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Despite the model dynamics, the actuation dynamics and constrains, and the environmental disturbances, the presented results are promising.
Modeling and optimization of complex systems traditionally have required significant programming efforts in order to encode the model dynamics, the cost functions and the constraints in a format suitable for state of the art numerical algorithms.
In this paper, the over-fitting problem can be relieved by embedding the model dynamics, the mass and energy balance constraints into our constrained optimization algorithms.
Let us note that when few parameters are identified as relevant for model dynamics, the previous analysis is performed for each of them trying to discover multiple dependencies.
To illustrate the model dynamics the set of differential equations were solved numerically using Matlab 7.0 software (R2007) with the robust implicit scheme "ode15s" (employing a modified backward Euler method; Shampine and Reichelt, 1997).
Hence, the approach should be robust subject to noise; third, it needs to be flexible enough for adding/removing physical constraints, such as model dynamics, the mass and energy balance constraints.
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The analysis of the model dynamics on the proposed time scales has allowed for the observation of some theoretical findings known from the behavioral economics [34 38], and which are impossible to observe when analyzing the model dynamics on the traditional homogeneous time scales (that is, with (muequiv mathrm{const.})).}
It should be noted that in several of these examples the original references only describe the model dynamics, not the full parameter estimation problems.
To account for model sensitivity to individual parameters, Latin hypercube sampling (LHS) was used to take many representative samples of the model dynamics across the parameter space.
We now examine the model dynamics at the prostate growth level.
The analysis of model dynamics for the bystander cells revealed that the number of arrested cells did not increase linearly with dose.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com