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Equilibrium of maximal monotone operator in a given set

100%
Zagrodny D.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2000
|
tom 20
|
nr 2
159-169
EN
Sufficient conditions for an equilibrium of maximal monotone operator to be in a given set are provided. This partially answers to a question posed in [10].
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Coupled analytical and numerical approach to uncovering new regulatory mechanisms of intracellular processes

100%
Śmieja J.
International Journal of Applied Mathematics and Computer Science
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2010
|
tom 20
|
nr 4
781-788
EN
The paper deals with the analysis of signaling pathways aimed at uncovering new regulatory processes regulating cell responses. First, general issues of comparing simulation and experimental data are discussed, and various aspects of data normalization are covered. Then, a model of a particular signaling pathway, induced by Interferon-β, is briefly introduced. It serves as an example illustrating how mathematical modeling can be used for inferring the structure of a regulatory system governing the dynamics of intracellular processes. In this pathway, experimental results suggest that a hitherto unknown process is responsible for a decrease in the levels of one of the important molecules used in the pathway. Then, equilibrium points of the model are analyzed, allowing the rejection of all but one explanation of the phenomena observed experimentally. Numerical simulations confirm that the model can mimic the dynamics of the processes in the pathway under consideration. Finally, some remarks about the applicability of the method based on an analysis of equilibrium points are made.
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