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The reduction in dimensions is necessary to decrease the degrees of freedom otherwise the computation times would increase to an unreasonable high.
However, as far as we know, there has been not any paper that the POD technique is used to decrease the degrees of freedom in the classical FDCN scheme for the 2D Sobolev equation.
A lot of numerical simulations (see, e.g., [15 28]) have verified that the proper orthogonal decomposition (POD) technique is a very effective approach to decrease the degrees of freedom for numerical models and alleviate the truncated error amassing in the numerical calculation.
Thus we observe that high mutation rates decrease the degrees of freedom and thereby restrict the chance of finding an individual based solution.
Adjusting for covariates with little variability would have produced imprecise estimates and decrease the degrees of freedom (which were critical, considering our small sample size).
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The receiver can be spatially isolated from the transmitter by leveraging multi-antenna beamforming to avoid self-interference, but such beamforming can also decrease the degrees-of-freedom of the intended uplink and downlink channels.
Measures taken since the late 1980s, however, have begun to decrease the degree of state control of economic activity.
An alternative planning scenario was proposed to decrease the degree of landscape fragmentation, increase the shape complexity of greenway patches and enhance the landscape connectivity.
To decrease the degree of locus heterogeneity, we analyzed subsets of families with similar clinical and demographic characteristics.
There are several biological factors that can increase or decrease the degree of intoxication when an individual drinks alcohol.
One important effect of random drift is to decrease the degree of heterozygosity in a population over time.
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