The Ljapunov-Schmidt reduction for some critical problems

This is a survey about the application of the Ljapunov-Schmidt reduction for some critical problems

A Convex Max-Flow Segmentation of LV Using Subject-Specific Distributions on Cardiac MRI

Abstract. This work studies the convex relaxation approach to the left ventricle (LV) segmentation which gives rise to a challenging multi-region seperation with the geometrical constraint. For each region, we consider the global Bhattacharyya metric prior to evaluate a gray-scale and a ra-dial distance distribution matching. In this regard, the studied problem amounts to finding three regions that most closely match their respective input distribution model. It was previously addressed by curve evolution, which leads to sub-optimal and computationally intensive algorithms, or by graph cuts, which result in heavy metrication errors (grid bias). The proposed convex relaxation approach solves the LV segmentation through a sequence of convex sub-problems. Each sub-problem leads to a novel bound of the Bhattacharyya measure and yields the convex formulation which paves the way to build up the efficient and reliable solver. In this respect, we propose a novel flow configuration that accounts for labeling-function variations, in comparison to the existing flow-maximization con-figurations. We show it leads to a new convex max-flow formulation which is dual to the obtained convex relaxed sub-problem and does give the exact and global optimums to the original non-convex sub-problem. In addition, we present such flow perspective gives a new and simple way to encode the geometrical constraint of optimal regions. A comprehen-sive experimental evaluation on sufficient patient subjects demonstrates that our approach yields improvements in optimality and accuracy over related recent methods.

Bi-directional Alfv\'en Cyclotron Instabilities in the Mega-Amp Spherical Tokamak

Alfv\'en cyclotron instabilities excited by velocity gradients of energetic beam ions were investigated in MAST experiments with super-Alfv\'enic NBI over a wide range of toroidal magnetic fields from ~0.34 T to ~0.585 T. In MAST discharges with high magnetic field, a discrete spectrum of modes in the sub-cyclotron frequency range is excited toroidally propagating counter to the beam and plasma current (toroidal mode numbers n < 0).Comment: 28 pages, 13 figures. This article has been submitted to Physics of Plasmas. After it is published, it will be found at http://scitation.aip.org/content/aip/journal/pop/brows

Blow-up solutions for linear perturbations of the Yamabe equation

For a smooth, compact Riemannian manifold (M,g) of dimension N \geg 3, we are interested in the critical equation $$\Delta_g u+(N-2/4(N-1) S_g+\epsilon h)u=u^{N+2/N-2} in M, u>0 in M,$$ where \Delta_g is the Laplace--Beltrami operator, S_g is the Scalar curvature of (M,g), $h\in C^{0,\alpha}(M)$, and $\epsilon$ is a small parameter

Molecular analysis of HBV genotypes and subgenotypes in the Central-East region of Tunisia

<p>Abstract</p> <p>Background</p> <p>In Tunisia, country of intermediate endemicity for Hepatitis B virus (HBV) infection, most molecular studies on the virus have been carried out in the North of the country and little is known about other regions. The aim of this study was to determine HBV genotype and subgenotypes in Central-East Tunisia. A total of 217 HBs antigen positive patients were enrolled and determination of genotype was investigated in 130 patients with detectable HBV DNA. HBV genotyping methods were: PCR-RFLP on the pre-S region, a PCR using type-specific primers in the S region (TSP-PCR) and partial sequencing in the pre-S region.</p> <p>Results</p> <p>Three genotypes (D, B and A) were detected by the PCR-RFLP method and two (D and A) with the TSP-PCR method, the concordance between the two methods was 93%. Sequencing and phylogenetic analysis of 32 strains, retrieved the same genotype (D and A) for samples with concordant results and genotype D for samples with discordant results. The sequences of discordant genotypes had a restriction site in the pre-S gene which led to erroneous result by the PCR-RFLP method. Thus, prevalence of genotype D and A was 96% and 4%, respectively. Phylogenetic analysis showed the predominance of two subgenotypes D1 (55%) and D7 (41%). Only one strain clustered with D3 subgenotype (3%).</p> <p>Conclusions</p> <p>Predominance of subgenotype D7 appears to occur in northern regions of Africa with transition to subgenotype D1 in the East of the continent. HBV genetic variability may lead to wrong results in rapid genotyping methods and sequence analysis is needed to clarify atypical results.</p

Aerodynamic investigations of ventilated brake discs.

