When is the Haar measure a Pietsch measure for nonlinear mappings?

We show that, as in the linear case, the normalized Haar measure on a compact topological group $G$ is a Pietsch measure for nonlinear summing mappings on closed translation invariant subspaces of $C(G)$. This answers a question posed to the authors by J. Diestel. We also show that our result applies to several well-studied classes of nonlinear summing mappings. In the final section some problems are proposed

All-optical 3D atomic loops generated with Bessel light fields

The propagation invariance of Bessel beams as well as their transversal structure are used to perform a comparative analysis of their effect on cold atoms for four different configurations and combinations thereof. We show that, even at temperatures for which the classical description of the atom center of mass motion is valid, the interchange of momentum, energy and orbital angular momentum between light and atoms yields efficient tools for all-optical trapping, transporting and, in general, manipulating the state of motion of cold atoms.Comment: 13 pages, 9 figure

A Poisson hierarchical modelling approach to detecting copy number variation in sequence coverage data.

BACKGROUND: The advent of next generation sequencing technology has accelerated efforts to map and catalogue copy number variation (CNV) in genomes of important micro-organisms for public health. A typical analysis of the sequence data involves mapping reads onto a reference genome, calculating the respective coverage, and detecting regions with too-low or too-high coverage (deletions and amplifications, respectively). Current CNV detection methods rely on statistical assumptions (e.g., a Poisson model) that may not hold in general, or require fine-tuning the underlying algorithms to detect known hits. We propose a new CNV detection methodology based on two Poisson hierarchical models, the Poisson-Gamma and Poisson-Lognormal, with the advantage of being sufficiently flexible to describe different data patterns, whilst robust against deviations from the often assumed Poisson model. RESULTS: Using sequence coverage data of 7 Plasmodium falciparum malaria genomes (3D7 reference strain, HB3, DD2, 7G8, GB4, OX005, and OX006), we showed that empirical coverage distributions are intrinsically asymmetric and overdispersed in relation to the Poisson model. We also demonstrated a low baseline false positive rate for the proposed methodology using 3D7 resequencing data and simulation. When applied to the non-reference isolate data, our approach detected known CNV hits, including an amplification of the PfMDR1 locus in DD2 and a large deletion in the CLAG3.2 gene in GB4, and putative novel CNV regions. When compared to the recently available FREEC and cn.MOPS approaches, our findings were more concordant with putative hits from the highest quality array data for the 7G8 and GB4 isolates. CONCLUSIONS: In summary, the proposed methodology brings an increase in flexibility, robustness, accuracy and statistical rigour to CNV detection using sequence coverage data

The Level of NMDA Receptor in the Membrane Modulates Amyloid-β Association and Perforation

Alzheimer’s disease is a neurodegenerative disorder that affects mostly the elderly. The main histopathological markers are the senile plaques formed by amyloid-β peptide (Aβ) aggregates that can perforate the plasma membrane of cells, increasing the intracellular calcium levels and releasing synaptic vesicles that finally lead to a delayed synaptic failure. Several membrane proteins and lipids interact with Aβ affecting its toxicity in neurons. Here, we focus on NMDA receptors (NMDARs) as proteins that could be modulating the association and neurotoxic perforation induced by Aβ on the plasma membrane. In fact, our results showed that decreasing NMDARs, using enzymatic or siRNA approaches, increased the association of Aβ to the neurons. Furthermore, overexpression of NMDARs also resulted in an enhanced association between NMDA and Aβ. Functionally, the reduction in membrane NMDARs augmented the process of membrane perforation. On the other hand, overexpressing NMDARs had a protective effect because Aβ was now unable to cause membrane perforation, suggesting a complex relationship between Aβ and NMDARs. Because previous studies have recognized that Aβ oligomers are able to increase membrane permeability and produce amyloid pores, the present study supports the conclusion that NMDARs play a critical protective role on Aβ actions in hippocampal neurons. These results could explain the lack of correlation between brain Aβ burden and clinically observed dementia

Sharp values for the constants in the polynomial Bohnenblust-Hille inequality

In this paper we prove that the complex polynomial Bohnenblust-Hille constant for $2$-homogeneous polynomials in ${\mathbb C}^2$ is exactly $\sqrt[4]{\frac{3}{2}}$. We also give the exact value of the real polynomial Bohnenblust-Hille constant for $2$-homogeneous polynomials in ${\mathbb R}^2$. Finally, we provide lower estimates for the real polynomial Bohnenblust-Hille constant for polynomials in ${\mathbb R}^2$ of higher degrees.Comment: 16 page