The spatial scan statistic is one of the main epidemiological tools to test for the presence of disease clusters in a geographical region. While the statistical significance of the most likely cluster is correctly assessed using the model assumptions, secondary clusters tend to have conservatively highP-values. In this paper, we propose a sequential version of the spatial scan statistic to adjust for the presence of other clusters in the study region. The procedure removes the effect due to the more likely clusters on less significant clusters by sequential deletion of the previously detected clusters. Using the Northeastern United States geography and population in a simulation study, we calculated the type I error probability and the power of this sequential test under different alternative models concerning the locations and sizes of the true clusters. The results show that the type I error probability of our method is close to the nominalαlevel and that for secondary clusters its power is higher than the standard unadjusted scan statistic.

Nonradiative charge recombination comprises a main pathway for energy losses that impedes the performance of all-inorganic perovskite solar cells. Grain boundaries (GBs) defects are unavoidable in low-temperature solution-processed perovskite polycrystalline films, but their role remains unclear. By performing ab initio nonadiabatic (NA) molecular dynamics simulations, we illustrate that electron–hole recombination in CsPbBr3 takes place over 100 ps, achieving a good agreement with experiment. Introduction of GBs into CsPbBr3 accelerates the recombination, while GBs doping with chlorine notably slow it down. Importantly, GBs do not create deep electron traps because they only narrow the band gap slightly. GBs localize electron wave functions at boundaries and activate additional phonon modes, leading to an enhanced NA coupling and a shortened coherence time. Consequently, the interplay between the three competitive factors accelerates the recombination by a factor of 2. Chlorine doping diminishes the mixing of electron and hole wave functions and reduces the NA coupling, which also shortens the coherence time further by introducing higher-frequency phonons, notably delaying the recombination. Our study establishes the atomistic mechanism that the acceleration and retardation in electron–hole recombination induced by GBs and chlorine doping in CsPbBr3 perovskite, providing new insights to improve the material properties via passivating the GB by chemical doping.

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We present insights into the role of vacancies and surface states in the d0 ferromagnetism of ZnS nanostructures.

In this article, multiple scan statistics of variable window sizes are derived for independent and identically distributed 0-1 Bernoulli trials. Both one and two dimensional, as well as, conditional and unconditional cases are treated. The advantage in using multiple scan statistics, as opposed to single fixed window scan statistics, is that they are more sensitive in detecting a change in the underlying distribution of the observed data. We show how to derive simple approximations for the significance level of these testing procedures and present numerical results to evaluate their performance.Combining test statistics, one-dimensional scan statistics, p-values, two-dimensional scan statistics, variable windows,