Rational tensor product Bézier volumes

AbstractFree form volumes in rational Bézier representation are derived via homogeneous coordinates. Some properties and constructions are presented and two applications of free form volumes are discussed: definition of solid primitives and curve and surface modelling by the way of volume deformation

The costs and benefits of a vaccination programme for Haemophilus influenzae type 8 disease

Haemophilus influenzae type b (Hib) infection is a major cause of severe bacterial infection in young children in South Africa and world-wide. These diseases can be prevented by immunisation with conjugate Hib vaccines. In South Africa, unlike some developed countries, Hib vaccines are not part of the routine immunisation schedule. The objective of this study was to measure the expected net benefits from a hypothetical programme of vaccination of the 1992 Cape Town birth cohort (N =46 537). Costs were calculated by summing the estimated direct medical care costs together with the indirect costs of Hib disease. The latter were calculated by valuing human life using alternative, and conservative human capital and willingness-to-pay measures. The difference between Hib disease costs (Le. the benefits which would be gained from a successful vaccination programme) and the costs of the vaccination programme itself (HibTITER, Praxis Biologicals) defined the expected net benefits. In the absence of an immunisation programme, the estimated economic costs of Hib disease in the 1992 Cape Town cohort ranged from R10,7 million to R11 ,8 million. The costs of introducing the vaccine would have amounted to R8,3 million. Had the vaccine been administered to the 1992 birth cohort, benefits would have exceeded costs by between R2,4 million and R3,5 million

The effect of Massachusetts health reform on 30 day hospital readmissions: retrospective analysis of hospital episode statistics

Objectives: To analyse changes in overall readmission rates and disparities in such rates, among patients aged 18-64 (those most likely to have been affected by reform), using all payer inpatient discharge databases (hospital episode statistics) from Massachusetts and two control states (New York and New Jersey). Design: Difference in differences analysis to identify the post-reform change, adjusted for secular changes unrelated to reform. Setting: US hospitals in Massachusetts, New York, and New Jersey. Participants: Adults aged 18-64 admitted for any cause, excluding obstetrical. Main outcome measure Readmissions at 30 days after an index admission. Results: After adjustment for known confounders, including age, sex, comorbidity, hospital ownership, teaching hospital status, and nurse to census ratio, the odds of all cause readmission in Massachusetts was slightly increased compared with control states post-reform (odds ratio 1.02, 95% confidence interval 1.01 to 1.04, P<0.05). Racial and ethnic disparities in all cause readmission rates did not change in Massachusetts compared with control states. In analyses limited to Massachusetts only, there were minimal overall differences in changes in readmission rates between counties with differing baseline uninsurance rates, but black people in counties with the highest uninsurance rates had decreased odds of readmission (0.91, 0.84 to 1.00) compared with black people in counties with lower uninsurance rates. Similarly, white people in counties with the highest uninsurance rates had decreased odds of readmission (0.96, 0.94 to 0.99) compared with white people in counties with lower uninsurance rates. Conclusions: In the United States, and in Massachusetts in particular, extending health insurance coverage alone seems insufficient to improve readmission rates. Additional efforts are needed to reduce hospital readmissions and disparities in this outcome

Stationary Random Fields on the Unitary Dual of a Compact Group

We generalise the notion of wide-sense stationarity from sequences of complex-valued random variables indexed by the integers, to fields of random variables that are labelled by elements of the unitary dual of a compact group. The covariance is positive definite, and so it is the Fourier transform of a finite central measure (the spectral measure of the field) on the group. Analogues of the Cramer and Kolmogorov theorems are extended to this framework. White noise makes sense in this context and so, for some classes of group, we can construct time series and investigate their stationarity. Finally we indicate how these ideas fit into the general theory of stationary random fields on hypergroups

Semiclassical approximations for Hamiltonians with operator-valued symbols

We consider the semiclassical limit of quantum systems with a Hamiltonian given by the Weyl quantization of an operator valued symbol. Systems composed of slow and fast degrees of freedom are of this form. Typically a small dimensionless parameter $\varepsilon\ll 1$ controls the separation of time scales and the limit $\varepsilon\to 0$ corresponds to an adiabatic limit, in which the slow and fast degrees of freedom decouple. At the same time $\varepsilon\to 0$ is the semiclassical limit for the slow degrees of freedom. In this paper we show that the $\varepsilon$-dependent classical flow for the slow degrees of freedom first discovered by Littlejohn and Flynn, coming from an \epsi-dependent classical Hamilton function and an $\varepsilon$-dependent symplectic form, has a concrete mathematical and physical meaning: Based on this flow we prove a formula for equilibrium expectations, an Egorov theorem and transport of Wigner functions, thereby approximating properties of the quantum system up to errors of order $\varepsilon^2$. In the context of Bloch electrons formal use of this classical system has triggered considerable progress in solid state physics. Hence we discuss in some detail the application of the general results to the Hofstadter model, which describes a two-dimensional gas of non-interacting electrons in a constant magnetic field in the tight-binding approximation.Comment: Final version to appear in Commun. Math. Phys. Results have been strengthened with only minor changes to the proofs. A section on the Hofstadter model as an application of the general theory was added and the previous section on other applications was remove

Tunable variation of optical properties of polymer capped gold nanoparticles

Optical properties of polymer capped gold nanoparticles of various sizes (diameter 3-6 nm) have been studied. We present a new scheme to extract size dependent variation of total dielectric function of gold nanoparticles from measured UV-Vis absorption data. The new scheme can also be used, in principle, for other related systems as well. We show how quantum effect, surface atomic co - ordination and polymer - nanoparticle interface morphology leads to a systematic variation in inter band part of the dielectric function of gold nanoparticles, obtained from the analysis using our new scheme. Careful analysis enables identification of the possible changes to the electronic band structure in such nanoparticles.Comment: 13 pages,7 figures, 1 tabl