Adaptive density estimation under dependence

Assume that $(X_t)_{t\in\Z}$ is a real valued time series admitting a common marginal density $f$ with respect to Lebesgue's measure. Donoho {\it et al.} (1996) propose a near-minimax method based on thresholding wavelets to estimate $f$ on a compact set in an independent and identically distributed setting. The aim of the present work is to extend these results to general weak dependent contexts. Weak dependence assumptions are expressed as decreasing bounds of covariance terms and are detailed for different examples. The threshold levels in estimators $\widehat f_n$ depend on weak dependence properties of the sequence $(X_t)_{t\in\Z}$ through the constant. If these properties are unknown, we propose cross-validation procedures to get new estimators. These procedures are illustrated via simulations of dynamical systems and non causal infinite moving averages. We also discuss the efficiency of our estimators with respect to the decrease of covariances bounds

Spin relaxation in nn-type ZnO quantum wells

We perform an investigation on the spin relaxation for $n$-type ZnO (0001) quantum wells by numerically solving the kinetic spin Bloch equations with all the relevant scattering explicitly included. We show the temperature and electron density dependence of the spin relaxation time under various conditions such as impurity density, well width, and external electric field. We find a peak in the temperature dependence of the spin relaxation time at low impurity density. This peak can survive even at 100 K, much higher than the prediction and measurement value in GaAs. There also exhibits a peak in the electron density dependence at low temperature. These two peaks originate from the nonmonotonic temperature and electron density dependence of the Coulomb scattering. The spin relaxation time can reach the order of nanosecond at low temperature and high impurity density.Comment: 6 pages, 4 figure

Wildlife disease elimination and 1 density dependence

Disease control by managers is a crucial response to emerging wildlife epidemics, yet the means of control may be limited by the method of disease transmission. In particular, it is widely held that population reduction, while effective for controlling diseases that are subject to density-dependent transmission, is ineffective for controlling diseases that are subject to frequency-dependent transmission. We investigate control for horizontally transmitted diseases with frequency-dependent transmission where the control is via nonselective (for infected animals) culling or harvesting and the population can compensate through density-dependent recruitment or survival. Using a mathematical model, we show that culling or harvesting can eradicate the disease, even when transmission dynamics are frequency-dependent. E 24 radication can be achieved under frequency-dependent transmission when density-dependent population regulation induces compensatory growth of new, healthy individuals, which has the net effect of reducing disease prevalence by dilution. We also show that if harvest is used simultaneously with vaccination and there is high enough transmission coefficient, application of both controls may be less efficient than when vaccination alone is used. We illustrate the effects of these control approaches on disease prevalence using assumed parameters for chronic wasting disease in deer where the disease is transmitted directly among deer and through the environment