Zeroth Poisson homology of symmetric powers of isolated quasihomogeneous surface singularities

Let X be a surface with an isolated singularity at the origin, given by the equation Q(x,y,z)=0, where Q is a weighted-homogeneous polynomial. In particular, this includes the Kleinian surfaces X = C^2/G for G < SL(2,C) finite. Let Y be the n-th symmetric power of X. We compute the zeroth Poisson homology of Y, as a graded vector space with respect to the weight grading. In the Kleinian case, this confirms a conjecture of Alev, that the zeroth Poisson homology of the n-th symmetric power of C^2/G is isomorphic to the zeroth Hochschild homology of the n-th symmetric power of the algebra of G-invariant differential operators on C. That is, the Brylinski spectral sequence degenerates in this case. In the elliptic case, this yields the zeroth Hochschild homology of symmetric powers of the elliptic algebras with three generators modulo their center, for the parameter equal to all but countably many points of the elliptic curve.Comment: 17 page

Health-related Quality of Life and Informed Decision-making in Lung Cancer Screening

Lung cancer is worldwide the most common form of cancer and the most common cause of death from cancer. It accounts for approximately 28% of all cancer deaths. World-wide 1.2 million people die from lung cancer each year. In the Netherlands, 9,918 people died from lung cancer in 2008. Lung cancer is often diagnosed in an advanced incurable stage. Despites advances in treatment, 85% or more patients will die within 5 years after diagnosis. In the Netherlands, the mortality-incidence ratio is 95%. Total costs of lung cancer in the Netherlands were estimated to be 193 million euro in 2005

The Role of Land in Economic Theory

Changes in land use and land cover are among the issues central to the study of global environmental change. In addition to their cumulative long-term global dimensions, such changes can have profound regional environmental implications during the life span of current generations. A better understanding of the dynamics in land and water use is thus critical for an informed debate of sustainability. Land use represents a critical intersection of economic and ecological systems. Land-use changes are most often directly linked with economic decisions. This recognition has led LUC to choose an economic framework as the organizing principle, resulting in a broad set of project activities geared towards providing a biophysical and geographical underpinning to the representation of land-based economic sectors in modeling land and water use decisions. This report addresses foremost researchers outside economics and should be viewed as a modest step towards reducing the deficit in transdisciplinary research, which, until now, has permitted only modest advances in closing the gaps between environment and economic analysis. The role of land in economic theory is surveyed, both from a conceptual and historical perspective. Land has been incorporated in economic theories in various ways. Originally, land used by agriculture was the main motivation for an economic treatment of land. This was gradually extended with various other land use categories. Neoclassical core economic theory gave less attention to land use, generally regarding it as a production factor of relatively little importance. Nevertheless specialized sub-fields within economics such as regional and urban economics met the demand for explicit spatial analysis including land use considerations. More recently, attention for environmental and resource problems has provided incentives for new perspectives on, and conceptualization of, land in economic analysis. To some extent, this is based on an interaction with other disciplines as well as on the use of spatially disaggregate methods of analysis

Latent class trees with the three-step approach

Latent class (LC) analysis is widely used in the social and behavioral sciences to find meaningful clusters based on a set of categorical variables. To deal with the common problem that a standard LC analysis may yield a large number classes and thus a solution that is difficult to interpret, recently an alternative approach has been proposed, called Latent Class Tree (LCT) analysis. It involves starting with a solution with a small number of "basic" classes, which may subsequently be split into subclasses at the next stages of an analysis. However, in most LC analysis applications, we not only wish to identify the relevant classes, but also want to see how they relate to external variables (covariates or distal outcomes). For this purpose, researchers nowadays prefer using the bias-adjusted three-step method. Here, we show how this bias-adjusted three-step procedure can be applied in the context of LCT modeling. More specifically, an R-package is presented that performs a three-step LCT analysis: it builds a LCT and allows checking how splits are related to the relevant external variables. The new tool is illustrated using a cross-sectional application with multiple indicators on social capital and demographics as external variables and with a longitudinal application with a mood variable measured multiple times during the day and personality traits as external variables

Building latent class growth trees

Researchers use latent class growth (LCG) analysis to detect meaningful subpopulations that display different growth curves. However, especially when the number of classes required to obtain a good fit is large, interpretation of the encountered class-specific curves might not be straightforward. To overcome this problem, we propose an alternative way of performing LCG analysis, which we call LCG tree (LCGT) modeling. For this purpose, a recursive partitioning procedure similar to divisive hierarchical cluster analysis is used: Classes are split until a certain criterion indicates that the fit does not improve. The advantage of the LCGT approach compared to the standard LCG approach is that it gives a clear insight into how the latent classes are formed and how solutions with different numbers of classes relate. The practical use of the approach is illustrated using applications on drug use during adolescence and mood regulation during the day

Neutrino-Driven Jets and Rapid-Process Nucleosynthesis

We have studied whether the jet in a collapse-driven supernova can be a key process for the rapid-process (r-process) nucleosynthesis. We have examined the features of a steady, subsonic, and rigidly rotating jet in which the centrifugal force is balanced by the magnetic force. As for the models in which the magnetic field is weak and angular velocity is small, we found that the r-process does not occur because the final temperature is kept to be too high and the dynamical timescale becomes too long when the neutrino luminosities are set to be high. Even if the luminosities of the neutrinos are set to be low, which results in the low final temperature, we found that the models do not give a required condition to produce the r-process matter. Furthermore, the amount of the mass outflow seems to be too little to explain the solar-system abundance ratio in such low-luminosity models. As for the models in which the magnetic field is strong and angular velocity is large, we found that the entropy per baryon becomes too small and the dynamical timescale becomes too long. This tendency is, of course, a bad one for the production of the r-process nuclei. As a conclusion, we have to say that it is difficult to cause a successful r-process nucleosynthesis in the jet models in this study.Comment: 34 pages and 6 postscript figures. submitted to Astrophysical Journa

Interdisciplinary design of a pervasive fall handling system

C