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Unfortunately the Volterra kernels are not orthogonal to each other (i.e., in the response, the n-th order interaction of the previous inputs is described by all kernels of order n or higher), and thus their estimation requires the simultaneous solution of a set of integral equations.
In the following, each of the three inputs is described.
The dynamics of AT1RGRN inputs are given in the Additional file 1, and the conversion between experimentally measured kinase dynamics and AT1RGRN model inputs is described in Normalization below.
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Several periodic inputs are described and compared.
A full list of scenarios is available in the Appendix, and the scenario inputs are described in more detail in the next section.
The basic characteristics of the model and the needed inputs are described in Section 2. The results are presented in Section 3 and discussed in Section 4. The HYB-Mars model is described in detail in the paper by Kallio et al. (2010) and references therein.
To account for the uncertainty associated with the cost estimates, inputs were described using probability distributions.
To capture the uncertainty associated with the estimates, inputs were described using probability distributions that captured the range (minimum, maximum) and most likely value.
In this section, the algorithm used for calculating seawater electrical conductivity from temperature, salinity, and pressure is first presented, and then the data serving as input is described.
Experimental results indicate that with an accurate model of the process energy balance, in which, for example, the recycle pump energy input is described, the Kalman filter approach is found to provide excellent prediction of conversion, for both high and low conversions, for this pilot-plant reactor system.
Recurrent electrical input is described by gse, where gs represents the strength of recurrent connectivity.
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