On the Milnor fibre and L numbers of semi-weighted homogeneous arrangements

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On the Milnor fibre and L numbers of semi-weighted homogeneous arrangements

Inthispaperwestudygermsofpolynomialsformedbytheproductofsemi-weighted homogeneous polynomials of the same type, which we call semi-weighted homogeneous arrangements. It is shown how the L numbers of such polynomials are computed using only their weights and degree of homogeneity. A key point of the main theorem is to find the number called polar ratio of this polynomial class. An important consequence is the description of the Euler characteristic of the Milnor fibre of such arrangements only depending on their weights and degree of homogeneity. The constancy of the L numbers in families formed by such arrangements is shown, with the deformed terms having weighted degree greater than the weighted degree of the initial germ. Moreover, using the results of Massey applied to families of function germs, we obtain the constancy of the homology of the Milnor fibre in this family of semi-weighted homogeneous arrangements.

Efficient random variable generation: ratio of uniforms and polar rejection sampling

Monte Carlo techniques, which require the generation of samples from some target density, are often the only alternative for performing Bayesian inference. Two classic sampling techniques to draw independent samples are the ratio of uniforms (RoU) and rejection sampling (RS). An efficient sampling algorithm is proposed combining the RoU and polar RS (i.e. RS inside a sector of a circle using polar coordinates). Its efficiency is shown in drawing samples from truncated Cauchy and Gaussian random variables, which have many important applications in signal processing and communications. RESUMEN. Método eficiente para generar algunas variables aleatorias de uso común en procesado de señal y comunicaciones (por ejemplo, Gaussianas o Cauchy truncadas) mediante la combinación de dos técnicas: "ratio of uniforms" y "rejection sampling".

An objective climatology of the dynamical forcing of polar lows in the Nordic seas

A new objective climatology of polar lows in the Nordic (Norwegian and Barents) seas has been derived from a database of diagnostics of objectively identified cyclones spanning the period January 2000 to April 2004. There are two distinct parts to this study: the development of the objective climatology and a characterization of the dynamical forcing of the polar lows identified. Polar lows are an intense subset of polar mesocyclones. Polar mesocyclones are distinguished from other cyclones in the database as those that occur in cold air outbreaks over the open ocean. The difference between the wet-bulb potential temperature at 700 hPa and the sea surface temperature (SST) is found to be an effective discriminator between the atmospheric conditions associated with polar lows and other cyclones in the Nordic seas. A verification study shows that the objective identification method is reliable in the Nordic seas region. After demonstrating success at identifying polar lows using the above method, the dynamical forcing of the polar lows in the Nordic seas is characterized. Diagnostics of the ratio of mid-level vertical motion attributable to quasi-geostrophic forcing from upper and lower levels (U/L ratio) are used to determine the prevalence of a recently proposed category of extratropical cyclogenesis, type C, for which latent heat release is crucial to development. Thirty-one percent of the objectively identified polar low events (36 from 115) exceeded the U/L ratio of 4.0, previously identified as a threshold for type C cyclones. There is a contrast between polar lows to the north and south of the Nordic seas. In the southern Norwegian Sea, the population of polar low events is dominated by type C cyclones. These possess strong convection and weak low-level baroclinicity. Over the Barents and northern Norwegian seas, the well-known cyclogenesis types A and B dominate. These possess stronger low-level baroclinicity and weaker convection.

Characterising the variability and extremes of the stratospheric polar vortices using 2D moment analysis

