Projective dynamics and first integrals

We present the theory of tensors with Young tableau symmetry as an efficient computational tool in dealing with the polynomial first integrals of a natural system in classical mechanics. We relate a special kind of such first integrals, already studied by Lundmark, to Beltrami's theorem about projectively flat Riemannian manifolds. We set the ground for a new and simple theory of the integrable systems having only quadratic first integrals. This theory begins with two centered quadrics related by central projection, each quadric being a model of a space of constant curvature. Finally, we present an extension of these models to the case of degenerate quadratic forms.Comment: 39 pages, 2 figure

Neutrino oscillation studies with IceCube-DeepCore

AbstractIceCube, a gigaton-scale neutrino detector located at the South Pole, was primarily designed to search for astrophysical neutrinos with energies of PeV and higher. This goal has been achieved with the detection of the highest energy neutrinos to date. At the other end of the energy spectrum, the DeepCore extension lowers the energy threshold of the detector to approximately 10 GeV and opens the door for oscillation studies using atmospheric neutrinos. An analysis of the disappearance of these neutrinos has been completed, with the results produced being complementary with dedicated oscillation experiments. Following a review of the detector principle and performance, the method used to make these calculations, as well as the results, is detailed. Finally, the future prospects of IceCube-DeepCore and the next generation of neutrino experiments at the South Pole (IceCube-Gen2, specifically the PINGU sub-detector) are briefly discussed

Breast cancer screening, outside the population-screening program, of women from breast cancer families without proven BRCA1/BRCA2 mutations: a simulation study

Purpose: We assessed the cost-effectiveness of mammography screening for women under the age of 50, from breast cancer families without proven BRCA1./BRCA2 mutations, because current criteria for screening healthy women from breast cancer families are not evidence-based. Methods: We did simulation studies with mathematical models on the cost-effectiveness of mammography screening, for women under the age of 50 with breast cancer family histories. Breast cancer screening was simulated with varying screening intervals (6, 12, 18, and 24 months) and screening cohorts (starting at ages 30, 35, 40, and 45, and continuing to age 50). Incremental costs of screening were compared with chose of women ages 50 to 52 years, the youngest age group currently routinely screened in the nationwide screening program of the Netherlands, to determine cost-effectiveness. Sensitivity analyses were done to explore the effects of model assumptions. The cost-effectiveness of breast cancer screening for women over the age of 50 was not debated. Results: The most effective screening interval was found to be 12 months, which, however, seems only to be cost-effective in a small group of women under the age of 50 with at least two affected relatives, including at least one affected in the first degree diagnosed under the age of 50. Significantly, early breast cancer screening never seemed to be cost-effective in women with only one affected first-degree or second-degree relative. Conclusion: Annual breast cancer screening with mammography for women under the age of 50 seems to be cost-effective in women with strong family histories of breast cancer, even when no BRCA1/BRCA2 mutation was found in affected family members