Mild parametrizations of power-subanalytic sets

We obtain two uniform parametrization theorems for families of bounded sets definable in $\mathbb R_{an}^{\mathbb R}$. Let $X = \{X_t \subset (0,1)^n \mid t \in T\}$ be a definable family of sets $X_t$ of dimension at most $m$. Firstly, $X_t$ admits a $C^r$-parametrization consisting of $cr^m$ maps for some positive constant $c = c(X)$, which is uniform in $t$. Secondly, $X_t$ admits a $C$-mild parametrization for any $C>1$, which is also uniform in $t$

Tomato resistance to Alternaria stem canker: localization in host genotypes and functional expression compared to non-host resistance

The Alternaria stem canker resistance locus (Asc-locus), involved in resistance to the fungal pathogen Alternaria alternata f. sp. lycopersici and in insensitivity to host-specific toxins (AAL-toxins) produced by the pathogen, was genetically mapped on the tomato genome. Susceptibility and resistance were assayed by testing a segregating F2 population for sensitivity to AAL-toxins in leaf bioassays. Linkage was observed to phenotypic markers solanifolium and sunny, both on chromosome 3. For the Asc-locus, a distance of 18 centiMorgan to solanifolium was calculated, corresponding to position 93 on chromosome 3. This map position of the resistance locus turned out to be the same in three different resistant tomato accessions, one Dutch and two American, that are at least 40 years apart. AAL-toxin sensitivity in susceptible and resistant tomato genotypes was compared with AAL-toxin sensitivity in a non-host Nicotiana tabacum during different levels of plant cell development. In susceptible and resistant tomato genotypes, inhibitory effects were demonstrated at all levels, except for leaves of resistant genotypes. However, during pollen and root development, inhibitory effects on susceptible genotypes were larger than on resistant genotypes. In the non-host Nicotiana tabacum, hardly any effects of AAL-toxins were demonstrated. Apparently, a cellular target site is present in tomato, but not in Nicotiana tabacum. It was concluded that three levels of AAL-toxin sensitivity exist: (1) a susceptible host sensitivity, (2) a resistant host sensitivity, (3) a non-host sensitivity, and that the resistance mechanism operating in tomato is different from that operating in Nicotiana tabacum.

Canonical Representations Related to Hyperbolic Spaces

AbstractWe extend the notion of canonical representation, introduced by A. M. Vershik, I. M. Gel'fand and M. I. Graev (1982, in “Representation Theory,” Cambridge Univ. Press, Cambridge, U.K.), to all (classical) rank one semisimple Lie groups. We determine the spectral decomposition of the canonical representations in detail

RASSF4: Regulator of plasma membrane PI(4,5)P2.

Phosphatidylinositol 4,5-bisphosphate (PI(4,5)P2) is a negatively charged phospholipid that plays a major role in recruiting and regulating proteins at the plasma membrane-cytosol interface. In this issue, Chen et al. (2017. J. Cell Biol. https://doi.org/10.1083/jcb.201606047) demonstrate that RAS association domain family 4 (RASSF4) positively influences PI(4,5)P2 synthesis through ARF6-dependent regulation of PIP5K