An SO(3)-monopole cobordism formula relating Donaldson and Seiberg-Witten invariants

We prove an analogue of the Kotschick-Morgan conjecture in the context of SO(3) monopoles, obtaining a formula relating the Donaldson and Seiberg-Witten invariants of smooth four-manifolds using the SO(3)-monopole cobordism. The main technical difficulty in the SO(3)-monopole program relating the Seiberg-Witten and Donaldson invariants has been to compute intersection pairings on links of strata of reducible SO(3) monopoles, namely the moduli spaces of Seiberg-Witten monopoles lying in lower-level strata of the Uhlenbeck compactification of the moduli space of SO(3) monopoles [arXiv:dg-ga/9710032]. In this monograph, we prove --- modulo a gluing theorem which is an extension of our earlier work in [arXiv:math/9907107] --- that these intersection pairings can be expressed in terms of topological data and Seiberg-Witten invariants of the four-manifold. This conclusion is analogous to the Kotschick-Morgan conjecture concerning the wall-crossing formula for Donaldson invariants of a four-manifold with $b_2^+=1$; that wall-crossing formula and the resulting structure of Donaldson invariants for four-manifolds with $b_2^+=1$ were established, assuming the Kotschick-Morgan conjecture, by Goettsche [arXiv:alg-geom/9506018] and Goettsche and Zagier [arXiv:alg-geom/9612020]. In this monograph, we reduce the proof of the Kotschick-Morgan conjecture to an extension of previously established gluing theorems for anti-self-dual SO(3) connections (see [arXiv:math/9812060] and references therein). Since the first version of our monograph was circulated, applications of our results have appeared in the proof of Property P for knots by Kronheimer and Mrowka [arXiv:math/0311489] and work of Sivek on Donaldson invariants for symplectic four-manifolds [arXiv:1301.0377].Comment: x + 229 page

Some implications of sampling choices on comparisons between satellite and model aerosol optical depth fields

The comparison of satellite and model aerosol optical depth (AOD) fields provides useful information on the strengths and weaknesses of both. However, the sampling of satellite and models is very different and some subjective decisions about data selection and aggregation must be made in order to perform such comparisons. This work examines some implications of these decisions, using GlobAerosol AOD retrievals at 550 nm from Advanced Along-Track Scanning Radiometer (AATSR) measurements, and aerosol fields from the GEOS-Chem chemistry transport model. It is recommended to sample the model only where the satellite flies over on a particular day; neglecting this can cause regional differences in model AOD of up to 0.1 on monthly and annual timescales. The comparison is observed to depend strongly upon thresholds for sparsity of satellite retrievals in the model grid cells. Requiring at least 25% coverage of the model grid cell by satellite data decreases the observed difference between the two by approximately half over land. The impact over ocean is smaller. In both model and satellite datasets, there is an anticorrelation between the proportion <i>p</i> of a model grid cell covered by satellite retrievals and the AOD. This is attributed to small <i>p</i> typically occuring due to high cloud cover and lower AODs being found in large clear-sky regions. Daily median AATSR AODs were found to be closer to GEOS-Chem AODs than daily means (with the root mean squared difference being approximately 0.05 smaller). This is due to the decreased sensitivity of medians to outliers such as cloud-contaminated retrievals, or aerosol point sources not included in the model

Cell cycle regulation of a Xenopus Wee1-like kinase

Using a polymerase chain reaction-based strategy, we have isolated a gene encoding a Wee1-like kinase from Xenopus eggs. The recombinant Xenopus Wee1 protein efficiently phosphorylates Cdc2 exclusively on Tyr- 15 in a cyclin-dependent manner. The addition of exogenous Wee1 protein to Xenopus cell cycle extracts results in a dose-dependent delay of mitotic initiation that is accompanied by enhanced tyrosine phosphorylation of Cdc2. The activity of the Wee1 protein is highly regulated during the cell cycle: the interphase, underphosphorylated form of Wee1 (68 kDa) phosphorylates Cdc2 very efficiently, whereas the mitotic, hyperphosphorylated version (75 kDa) is weakly active as a Cdc2-specific tyrosine kinase. The down-modulation of Wee1 at mitosis is directly attributable to phosphorylation, since dephosphorylation with protein phosphatase 2A restores its kinase activity. During interphase, the activity of this Wee1 homolog does not vary in response to the presence of unreplicated DNA. The mitosis-specific phosphorylation of Wee1 is due to at least two distinct kinases: the Cdc2 protein and another activity (kinase X) that may correspond to an MPM-2 epitope kinase. These studies indicate that the down-regulation of Wee1-like kinase activity at mitosis is a multistep process that occurs after other biochemical reactions have signaled the successful completion of S phase

The Cepheid Distance Scale: recent progress in fundamental techniques

This review examines progress on the Pop I, fundamental-mode Cepheid distance scale with emphasis on recent developments in geometric and quasi-geometric techniques for Cepheid distance determination. Specifically I examine the surface brightness method, interferometric pulsation method, and trigonometric measurements. The three techniques are found to be in excellent agreement for distance measures in the Galaxy. The velocity p-factor is of crucial importance in the first two of these methods. A comparison of recent determinations of the p-factor for Cepheids demonstrates that observational measures of p and theoretical predictions agree within their uncertainties for Galactic Cepheids.Comment: An invited review at the Santa Fe, NM, conference -- Stellar Pulsation: Challenges for Theory and Observation; May 31-June 5, 2009 10 pages, 8 figure

Assessment of the environmental toxicity and carcinogenicity of tungsten-based shot.

The toxicity of elemental tungsten released from discharged shot was assessed against previous studies that established a 1% toxic threshold for soil organisms. Extremely heavy theoretical shot loadings of 69,000 shot/ha were used to generate estimated environmental concentrations (EEC) for two brands of tungsten-based shot containing 51% and 95% tungsten. The corresponding tungsten EEC values were 6.5–13.5 mg W/kg soil, far below the 1% toxic threshold. The same shot loading in water produced tungsten EEC values of 2.1–4.4 mg W/L, levels that are not toxic under experimental conditions. Pure tungsten has not been shown to exhibit carcinogenic properties when ingested or embedded in animal tissues, but nickel, with which it is often alloyed, has known carcinogenicity. Given the large number of waterfowl that carry shot embedded in their body, it is advisable to screen lead shot substitutes for their carcinogenic potential through intra-muscular implantation