Polarizations and Nullcone of Representations of Reductive Groups

The paper starts with the following simple observation. Let V be a representation of a reductive group G, and let f_1,f_2,...,f_n be homogeneous invariant functions. Then the polarizations of f_1,f_2,...,f_n define the nullcone of k 0} h(t) x = 0 for all x in L. This is then applied to many examples. A surprising result is about the group SL(2,C) where almost all representations V have the property that all linear subspaces of the nullcone are annihilated. Again, this has interesting applications to the invariants on several copies. Another result concerns the n-qubits which appear in quantum computing. This is the representation of a product of n copies of $SL_2$ on the n-fold tensor product C^2 otimes C^2 otimes ... otimes C^2. Here we show just the opposite, namely that the polarizations never define the nullcone of several copies if n <= 3. (An earlier version of this paper, distributed in 2002, was split into two parts; the first part with the title ``On the nullcone of representations of reductive groups'' is published in Pacific J. Math. {bf 224} (2006), 119--140.

A bootstrap-based method to achieve optimality on estimating the extreme-value index

Estimators of the extreme-value index are based on a set of upper order statistics. We present an adaptive method to choose the number of order statistics involved in an optimal way, balancing variance and bias components. Recently this has been achieved for the similar but somewhat less involved case of regularly varying tails (Drees and Kaufmann(1997); Danielsson et al.(1996)). The present paper follows the line of proof of the last mentioned paper

Population-based mammography screening below age 50: balancing radiation-induced vs prevented breast cancer deaths

Introduction:Exposure to ionizing radiation at mammography screening may cause breast cancer. Because the radiation risk increases with lower exposure age, advancing the lower age limit may affect the balance between screening benefits and risks. The present study explores the benefit-risk ratio of screening before age 50.Methods:The benefits of biennial mammography screening, starting at various ages between 40 and 50, and continuing up to age 74 were examined using micro-simulation. In contrast with previous studies that commonly used excess relative risk models, we assessed the radiation risks using the latest BEIR-VII excess abso

Overdetection, overtreatment and costs in prostate-specific antigen screening for prostate cancer

Background:Prostate cancer screening with prostate-specific antigen (PSA) has shown to reduce prostate cancer mortality in the European Randomised study of Screening for Prostate Cancer (ERSPC) trial. Overdetection and overtreatment are substantial unfavourable side effects with consequent healthcare costs. In this study the effects of introducing widespread PSA screening is evaluated.Methods:The MISCAN model was used to simulate prostate cancer growth and detection in a simulated cohort of 100 000 men (European standard population) over 25 years. PSA screening from age 55 to 70 or 75, with 1, 2 and 4-year-intervals is simulated. Number of diagnoses, PSA tests, biopsies, treatments, deaths and corresponding costs for 100 000 men and for United Kingdom and United States are compared.Results:Without screening 2378 men per 100 000 were predicted to be diagnosed with prostate cancer compared with 4956 men after screening at 4-year intervals. By introducing screening, the costs would increase with 100% to \[euro]60 695 000. Overdetection is related to 39% of total costs (\[euro]23 669 000). Screening until age 75 is relatively most expensive because of the costs of overtreatment.Conclusion:Introduction of PSA screening will increase total healthcare costs for prostate cancer substantially, of which the actual screening costs will be a small part

Linking ecology to genetics to better understand adaptation and evolution: a review in marine macrophytes

Ecological processes and intra-specific genetic diversity reciprocally affect each other. While the importance of uniting ecological variables and genetic variation to understand species’ plasticity, adaptation, and evolution is increasingly recognized, only few studies have attempted to address the intersection of population ecology and genetics using marine macrophyte as models. Representative empirical case studies on genetic diversity are reviewed that explore ecological and evolutionary processes in marine macrophytes. These include studies on environment-induced phenotypic plasticity and associated ecological adaptation; population genetic variation and structuring driven by ecological variation; and ecological consequences mediated by intraspecific and interspecific diversity. Knowledge gaps are also discussed that impede the connection of ecology and genetics in macrophytes and possible approaches to address these issues. Finally, an eco-evolutionary perspective is advocated, by incorporating structural-tofunctional genomics and life cycle complexity, to increase the understanding of the adaptation and evolution of macrophytes in response to environmental heterogeneity.info:eu-repo/semantics/publishedVersio

To be screened or not to be screened Modeling the consequences of PSA screening for the individual

Background:Screening with prostate-specific antigen (PSA) can reduce prostate cancer mortality, but may advance diagnosis and treatment in time and lead to overdetection and overtreatment. We estimated benefits and adverse effects of PSA screening for individuals who are deciding whether or not to be screened.Methods:Using a microsimulation model, we estimated lifetime probabilities of prostate cancer diagnosis and death, overall life expectancy and expected time to diagnosis, both with and without screening. We calculated anticipated loss in quality of life due to prostate cancer diagnosis and treatment that would be acceptable to decide in favour of screening.Results:Men who were screened had a gain in life expectancy of 0.08 years but their expected time to diagnosis decreased by 1.53 life-years. Of the screened men, 0.99% gained on average 8.08 life-years and for 17.43% expected time to diagnosis decreased by 8.78 life-years. These figures imply that the anticipated loss in quality of life owing to diagnosis and treatment should not exceed 4.8%, for screening to have a positive effect on quality-adjusted life expectancy.Conclusion:The decision to be screened should depend on personal preferences. The negative impact of screening might be reduced by screening men who are more willing to accept the side effects from treatment

Treatment of local-regional prostate cancer detected by PSA screening: Benefits and harms according to prognostic factors

Background:Men with screen-detected prostate cancer can choose to undergo immediate curative treatment or enter into an expectant management programme. We quantified how the benefits and harms of immediate treatment vary according to the prognostic factors of clinical T-stage, Gleason score, and patient age.Methods:A microsimulation model based on European Randomized Study of Screening for Prostate Cancer data was used to predict the benefits and harms of immediate treatment versus delayed treatment of local-regional prostate cancer in men aged 55-74 years. Benefits included life-years gained and reduced probability of death from prostate cancer. Harms included lead time and probability of overdiagnosis.Results:The ratio of mean lead time to mean life-years gained ranged from 1.8 to 31.2, and the additional number of treatments required per prostate cancer death prevented ranged from 0.3 to 11.6 across the different prognostic groups. Both harm-benefit ratios were lowest, most favourable, for men aged 55-59 years and diagnosed with moderate-risk prostate cancer. Ratios were high for men aged 70-74 years regardless of clinical T-stage and Gleason score.Conclusion:Men aged 55-59 years with moderate-risk prostate cancer are predicted to derive greatest benefit from immediate curative treatment. Immediate treatment is least favourable for men aged 70-74 years with either low-risk or high-risk prostate cancer