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The probabilistic approach allows one to capture the temporal behaviour of queues, and to measure the uncertainty of a queue state prediction by computing the evolution of its probability in time, assumed any temporal distribution of the arrivals.
The parallel model represents the classical relaxation of a large assembly of individual relaxing entities such as dipoles, each of which relaxes with an exponential probability in time but has a different relaxation time t k.
Here we obtained results by integration of the probability in time
We started by simulating the XCI process in XX diploid female ES cells throughout a 10 day differentiation period, using a fixed probability in time to run the simulations, and compared the resulting distributions with experimental data obtained with differentiating XX female ES cells.
Since at the early stage of the epidemic there are usually large fluctuations in the number of imported local transmission cases, we measure the probability in time of observing a given ratio Q by averaging over 2,000 realization of the global simulation.
The phase distribution exhibited by isolated spikes may equally be interpreted as a modulation of the spiking probability in time.
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Other estimators for the concordance probability in time-to-event data can be found in Gönen and Heller [ 26] and Uno et al [ 27].
In a different approach, we used the same probabilities in time for diploid female XX cells in a mathematical model, and obtained distributions of different cell populations that supported our findings with the stochastic simulations (Text S1, and Figure S1B).
The program allows the use of different probabilities in time, a different number of X chromosomes per cell, and a different rate of cell division depending on the number of Xi's.
The change of transition probabilities in time was evaluated, e.g. the probability of continuing ICS use of starters in the first two years (51%) of follow-up increased to more than 70% in the following years.
This is a standard procedure in computational studies of learning processes that require inference on conditional probabilities in time series (cf. Behrens et al. 2007; Daunizeau, den Ouden, Pessiglione, Kiebel, Friston et al. 2010).
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