Comparative dissociation of peptide polyanions by electron impact and photo-induced electron detachment

We compare product-ion mass spectra produced by electron detachment dissociation (EDD) and electron photodetachment dissociation (EPD) of multi-deprotonated peptides on a Fourier transform and a linear ion trap mass spectrometer, respectively. Both methods, EDD and EPD, involve the electron emission-induced formation of a radical oxidized species from a multi-deprotonated precursor peptide. Product-ion mass spectra display mainly fragment ions resulting from backbone cleavages of C_α-C bond ruptures yielding a and x ions. Fragment ions originating from N-C_α backbone bond cleavages are also observed, in particular by EPD. Although EDD and EPD methods involve the generation of a charge-reduced radical anion intermediate by electron emission, the product ion abundance distributions are drastically different. Both processes seem to be triggered by the location and the recombination of radicals (both neutral and cation radicals). Therefore, EPD product ions are predominantly formed near tryptophan and histidine residues, whereas in EDD the negative charge solvation sites on the backbone seem to be the most favorable for the nearby bond dissociation.     

Transverse Laplacians for Substitution Tilings

Pearson and Bellissard recently built a spectral triple – the data of Riemannian noncommutative geometry – for ultrametric Cantor sets. They derived a family of Laplace–Beltrami like operators on those sets. Motivated by the applications to specific examples, we revisit their work for the transversals of tiling spaces, which are particular self-similar Cantor sets. We use Bratteli diagrams to encode the self-similarity, and Cuntz–Krieger algebras to implement it. We show that the abscissa of convergence of the ζ-function of the spectral triple gives indications on the exponent of complexity of the tiling. We determine completely the spectrum of the Laplace–Beltrami operators, give an explicit method of calculation for their eigenvalues, compute their Weyl asymptotics, and a Seeley equivalent for their heat kernels.     

Deformable two-dimensional photonic crystal slab for cavity optomechanics

We have designed photonic crystal suspended membranes with optimized optical and mechanical properties for cavity optomechanics. Such resonators sustain vibration modes in the megahertz range with quality factors of a few thousand. Thanks to a two-dimensional square lattice of holes, their reflectivity at normal incidence at 1064?nm reaches values as high as 95%. These two features, combined with the very low mass of the membrane, open the way to the use of such periodic structures as deformable end mirrors in Fabry-Perot cavities for the investigation of cavity optomechanical effects.     

How much randomness is needed for statistics?

In algorithmic randomness, when one wants to define a randomness notion with respect to some non-computable measure λ, a choice needs to be made. One approach is to allow randomness tests to access the measure λ as an oracle (which we call the “classical approach”). The other approach is the opposite one, where the randomness tests are completely effective and do not have access to the information contained in λ (we call this approach “Hippocratic”). While the Hippocratic approach is in general much more restrictive, there are cases where the two coincide. The first author showed in 2010 that in the particular case where the notion of randomness considered is Martin-Löf randomness and the measure λ is a Bernoulli measure, classical randomness and Hippocratic randomness coincide. In this paper, we prove that this result no longer holds for other notions of randomness, namely computable randomness and stochasticity.     

Closed subgroups as Ditkin sets

We prove that every closed subgroup of a locally compact group is locally p  -Ditkin for 1<p<∞$1<p<\infty$.