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On parameter estimation in an in vitro compartmental model for drug-induced enzyme production in pharmacotherapy

Jurjen Duintjer Tebbens, Ctirad Matonoha, Andreas Matthios, Štěpán Papáček (2019)

Applications of Mathematics

A pharmacodynamic model introduced earlier in the literature for in silico prediction of rifampicin-induced CYP3A4 enzyme production is described and some aspects of the involved curve-fitting based parameter estimation are discussed. Validation with our own laboratory data shows that the quality of the fit is particularly sensitive with respect to an unknown parameter representing the concentration of the nuclear receptor PXR (pregnane X receptor). A detailed analysis of the influence of that parameter...

On phase segregation in nonlocal two-particle Hartree systems

Walter Aschbacher, Marco Squassina (2009)

Open Mathematics

We prove the phase segregation phenomenon to occur in the ground state solutions of an interacting system of two self-coupled repulsive Hartree equations for large nonlinear and nonlocal interactions. A self-consistent numerical investigation visualizes the approach to this segregated regime.

On polynomial robustness of flux reconstructions

Miloslav Vlasák (2020)

Applications of Mathematics

We deal with the numerical solution of elliptic not necessarily self-adjoint problems. We derive a posteriori upper bound based on the flux reconstruction that can be directly and cheaply evaluated from the original fluxes and we show for one-dimensional problems that local efficiency of the resulting a posteriori error estimators depends on p 1 / 2 only, where p is the discretization polynomial degree. The theoretical results are verified by numerical experiments.

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