The results show that if the length of the initial occupying area is longer than a critical size for the predators or the length of the initial occupying area is shorter than a critical size, but the moving coefficient of free boundary is relatively big, then the spreading of predators always happens under relatively small rate of death for the predator.
On the other hand, it is found that if the initial value of free boundary is smaller than a threshold value and the moving coefficient of free boundary is relatively small depending on initial size of predator or the rate of death is relatively big, the predators fail in spreading to new environment.
To provide additional information related with the discussion, two new set of data are worked out: (1) significant wave height obtained in the Gulf of Cádiz (hindcast data, WANA 1952046) with extremal index 0.32, and (2) a simulated series with an ARMA model, autoregressive coefficient 0.95, zero moving average coefficient and an extremal index equal to 0.3.
b Moving correlation coefficient of two color profiles, calculated for a 20 m window with width indicated by orange bar.
The residuals are obtained starting from the same model (nabla hbox {TICD}_{t}=e_{t}+0.4995e_{t-1}), by writing (e_{t}=nabla hbox {TICD}_{t}-0.4995e_{t-1}) where the cell V49 contains the moving average coefficient 0.4995.
The null hypothesis of interest is (H_{0}:psi _{f}=0), so that the model under the null is a univariate Ar(1) white noise process, while the signal under the alternative is an Arma 1, 1) instead with moving average coefficient (psi _{f}).
The null hypothesis of interest is (H_{0}:delta _{f}=0), so that the model under the null is still a random walk signal plus white noise, while the signal under the alternative is an Ima 1, 2) with second moving average coefficient (delta _{f}).
The null hypothesis of interest is (H_{0}:psi _{f}=0), so that the model under the null is still a random walk signal plus white noise, while the signal under the alternative is an Ima 1, 1) with moving average coefficient ( psi _{f}).
where ϕ(L =1−ϕ 1 L−ϕ 2 L 2−ϕ 3 L 3−⋯−ϕ p L p and θ(L =1−θ 1 L−θ 2 L 2−θ 3 L 3−⋯−θ p L q. (B^_{l}) is the correlated normally distributed random variable, e l is an uncorrelated Gaussian noise, θ l is moving average coefficient, and L is the lag operator.
Cerebrovascular autoregulation was assessed by calculating a moving correlation coefficient (the index of cerebrovascular autoregulation, Mx) between MAP and FV as described previously [ 19].
A cerebrovascular pressure reactivity index (PRx) can be determined as the moving correlation coefficient between the mean intracranial pressure (ICP) and mean arterial blood pressure.
