A geometric view of cryptographic equation solving

This paper considers the geometric properties of the Relinearisation algorithm and of the XL algorithm used in cryptology for equation solving. We give a formal description of each algorithm in terms of projective geometry, making particular use of the Veronese variety. We establish the fundamental geometrical connection between the two algorithms and show how both algorithms can be viewed as being equivalent to the problem of finding a matrix of low rank in the linear span of a collection of matrices, a problem sometimes known as the MinRank problem. Furthermore, we generalise the XL algorithm to a geometrically invariant algorithm, which we term the GeometricXL algorithm. The GeometricXL algorithm is a technique which can solve certain equation systems that are not easily soluble by the XL algorithm or by Groebner basis methods

Greenhouse gas emissions (CO2, CH4, and N2O) from several perialpine and alpine hydropower reservoirs by diffusion and loss in turbines

We investigated greenhouse gas emissions (CO2, CH4, and N2O) from reservoirs located across an altitude gradient in Switzerland. These are the first results of greenhouse gas emissions from reservoirs at high elevations in the Alps. Depth profiles were taken in 11 reservoirs located at different altitudes between the years 2003 and 2006. Diffusive trace gas emissions were calculated using surface gas concentrations, wind speeds and transfer velocities. Additionally, methane entering with the inflowing water and methane loss at the turbine was assessed for a subset of the reservoirs. All reservoirs were emitters of carbon dioxide and methane with an average of 970±340mgm−2day−1 (results only from four lowland and one subalpine reservoir) and 0.20±0.15mgm−2day−1, respectively. One reservoir (Lake Wohlen) emitted methane at a much higher rate (1.8±0.9mgm−2day−1) than the other investigated reservoirs. There was no significant difference in methane emissions across the altitude gradient, but average dissolved methane concentrations decreased with increasing elevation. Only lowland reservoirs were sources for N2O (72±22μgm−2day−1), while the subalpine and alpine reservoirs were in equilibrium with atmospheric concentrations. These results indicate reservoirs from subalpine/alpine regions to be only minor contributors of greenhouse gases to the atmosphere compared to other reservoir

Effects of alcohol consumption on mortality in patients with Type 2 diabetes mellitus

Aims/hypothesis: Moderate alcohol intake has been associated with increased life expectancy due to reduced mortality from cardiovascular disease. We prospectively examined the effects of alcohol consumption on mortality in Type 2 diabetic patients in Switzerland. Methods: A total of 287 patients with Type 2 diabetes mellitus (125 women, 162 men), recruited in Switzerland for the WHO Multinational Study of Vascular Disease in Diabetes, were included in this study. After a follow-up period of 12.6±0.6 years (means ± SD), mortality from CHD and from all causes was assessed. Results: During the follow-up, 70 deaths occurred (21 from CHD, 49 from other causes). Compared with non-drinkers, alcohol consumers who drank alcohol 1 to 15g, 16 to 30g and 30g or more per day had the following risk rates of death from CHD: 0.87 (95% CI: 0.25 to 2.51, NS), 0.00 (95% CI: 0.00 to 0.92, p less than 0.05) and 0.37 (95% CI, 0.01 to 2.42, NS), respectively. The corresponding risk rates of death from all causes were 1.27 (95% CI: 0.68 to 2.28, NS), 0.36 (95% CI: 0.09 to 0.99, p less than 0.05) and 1.66 (95% CI: 0.76 to 3.33, NS). Conclusions/interpretation: In Swiss Type 2 diabetic patients moderate alcohol consumption of 16 to 30g per day was associated with reduced mortality from CHD and from all causes. Alcohol intake above 30g per day was associated with a tendency towards increased all-cause mortalit

Oxidation and emission of methane in a monomictic lake (Rotsee, Switzerland)

The build-up of methane in the hypolimnion of the eutrophic Lake Rotsee (Lucerne, Switzerland) was monitored over a full year. Sources and sinks of methane in the water column were characterized by measuring concentrations and carbon isotopic composition. In fall, high methane concentrations (up to 1mM) were measured in the anoxic water layer. In the oxic layer, methane concentrations were much lower and the isotopic composition shifted towards heavy carbon isotopes. Methane oxidation rates peaked at the interface between oxic and anoxic water layers at around 8-10m depth. The electron balance between the oxidants oxygen, sulphate, and nitrate, and the reductants methane, sulphide and ammonium, matched very well in the chemocline during the stratified season. The profile of carbon isotopic composition of methane showed strong indications for methane oxidation at the chemocline (including the oxycline). Aerobic methane oxidizing bacteria were detected at the interface using fluorescence in situ hybridization. Sequencing the responsible organisms from DGGE bands revealed that aerobic methanotrophs type I closely related to Methylomonas were present. Sulphate consumption occurred at the sediment surface and, only towards the end of the stagnation period, matched with a zone of methane consumption. In any case, the flux of sulphate below the chemocline was not sufficient to oxidize all the methane and other oxidants like nitrate, iron or manganese are necessary for the observed methane oxidation. Although most of the methane was oxidized either aerobically or anaerobically, Lake Rotsee was still a source of methane to the atmosphere with emission rates between 0.2mgCH4m−2day−1 in February and 7mgCH4m−2day−1 in Novembe

Metabolic and hormonal studies of Type 1 (insulin-dependent) diabetic patients after successful pancreas and kidney transplantation

Long-term normalization of glucose metabolism is necessary to prevent or ameliorate diabetic complications. Although pancreatic grafting is able to restore normal blood glucose and glycated haemoglobin, the degree of normalization of the deranged diabetic metabolism after pancreas transplantation is still questionable. Consequently glucose, insulin, C-peptide, glucagon, and pancreatic polypeptide responses to oral glucose and i.v. arginine were measured in 36 Type 1 (insulin-dependent) diabetic recipients of pancreas and kidney allografts and compared to ten healthy control subjects. Despite normal HbA1 (7.2±0.2%; normal <8%) glucose disposal was normal only in 44% and impaired in 56% of the graft recipients. Normalization of glucose tolerance was achieved at the expense of hyperinsulinaemia in 52% of the subjects. C-peptide and glucagon were normal, while pancreatic polypeptide was significantly higher in the graft recipients. Intravenous glucose tolerance (n=21) was normal in 67% and borderline in 23%. Biphasic insulin release was seen in patients with normal glucose tolerance. Glucose tolerance did not deteriorate up to 7 years post-transplant. In addition, stress hormone release (cortisol, growth hormone, prolactin, glucagon, catecholamines) to insulin-induced hypoglycaemia was examined in 20 graft recipients and compared to eight healthy subjects. Reduced blood glucose decline indicates insulin resistance, but glucose recovery was normal, despite markedly reduced catecholamine and glucagon release. These data demonstrate the effectiveness of pancreatic grafting in normalizing glucose metabolism, although hyperinsulinaemia and deranged counterregulatory hormone response are observed frequently

Tamoxifen Initiation After Ductal Carcinoma In Situ

Endocrine therapy initiation after ductal carcinoma in situ (DCIS) is highly variable and largely unexplained. National guidelines recommend considering tamoxifen for women with estrogen receptor-positive (ER+) DCIS or who undergo excision alone. We evaluated endocrine therapy use after DCIS over a 15-year period in an integrated health care setting to identify factors related to initiation