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We develop an importance sampling simulation scheme for estimating an extremely small probability of system failure with respect to a time-dependent stochastic system excited by stationary random noise having a specified power spectrum.
"No star we know of has anything but an extremely small probability of entering the inner solar system," says Bailer-Jones.
I show that this leads to an extremely small probability for observing a value of the cosmological constant equal to or greater than what we now measure, in marked contrast with the usual result.
Because of the extremely small probability of the impact (only one in a billion), "the 1999 AN10 matter has no relevance to the 'man-on-the-street' whatsoever," according to Clark Chapman of the Southwestern Research Institute in Boulder.
If one adopts the probabilistic interpretation of the standard theory, this means that even when the measurement process is over, there is a nonzero (even though extremely small) probability of finding its pointer in an arbitrary position, instead of the one corresponding to the registered outcome.
It is obviously true that, for the given wave function, the quantum rules entail that if a measurement were performed the table could be found (with an extremely small probability) to be kilometers far away, but this is not the measurement or the macro-objectification problem of the standard theory.
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It is based on Monte Carlo simulation, however, extremely small probabilities can be estimated with reasonable computational effort.
The author advises practicing sustainable risk management: Never mind that catastrophic risks have extremely small probabilities; build scenarios for them and design strategies for surviving them anyway.
Following the recommendations presented in [35], we implemented our own HMM framework by using logarithms of probabilities, in order to handle in a numerically stable manner the extremely small probabilities that appear for relatively long observation sequences.
As shown in Fig. 8, there're five kinds of power output representatives with the highest occurrence probabilities, the corresponding output of 0.05, 0.1, 0.15, 0.2 and 0.25 of the rated output are selected in order to describe the situation more accurately, since a linear output steps would result in a series of useless output states with extremely small probabilities.
Application of pair-HMMs to biological sequence analysis involves computing extremely small probabilities, which decrease exponentially with the sequence length.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com