Local maximum points of explicitly quasiconvex functions

This work concerns generalized convex real-valued functions defined on a nonempty convex subset of a real topological linear space. Its aim is twofold: first, to show that any local maximum point of an explicitly quasiconvex function is a global minimum point whenever it belongs to the intrinsic core of the function’s domain and second, to characterize strictly convex normed spaces by applying this property for a particular class of convex functions

The role of duality in optimization problems involving entropy functionals with applications to information theory

We consider infinite-dimensional optimization problems involving entropy-type functionals in the objective function as well as as in the constraints. A duality theory is developed for such problems and applied to the reliability rate function problem in information theory.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45233/1/10957_2004_Article_BF00939682.pd

Cross activity of orthologous WRKY transcription factors in wheat and Arabidopsis

WRKY proteins are transcription factors involved in many plant processes including plant responses to pathogens. Here, the cross activity of TaWRKY78 from the monocot wheat and AtWRKY20 from the dicot Arabidopsis on the cognate promoters of the orthologous PR4-type genes wPR4e and AtHEL of wheat and Arabidopsis, respectively, was investigated. In vitro analysis showed the ability of TaWRKY78 to bind a –17/+80 region of the wPR4e promoter, containing one cis-acting W-box. Moreover, transient expression analysis performed on both TaWRKY78 and AtWRKY20 showed their ability to recognize the cognate cis-acting elements present in the wPR4e and AtHEL promoters, respectively. Finally, this paper provides evidence that both transcription factors are able to cross-regulate the orthologous PR4 genes with an efficiency slightly lower than that exerted on the cognate promoters. The observation that orthologous genes are subjected to similar transcriptional control by orthologous transcription factors demonstrates that the terminal stages of signal transduction pathways leading to defence are conserved and suggests a fundamental role of PR4 genes in plant defence. Moreover, these results corroborate the hypothesis that gene orthology imply similar gene function and that diversification between monocot and dicot has most likely occurred after the specialization of WRKY function