Search

The Jordan-Kinderlehrer-Otto (JKO) scheme is a procedure for finding time-discrete approximations to solutions of diffusion equations using variational problems involving the optimal transportation problem. On the other hand, the Harnack inequality is a well-known inequality in the regularity theory of second-order elliptic and parabolic equations. In this paper, we establish a link between Harnack inequalities and the JKOscheme by establishing a version of theHarnack inequality for the time-discrete approximations mentioned above in the case of the heat equation on the flat torus. [ABSTRACT FROM AUTHOR]

We prove continuity of certain cost functions arising from optimal control of affine control systems. We give sharp sufficient conditions for this continuity. As an application, we prove a version of weak KAM theorem and consider the Aubry–Mather problems corresponding to these systems. [ABSTRACT FROM AUTHOR]

Metabolic control analysis (MCA) provides a quantitative description of substrate flux in response to changes in system parameters of complex enzyme systems. Medical applications of the approach include the following: understanding the threshold effect in the manifestation of metabolic diseases; investigating the gene dose effect of aneuploidy in inducing phenotypic transformation in cancer; correlating the contributions of individual genes and phenotypic characteristics in metabolic disease (e.g., diabetes); identifying candidate enzymes in pathways suitable as targets for cancer therapy; and elucidating the function of "silent" genes by identifying metabolic features shared with genes of known pathways. MCA complements current studies of genomics and proteomics, providing a link between biochemistry and functional genomics that relates the expression of genes and gene products to cellular biochemical and physiological events. Thus, it is an important tool for the study of genotype-phenotype correlations. It allows genes to be ranked according to their importance in controlling and regulating cellular metabolic networks. We can expect that MCA will have an increasing impact on the choice of targets for intervention in drug discovery. [ABSTRACT FROM AUTHOR]