A number of groups have reported that the stress-induced leakage current (SILC) follows a power law dependence on the stress time. In this study, we observed that the power-law behavior is only an approximation of the fast rising part of a more complex behavior. SILC rises during initial stress stage and saturates after long stress time. Based on the trap-assisted tunneling (TAT) model, we show that the stress time dependence of SILC is better described as the depletion of multi-precursors of traps. Although the new model involves many fitting parameters, we show that the fitting results are consistent with the physical interpretation of these parameters. To further support the physical interpretation, we examined these parameters with annealing experiments.
Variance is a popular and often necessary component of aggregation queries. It is typically used as a secondary measure to ascertain statistical properties of the result such as its error. Yet, it is more expensive to compute than primary measures such as SUM, MEAN, and COUNT. There exist numerous techniques to compute variance. While the definition of variance implies two passes over the data, other mathematical formulations lead to a single-pass computation. Some single-pass formulations, however , can suffer from severe precision loss, especially for large datasets. In this paper, we study variance implementations in various real-world systems and find that major database systems such as PostgreSQL 9.4 and most likely System X, a major commercial closed-source database, use a representation that is efficient, but suffers from floating point precision loss resulting from catastrophic cancellation. We review literature over the past five decades on variance calculation in both the statistics and database communities, and summarize recommendations on implementing variance functions in various settings, such as approximate query processing and large-scale distributed aggregation. Interestingly, we recommend using the mathematical formula for computing variance if two passes over the data are acceptable due to its precision, paral-lelizability, and surprisingly computation speed.
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