In this study, full-genome DNA microarrays based on the sequence of Staphylococcus aureus N315 were used to compare the transcriptome of a clinical S. aureus strain with a normal phenotype to that of its isogenic mutant with a stable small-colony-variant (SCV) phenotype (hemB::ermB). In addition to standard statistical analyses, systems biology advances… (More)
We give a complete characterisation of the sets in which Peano derivatives of functions, which are definable in an o-minimal expansion of a real closed field, are continuously respectively Fréchet differentiable.
Let M be an o-minimal expansion of the real exponential field which possesses smooth cell decomposition. We prove that for every definable open set, the definable indefinitely continuously differentiable functions are a dense subset of the definable continuous function with respect to the o-minimal Whitney topology.
Given an o-minimal expansion M of a real closed field R which is not polynomially bounded. Let P ∞ denote the definable indefinitely Peano differentiable functions. If we further assume that M admits P ∞ cell decomposition , each definable closed set A ⊂ R n is the zero-set of a P ∞ function f : R n → R. This implies P ∞ approximation of definable… (More)
DNA methylation and demethylation are important epigenetic regulatory mechanisms in eukaryotic cells and, so far, only partially understood. We exploit the minimalistic biological ciliate system to understand the crosstalk between DNA modification and chromatin structure. In the macronucleus of these cells, the DNA is fragmented into individual short DNA… (More)
Let M be an o-minimal structure over the real closed field R. We prove the definable smoothing of definable Lipschitz continuous functions. In the case of Lipschitz functions of one variable we are even able to preserve the Lipschitz constant.
Peano differentiability is a notion of higher order differentiability in the ordinary sense. H. W. Oliver gave sufficient conditions for the m th Peano derivative to be a derivative in the ordinary sense in the case of functions of a real variable. Here we generalize this theorem to functions of several variables.
The proof of the Riemann mapping theorem is not constructive. We study versions of it for sets and functions which are definable in an o-minimal expansion of the real field. The diffeomorphisms between the subsets and the unit-ball can be chosen definable if we only request them to be continuously differentiable. For many structures expanding the real… (More)
We present a canonical proof of both the strict and weak Posi-tivstellensatz for rings of differentiable and smooth functions. The construction preserves definability in expansions of the real field, and it works in definably complete expansions of real closed fields as well as for real-valued functions on Banach spaces.