Weak perturbations of the p-Laplacian

We consider the p-Laplacian in R^d perturbed by a weakly coupled potential. We calculate the asymptotic expansions of the lowest eigenvalue of such an operator in the weak coupling limit separately for p>d and p=d and discuss the connection with Sobolev interpolation inequalities.Comment: 20 page

High-resolution electron microscopy of dislocation ribbons in a CMSX-4 superalloy single crystal

High-resolution scanning transmission electron microscopy (STEM) has been used to study the structure of dislocations in single crystal superalloy samples that have been subjected to conditions that favour the primary creep regime. The study has revealed the detailed structure of extended a2〈112〉 dislocations as they shear the γ′ precipitates during creep. These dislocations dissociate in a manner that is consistent with predictions made using the phase-field model of dislocations and also suggests the importance of the reordering process during their movement. The shearing done by the a〈1 1 2〉 dislocations was also found to distort the γ/γ′ interface, changing its appearance from linear to a "saw tooth" pattern. Another important observation was the segregation of alloying elements with a high atomic mass to the stacking faults, presumably to reduce their energies during shear. Numerous a2〈110〉 dissociated dislocations were also observed in the γ channels of the superalloy. The high resolution provided by the STEM imaging enables one to study the high-energy faults that are usually difficult to observe in conventional weak-beam TEM, such as complex intrinsic and extrinsic stacking faults in the γ′ and intrinsic stacking faults in the γ, and to make estimates of their energies

Repeated reunions and splits feature the highly dynamic evolution of 5S and 35S ribosomal RNA genes (rDNA) in the Asteraceae family

<p>Abstract</p> <p>Background</p> <p>In flowering plants and animals the most common ribosomal RNA genes (rDNA) organisation is that in which 35S (encoding 18S-5.8S-26S rRNA) and 5S genes are physically separated occupying different chromosomal loci. However, recent observations established that both genes have been unified to a single 35S-5S unit in the genus <it>Artemisia </it>(Asteraceae), a genomic arrangement typical of primitive eukaryotes such as yeast, among others. Here we aim to reveal the origin, distribution and mechanisms leading to the linked organisation of rDNA in the Asteraceae by analysing unit structure (PCR, Southern blot, sequencing), gene copy number (quantitative PCR) and chromosomal position (FISH) of 5S and 35S rRNA genes in ~200 species representing the family diversity and other closely related groups.</p> <p>Results</p> <p>Dominant linked rDNA genotype was found within three large groups in subfamily Asteroideae: tribe Anthemideae (93% of the studied cases), tribe Gnaphalieae (100%) and in the "Heliantheae alliance" (23%). The remaining five tribes of the Asteroideae displayed canonical non linked arrangement of rDNA, as did the other groups in the Asteraceae. Nevertheless, low copy linked genes were identified among several species that amplified unlinked units. The conserved position of functional 5S insertions downstream from the 26S gene suggests a unique, perhaps retrotransposon-mediated integration event at the base of subfamily Asteroideae. Further evolution likely involved divergence of 26S-5S intergenic spacers, amplification and homogenisation of units across the chromosomes and concomitant elimination of unlinked arrays. However, the opposite trend, from linked towards unlinked arrangement was also surmised in few species indicating possible reversibility of these processes.</p> <p>Conclusions</p> <p>Our results indicate that nearly 25% of Asteraceae species may have evolved unusual linked arrangement of rRNA genes. Thus, in plants, fundamental changes in intrinsic structure of rDNA units, their copy number and chromosomal organisation may occur within relatively short evolutionary time. We hypothesize that the 5S gene integration within the 35S unit might have repeatedly occurred during plant evolution, and probably once in Asteraceae.</p

Endogenous pararetrovirus sequences associated with 24 nt small RNAs at the centromeres of Fritillaria imperialis L. (Liliaceae), a species with a giant genome

Funded by: Leonardo da Vinci programme, Marie Curie programme, Natural Environment Research Council. Grant Number: NE/G01724/1, Czech Science Foundation. Grant Number: P501/13/10057S

Measuring enzyme activity in single cells

Seemingly identical cells can differ in their biochemical state, function and fate, and this variability plays an increasingly recognized role in organism-level outcomes. Cellular heterogeneity arises in part from variation in enzyme activity, which results from interplay between biological noise and multiple cellular processes. As a result, single-cell assays of enzyme activity, particularly those that measure product formation directly, are crucial. Recent innovations have yielded a range of techniques to obtain these data, including image-, flow- and separation-based assays. Research to date has focused on easy-to-measure glycosylases and clinically-relevant kinases. Expansion of these techniques to a wider range and larger number of enzymes will answer contemporary questions in proteomics and glycomics, specifically with respect to biological noise and cellular heterogeneity