Existence and uniqueness of relative incidence estimates in case-series analysis

Case-series analysis is used to estimate relative incidences of clinical events in defined time intervals after vaccination compared to a control period. It has advantages, in terms of both a reduction in data collection effort, because it uses only data on cases, and a reduction in the resultant variances of estimates, due to individuals being self-controlled. The existence and uniqueness of relative incidence estimates in case-series analysis are investigated. For the relative incidence of a clinical event, a simple condition for existence and uniqueness of the estimate of the parameter vector in a case-series model is established. An algorithm is developed to examine the established condition, which provides a clue for remedy when the condition for existence and uniqueness is not satisfied

Asymptotic behavior of the growth-fragmentation equation with bounded fragmentation rate

We are interested in the large time behavior of the solutions to the growth-fragmentation equation. We work in the space of integrable functions weighted with the principal dual eigenfunction of the growth-fragmentation operator. This space is the largest one in which we can expect convergence to the steady size distribution. Although this convergence is known to occur under fairly general conditions on the coefficients of the equation, we prove that it does not happen uniformly with respect to the initial data when the fragmentation rate in bounded. First we get the result for fragmentation kernels which do not form arbitrarily small fragments by taking advantage of the Dyson-Phillips series. Then we extend it to general kernels by using the notion of quasi-compactness and the fact that it is a topological invariant

Understanding the bulk electronic structure of Ca1-xSrxVO3

We investigate the electronic structure of Ca1-xSrxVO3 using careful state-of-the-art experiments and calculations. Photoemission spectra using synchrotron radiation reveal a hitherto unnoticed polarization dependence of the photoemission matrix elements for the surface component leading to a substantial suppression of its intensity. Bulk spectra extracted with the help of experimentally determined electron escape depth and estimated suppression of surface contributions resolve outstanding puzzles concerning the electronic structure in Ca1-xSrxVO3.Comment: 4 pages including 3 figure

Three-dimensional quasi-periodic shifted Green function throughout the spectrum--including Wood anomalies

This work presents an efficient method for evaluation of wave scattering by doubly periodic diffraction gratings at or near "Wood anomaly frequencies". At these frequencies, one or more grazing Rayleigh waves exist, and the lattice sum for the quasi-periodic Green function ceases to exist. We present a modification of this sum by adding two types of terms to it. The first type adds linear combinations of "shifted" Green functions, ensuring that the spatial singularities introduced by these terms are located below the grating and therefore outside of the physical domain. With suitable coefficient choices these terms annihilate the growing contributions in the original lattice sum and yield algebraic convergence. Convergence of arbitrarily high order can be obtained by including sufficiently many shifts. The second type of added terms are quasi-periodic plane wave solutions of the Helmholtz equation which reinstate certain necessary grazing modes without leading to blow-up at Wood anomalies. Using the new quasi-periodic Green function, we establish, for the first time, that the Dirichlet problem of scattering by a smooth doubly periodic scattering surface at a Wood frequency is uniquely solvable. We also present an efficient high-order numerical method based on the this new Green function for the problem of scattering by doubly periodic three-dimensional surfaces at and around Wood frequencies. We believe this is the first solver in existence that is applicable to Wood-frequency doubly periodic scattering problems. We demonstrate the proposed approach by means of applications to problems of acoustic scattering by doubly periodic gratings at various frequencies, including frequencies away from, at, and near Wood anomalies