The mean state, variability and extreme variability of the stratospheric polar vortices, with an emphasis on the Northern Hemisphere vortex, are examined using 2-dimensional moment analysis and Extreme Value Theory (EVT). The use of moments as an analysis to ol gives rise to information about the vortex area, centroid latitude, aspect ratio and kurtosis. The application of EVT to these moment derived quantaties allows the extreme variability of the vortex to be assessed. The data used for this study is ECMWF ERA-40 potential vorticity fields on interpolated isentropic surfaces that range from 450K-1450K. Analyses show that the most extreme vortex variability occurs most commonly in late January and early February, consistent with when most planetary wave driving from the troposphere is observed. Composites around sudden stratospheric warming (SSW) events reveal that the moment diagnostics evolve in statistically different ways between vortex splitting events and vortex displacement events, in contrast to the traditional diagnostics. Histograms of the vortex diagnostics on the 850K (∼10hPa) surface over the 1958-2001 period are fitted with parametric distributions, and show that SSW events comprise the majority of data in the tails of the distributions. The distribution of each diagnostic is computed on various surfaces throughout the depth of the stratosphere, and shows that in general the vortex becomes more circular with higher filamentation at the upper levels. The Northern Hemisphere (NH) and Southern Hemisphere (SH) vortices are also compared through the analysis of their respective vortex diagnostics, and confirm that the SH vortex is less variable and lacks extreme events compared to the NH vortex. Finally extreme value theory is used to statistically mo del the vortex diagnostics and make inferences about the underlying dynamics of the polar vortices.

Simulations of physics and chemistry of polar stratospheric clouds with a general circulation model

A polar stratospheric cloud submodel has been developed and incorporated in a general circulation model including atmospheric chemistry (ECHAM5/MESSy). The formation and sedimentation of polar stratospheric cloud (PSC) particles can thus be simulated as well as heterogeneous chemical reactions that take place on the PSC particles. For solid PSC particle sedimentation, the need for a tailor-made algorithm has been elucidated. A sedimentation scheme based on first order approximations of vertical mixing ratio profiles has been developed. It produces relatively little numerical diffusion and can deal well with divergent or convergent sedimentation velocity fields. For the determination of solid PSC particle sizes, an efficient algorithm has been adapted. It assumes a monodisperse radii distribution and thermodynamic equilibrium between the gas phase and the solid particle phase. This scheme, though relatively simple, is shown to produce particle number densities and radii within the observed range. The combined effects of the representations of sedimentation and solid PSC particles on vertical H2O and HNO3 redistribution are investigated in a series of tests. The formation of solid PSC particles, especially of those consisting of nitric acid trihydrate, has been discussed extensively in recent years. Three particle formation schemes in accordance with the most widely used approaches have been identified and implemented. For the evaluation of PSC occurrence a new data set with unprecedented spatial and temporal coverage was available. A quantitative method for the comparison of simulation results and observations is developed and applied. It reveals that the relative PSC sighting frequency can be reproduced well with the PSC submodel whereas the detailed modelling of PSC events is beyond the scope of coarse global scale models. In addition to the development and evaluation of new PSC submodel components, parts of existing simulation programs have been improved, e.g. a method for the assimilation of meteorological analysis data in the general circulation model, the liquid PSC particle composition scheme, and the calculation of heterogeneous reaction rate coefficients. The interplay of these model components is demonstrated in a simulation of stratospheric chemistry with the coupled general circulation model. Tests against recent satellite data show that the model successfully reproduces the Antarctic ozone hole.

Feldspar Pb-isotope ratios for earliest Pleistocene sediments of the sub-polar North Atlantic Ocean

Relatively little is known in detail about the locations of the early Pleistocene ice-sheets responsible for ice-rafted debris (IRD) inputs to the sub-polar North Atlantic Ocean during intensification of northern hemisphere glaciation (iNHG). To shed new light on this problem, we present the first combined in-depth analysis of IRD flux and geochemical provenance of individual sand-sized IRD deposited in the sub-polar North Atlantic Ocean during the earliest large amplitude Pleistocene glacial, marine isotope stage (MIS) 100 (~2.52 Ma), arguably the key glacial during iNHG. IRD provenance is assessed using laser ablation lead (Pb) isotope analyses of single feldspar grains. We find that the Pb-isotope composition (206Pb/204Pb, 207Pb/204Pb and 208Pb/204Pb) of individual ice-rafted (>150 µm) feldspars deposited at DSDP Site 611A, ODP Site 981 and IODP Site U1308 during MIS 100 records a shift from predominantly Archaean-aged circum-North Atlantic Ocean continental sources during early glacial ice-rafting events to dominantly Palaeozoic and Proterozoic-aged sources during full glacial conditions. The distribution of feldspars in Pb-Pb space for full glacial MIS 100 more closely resembles that documented for feldspars deposited at the centre of the last glacial IRD belt (at IODP/DSDP Site U1308/609) during ambient (non-Heinrich-event) ice-rafting episodes of MIS 2 (~23.8 ka) than that documented for MIS 5d (~106 ka). Comparison of our early Pleistocene and last glacial cycle datasets suggests that MIS 100 was characterised by abundant iceberg calving from large ice-sheets on multiple continents in the high northern latitudes (not just on Greenland).

