Microwave Scanning Radiometer – Earth Observing System (AMSR-E) sensor, thermal remote sensing using the Atmosphere-Land Exchange Inverse (ALEXI) surface energy balance algorithm, and physically based land surface modeling using the Noah land surface model. It was found that the three soil moisture monitoring methods yield similar drought anomaly estimates in areas characterized by extremely low or by moderate vegetation cover, particularly during the below-average 2011 long rainy season. Systematic discrepancies were found, however, in regions of moderately low vegetation cover and high vegetation cover, especially during the failed 2010 short rains. The merged, TCA-weighted soil moisture composite product takes advantage of the relative strengths of each method, as judged by the consistency of anomaly estimates across independent methods. This approach holds potential as a remote soil moisture-based drought monitoring system that is robust across the diverse climatic and ecological zones of East Africa

Examining Rapid Onset Drought Development Using the Thermal Infrared–Based Evaporative Stress Index

Reliable indicators of rapid drought onset can help to improve the effectiveness of drought early warning systems. In this study, the evaporative stress index (ESI), which uses remotely sensed thermal infrared imagery to estimate evapotranspiration (ET), is compared to drought classifications in the U.S. Drought Monitor (USDM) and standard precipitation-based drought indicators for several cases of rapid drought development that have occurred across the United States in recent years. Analysis of meteorological time series from the North American Regional Reanalysis indicates that these events are typically characterized by warm air temperature and low cloud cover anomalies, often with high winds and dewpoint depressions that serve to hasten evaporative depletion of soil moisture reserves. Standardized change anomalies depicting the rate at which various multiweek ESI composites changed over different time intervals are computed to more easily identify areas experiencing rapid changes in ET. Overall, the results demonstrate that ESI change anomalies can provide early warning of incipient drought impacts on agricultural systems, as indicated in crop condition reports collected by the National Agricultural Statistics Service. In each case examined, large negative change anomalies indicative of rapidly drying conditions were either coincident with the introduction of drought in the USDM or lead the USDM drought depiction by several weeks, depending on which ESI composite and time-differencing interval was used. Incorporation of the ESI as a data layer used in the construction of the USDM may improve timely depictions of moisture conditions and vegetation stress associated with flash drought events

A continuous source of translationally cold dipolar molecules

The Stark interaction of polar molecules with an inhomogeneous electric field is exploited to select slow molecules from a room-temperature reservoir and guide them into an ultrahigh vacuum chamber. A linear electrostatic quadrupole with a curved section selects molecules with small transverse and longitudinal velocities. The source is tested with formaldehyde (H2CO) and deuterated ammonia (ND3). With H2CO a continuous flux is measured of approximately 10^9/s and a longitudinal temperature of a few K. The data are compared with the result of a Monte Carlo simulation.Comment: 4 pages, 4 figures v2: small changes in the abstract, text and references. Figures 1 & 2 regenerated to prevent errors in the pd

Superpotentials for M-theory on a G_2 holonomy manifold and Triality symmetry

For $M$-theory on the $G_2$ holonomy manifold given by the cone on {\bf S^3}\x {\bf S^3} we consider the superpotential generated by membrane instantons and study its transformations properties, especially under monodromy transformations and triality symmetry. We find that the latter symmetry is, essentially, even a symmetry of the superpotential. As in Seiberg/Witten theory, where a flat bundle given by the periods of an universal elliptic curve over the $u$-plane occurs, here a flat bundle related to the Heisenberg group appears and the relevant universal object over the moduli space is related to hyperbolic geometry.Comment: 58 pages, latex; references adde

Assimilation of GPM Retrieved Surface Meteorology Variables with ICE-POP Case Studies

Built upon Tropical Rainfall Measuring Mission (TRMM) legacy for next-generation global observation of rain and snow. The GPM has a broad global coverage ~70S 70N with a swath of 245/125-km for the Ka (35.5 GHz)/Ku (13.6 GHz) band radar, and 850-km for the 13-channel GMI. GPM also features better retrievals for heavy, moderate, and light rain and snowfall