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Both the linear regressions of increasing annual averages and the evolving probability distribution of the SWH climate, demonstrating the non-stationarity of the Pacific Northwest wave climate, translate into substantial increases in extreme value projections, important in coastal engineering design and in quantifying coastal hazards.

The network (Figure 3) was used to infer the various hidden states (e.g. magmatic unrest or ascent) and calculate an evolving probability of eruption using the sequence of observations made between July 1975 and March 1977 (see Additional file 5 and Figure 5).

For a system initially in a macrostate with Boltzmann entropy SB, and evolving, with probability pi, into a macrostate i with Boltzmann entropy SBi, it is possible that ∑i piSBi < SB (it is even possible that ∀i SBi < SB).

While individual cells may evolve a probability of symmetric division value of 1, they are not expected to remain there.

With more moderate emigration probabilities evolving (μ, σ both low, or intermediate μ and high σ), our simulations predict that endosymbionts reach infection rates beyond 80% in non extinct host or endosymbiont metapopulations (Fig 3A).

According to Eells, the probabilities evolve as follows.

Figure 8 shows how the crossover and mutation probabilities evolve over the generations for the two cases.

We describe a subject's transition probability evolving over time using logistic regression models for his or her past outcomes and covariates.

We assume that these probabilities evolve over slots according to a finite-state Markov chain and thus the steady state is measurable and is denoted by p b, c and p r, c.

The evolving mean population dispersal probabilities approached equilibrium after less than 2000 generations in all simulation experiments.

As suggested by Davoli and de Lange (2011), such significant changes in tumour phenotypes is most likely caused by an enhanced ability of tetraploid tumours to sustain a higher incidence of mutations, thereby increasing the probability of adaptive changes and increasing the probability that evolving tumours will accumulate mutations needed to progress to a malignant state.

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