Experiments on polar seaweeds

Organisms populating benthic shallow water systems of both polar regions are adapted to a particularly harsh environment. We studied effects of freezing and the combination of high light intensities and low water temperatures on photosynthesis of key macroalgal species from the Arctic intertidal (Fucus distichus) and Antarctic subtidal (Palmaria decipiens). Photosynthetic activity of F. distichus specimens was monitored during the freezing process; there was a marked decrease in quantum yield with decreasing temperatures, and a rapid recovery as soon as temperatures increased again. Thus, under the experimental conditions tested, no indication of photodamage was found. Specimens of Palmaria were exposed to a combination of high light intensities and low water temperatures. A persistent impairment of photosynthetic activity occurred at 0°C at light intensities of 400 µmol photons m-2 s-1. In all treatments, there was a decreasing ratio of phycobiliproteins to chlorophyll a. Overall, the two studies provide baseline data for interpreting physiological responses of two important macroalgal species in an extreme environment, the polar coastal ecosystem.

Carbon/Nitrogen ratio of plant tissues and biomass of belowground consumers after 11 years of experimental treatment, Toolik lake

Theory and observation indicate that changes in the rate of primary production can alter the balance between the bottom-up influences of plants and resources and the top-down regulation of herbivores and predators on ecosystem structure and function. The Exploitation Ecosystem Hypothesis (EEH) posited that as aboveground net primary productivity (ANPP) increases, the additional biomass should support higher trophic levels. We developed an extension of EEH to include the impacts of increases in ANPP on belowground consumers in a similar manner as aboveground, but indirectly through changes in the allocation of photosynthate to roots. We tested our predictions for plants aboveground and for phytophagous nematodes and their predators belowground in two common arctic tundra plant communities subjected to 11 years of increased soil nutrient availability and/or exclusion of mammalian herbivores. The less productive dry heath (DH) community met the predictions of EEH aboveground, with the greatest ANPP and plant biomass in the fertilized plots protected from herbivory. A palatable grass increased in fertilized plots while dwarf evergreen shrubs and lichens declined. Belowground, phytophagous nematodes also responded as predicted, achieving greater biomass in the higher ANPP plots, whereas predator biomass tended to be lower in those same plots (although not significantly). In the higher productivity moist acidic tussock (MAT) community, aboveground responses were quite different. Herbivores stimulated ANPP and biomass in both ambient and enriched soil nutrient plots; maximum ANPP occurred in fertilized plots exposed to herbivory. Fertilized plots became dominated by dwarf birch (a deciduous shrub) and cloudberry (a perennial forb); under ambient conditions these two species coexist with sedges, evergreen dwarf shrubs, and Sphagnum mosses. Phytophagous nematodes did not respond significantly to changes in ANPP, although predator biomass was greatest in control plots. The contrasting results of these two arctic tundra plant communities suggest that the predictions of EEH may hold for very low ANPP communities, but that other factors, including competition and shifts in vegetation composition toward less palatable species, may confound predicted responses to changes in productivity in higher ANPP communities such as the MAT studied here.

Major and minor element concentrations in the livers of polar bears (Ursus maritimus) from Greenland, Canada and Alaska

To assess geographic distributions of elements in the Arctic we compared essential and non-essential elements in the livers of polar bears (Ursus maritimus) collected from five regions within Canada in 2002, in Alaska between 1994 and 1999 and from the northwest and east coasts of Greenland between 1988 and 2000. As, Hg, Pb and Se varied with age, and Co and Zn with gender, which limited spatial comparisons across all populations to Cd, which was highest in Greenland bears. Collectively, geographic relationships appeared similar to past studies with little change in concentration over time in Canada and Greenland for most elements; Hg and Se were higher in some Canadian populations in 2002 as compared to 1982 and 1984. Concentrations of most elements in the polar bears did not exceed toxicity thresholds, although Cd and Hg exceeded levels correlated with the formation of hepatic lesions in laboratory animals.

