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In this section, we investigate the influence of a perturbation of initial data to the solutions.
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We present the orbit determination results, focusing on the benefits of adding GPS data to the solution.
In light of the uncertainty inherently presents in experimental data, a combination of Tikhonov regularization and optimal design of experiments (or data selection) is proposed to remedy uncertainty amplification from the data to the solution and circumvent unreliable screening.
A second probe laser aligned parallel to the surface is deflected by these temperature variations, and the thermal diffusivity is then found by fitting amplitude and phase shift data to the solution of the three-dimensional diffusion equation.
Effective oxygen diffusivities in gels (DO2g) and water (DO2w) were obtained after fitting experimental data to the analytical solution (data from side-dot) and the numerical solution (data from bottom-dot) to Fick's second law.
Based on the Bayesian framework, the MCMC method uses the existing data to constrain the solutions, which not only satisfies the statistical characteristics of the inversion parameters but also integrates the prior information to improve the inversion accuracy.
Whereas conventional meshless methods utilize the lowest-order solution data to reconstruct the solution and its derivatives in the neighborhood of the reference node, the present method increases the usage of available information at the nodes by interpolating over nodal set of vector data.
A logical solution for many problems is to clean the data to enhance the solution quality: exploring the data set for possible problems and endeavoring to clean the errors.
In that case, there are not enough GPS code data to calibrate the solution, and additional GLONASS code data allows us to retrieve a correct absolute value for the solution.
The group has so far managed to process just 24 base pairs at a time--the input data added to the solution--and only on artificial DNA.
The analytical solutions are compared with experiment data to show that the solutions accurately predict the sediment height and concentration as a function of time and loading conditions.
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