Efficient estimation of AUC in a sliding window

In many applications, monitoring area under the ROC curve (AUC) in a sliding window over a data stream is a natural way of detecting changes in the system. The drawback is that computing AUC in a sliding window is expensive, especially if the window size is large and the data flow is significant. In this paper we propose a scheme for maintaining an approximate AUC in a sliding window of length $k$. More specifically, we propose an algorithm that, given $\epsilon$, estimates AUC within $\epsilon / 2$, and can maintain this estimate in $O((\log k) / \epsilon)$ time, per update, as the window slides. This provides a speed-up over the exact computation of AUC, which requires $O(k)$ time, per update. The speed-up becomes more significant as the size of the window increases. Our estimate is based on grouping the data points together, and using these groups to calculate AUC. The grouping is designed carefully such that ($i$) the groups are small enough, so that the error stays small, ($ii$) the number of groups is small, so that enumerating them is not expensive, and ($iii$) the definition is flexible enough so that we can maintain the groups efficiently. Our experimental evaluation demonstrates that the average approximation error in practice is much smaller than the approximation guarantee $\epsilon / 2$, and that we can achieve significant speed-ups with only a modest sacrifice in accuracy

CO observations and investigation of triggered star formation towards N10 infrared bubble and surroundings

We studied the environment of the dust bubble N10 in molecular emission. Infrared bubbles, first detected by the GLIMPSE survey at 8.0 $\mu$m, are ideal regions to investigate the effect of the expansion of the HII region on its surroundings eventual triggered star formation at its borders. In this work, we present a multi-wavelength study of N10. This bubble is especially interesting as infrared studies of the young stellar content suggest a scenario of ongoing star formation, possibly triggered, on the edge of the HII region. We carried out observations of $^{12}$CO(1-0) and $^{13}$CO(1-0) emission at PMO 13.7-m towards N10. We also analyzed the IR and sub-mm emission on this region and compare those different tracers to obtain a detailed view of the interaction between the expanding HII region and the molecular gas. We also estimated the parameters of the denser cold dust condensation and of the ionized gas inside the shell. Bright CO emission was detected and two molecular clumps were identified, from which we have derived physical parameters. We also estimate the parameters for the densest cold dust condensation and for the ionized gas inside the shell. The comparison between the dynamical age of this region and the fragmentation time scale favors the "Radiation-Driven Implosion" mechanism of star formation. N10 reveals to be specially interesting case with gas structures in a narrow frontier between HII region and surrounding molecular material, and with a range of ages of YSOs situated in region indicating triggered star formation.Comment: Version 2 - Submmited to ApJ (under review

A NOTE ON TRANSIENT HEAT TRANSFER PROBLEMS WITH TEMPERATURE-DEPENDENT THERMAL CONDUCTIVITY AND THERMAL DIFFUSIVITY

In this work it is presented a numerical procedure for solving transient heat transfer problems in which the thermal diffusivity is strongly dependent on the temperature, with the aid of the Kirchhoff transformation associated to an usual finite difference approach. The first step consists of eliminating the nonlinear terms associated to the derivatives with respect to the position, by means of a Kirchhoff transformation, giving rise to a partial differential equation with only one nonlinear term (involving the coefficient of the derivative with respect to the time). The advance in time is carried out assuming the thermal diffusivity evaluated at a known temperature, giving rise to a semi-implicit scheme. Comparisons between this approach and the usual hypothesis are carried out in order to illustrate the effect of the dependence between the temperature and the thermal diffusivity. Some typical results are presented, based on the (6H-SiC) Silicon Carbide properties

Tropical Homegardens in Riverine Communities of Amazonian Estuary, Marajó Island, Brazil.

Neste trabalho, apresenta-se descrição de quintais tropicais em comunidades ribeirinhas no Estuário amazônico