(Table 2) Mercury and selenium concentration in the brain stem of wild polar bears (Ursus maritimus), east Greenland

Polar bears (Ursus maritimus) are exposed to high concentrations of mercury because they are apex predators in the Arctic ecosystem. Although mercury is a potent neurotoxic heavy metal, it is not known whether current exposures are of neurotoxicological concern to polar bears. We tested the hypotheses that polar bears accumulate levels of mercury in their brains that exceed the estimated lowest observable adverse effect level (20 µg/g dry wt) for mammalian wildlife and that such exposures are associated with subtle neurological damage, as determined by measuring neurochemical biomarkers previously shown to be disrupted by mercury in other high-trophic wildlife. Brain stem (medulla oblongata) tissues from 82 polar bears subsistence hunted in East Greenland were studied. Despite surprisingly low levels of mercury in the brain stem region (total mercury = 0.36 ± 0.12 µg/g dry wt), a significant negative correlation was measured between N-methyl-D-aspartate (NMDA) receptor levels and both total mercury (r = -0.34, p < 0.01) and methylmercury (r = -0.89, p < 0.05). No relationships were observed among mercury, selenium, and several other neurochemical biomarkers (dopamine-2, gamma-aminobutyric acid type A, muscarinic cholinergic, and nicotinic cholinergic receptors; cholinesterase and monoamine oxidase enzymes). These data show that East Greenland polar bears do not accumulate high levels of mercury in their brain stems. However, decreased levels of NMDA receptors could be one of the most sensitive indicators of mercury's subclinical and early effects.

Compression and expansion index and void ratio of samples from Lomonosov Ridge and Yermak Plateau

With the coupled use of multibeam swath bathymetry, high-resolution subbottom profiling and sediment coring from icebreakers in the Arctic Ocean, there is a growing awareness of the prevalence of Quaternary ice-grounding events on many of the topographic highs found in present water depths of <1000 m. In some regions, such as the Lomonosov Ridge and Yermak Plateau, overconsolidated sediments sampled through either drilling or coring are found beneath seismically imaged unconformities of glacigenic origin. However, there exists no comprehensive analysis of the geotechnical properties of these sediments, or how their inferred stress state may be related to different glacigenic processes or types of ice-loading. Here we combine geophysical, stratigraphic and geotechnical measurements from the Lomonosov Ridge and Yermak Plateau and discuss the glacial geological implications of overconsolidated sediments. The degree of overconsolidation, determined from measurements of porosity and shear strength, is shown to result from consolidation and/or deformation below grounded ice and, with the exception of a single region on the Lomonosov Ridge, cannot be explained by erosion of overlying sediments. We demonstrate that the amount and depth of porosity loss associated with a middle Quaternary (~ 790-950 thousand years ago - ka) grounding on the Yermak Plateau is compatible with sediment consolidation under an ice sheet or ice rise. Conversely, geotechnical properties of sediments from beneath late Quaternary ice-groundings in both regions, independently dated to Marine Isotope Stage (MIS) 6, indicate a more transient event commensurate with a passing tabular iceberg calved from an ice shelf.

Mercury content and isotopic composition of teeth, and sex and age of skulls of polar bears collected in Svalbard

We examined the use of mercury (Hg) and nitrogen and carbon stable isotopes in teeth of polar bear (Ursus maritimus) from Svalbard as biotracers of temporal changes in Hg pollution exposure between 1964 and 2003. Teeth were regarded as a good matrix of the Hg exposure, and in total 87 teeth of polar bears were analysed. Dental Hg levels ranged from 0.6 to 72.3 ng/g dry weight and increased with age during the first 10 years of life. A decreasing time trend in Hg concentrations was observed over the recent four decades while no temporal changes were found in the stable isotope ratios of nitrogen (d15N) and carbon (d13C). This suggests that the decrease of Hg concentrations over time was more likely due to a lower environmental Hg exposure in this region rather than a shift in the feeding habits of Svalbard polar bears.