The heat dissipation and performance of a ventilated brake disc strongly depends on the aerodynamic characteristics of the flow through the rotor passages. The aim of this investigation was to provide an improved understanding of ventilated brake rotor flow phenomena, with a view to improving heat dissipation, as well as providing a measurement data set for validation of computational fluid dynamics methods. The flow fields at the exit of four different brake rotor geometries, rotated in free air, were measured using a five-hole pressure probe and a hot-wire anemometry system. The principal measurements were taken using two-component hot-wire techniques and were used to determine mean and unsteady flow characteristics at the exit of the brake rotors. Using phase-locked data processing, it was possible to reveal the spatial and temporal flow variation within individual rotor passages. The effects of disc geometry and rotational speed on the mean flow, passage turbulence intensity, and mass flow were determined. The rotor exit jet and wake flow were clearly observed as characterized by the passage geometry as well as definite regions of high and low turbulence. The aerodynamic flow characteristics were found to be reasonably independent of rotational speed but highly dependent upon rotor geometry

Review article: MHD wave propagation near coronal null points of magnetic fields

We present a comprehensive review of MHD wave behaviour in the neighbourhood of coronal null points: locations where the magnetic field, and hence the local Alfven speed, is zero. The behaviour of all three MHD wave modes, i.e. the Alfven wave and the fast and slow magnetoacoustic waves, has been investigated in the neighbourhood of 2D, 2.5D and (to a certain extent) 3D magnetic null points, for a variety of assumptions, configurations and geometries. In general, it is found that the fast magnetoacoustic wave behaviour is dictated by the Alfven-speed profile. In a $\beta=0$ plasma, the fast wave is focused towards the null point by a refraction effect and all the wave energy, and thus current density, accumulates close to the null point. Thus, null points will be locations for preferential heating by fast waves. Independently, the Alfven wave is found to propagate along magnetic fieldlines and is confined to the fieldlines it is generated on. As the wave approaches the null point, it spreads out due to the diverging fieldlines. Eventually, the Alfven wave accumulates along the separatrices (in 2D) or along the spine or fan-plane (in 3D). Hence, Alfven wave energy will be preferentially dissipated at these locations. It is clear that the magnetic field plays a fundamental role in the propagation and properties of MHD waves in the neighbourhood of coronal null points. This topic is a fundamental plasma process and results so far have also lead to critical insights into reconnection, mode-coupling, quasi-periodic pulsations and phase-mixing.Comment: 34 pages, 5 figures, invited review in Space Science Reviews => Note this is a 2011 paper, not a 2010 pape

Influence of plasma turbulence on microwave propagation

It is not fully understood how electromagnetic waves propagate through plasma density fluctuations when the size of the fluctuations is comparable with the wavelength of the incident radiation. In this paper, the perturbing effect of a turbulent plasma density layer on a traversing microwave beam is simulated with full-wave simulations. The deterioration of the microwave beam is calculated as a function of the characteristic turbulence structure size, the turbulence amplitude, the depth of the interaction zone and the size of the waist of the incident beam. The maximum scattering is observed for a structure size on the order of half the vacuum wavelength. The scattering and beam broadening was found to increase linearly with the depth of the turbulence layer and quadratically with the fluctuation strength. Consequences for experiments and 3D effects are considered.Comment: 16 pages, 13 figures. This is an author-created, un-copyedited version of an article submitted for publication in Plasma Physics and Controlled Fusion. IoP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from i

Genome profiling of ERBB2-amplified breast cancers

<p>Abstract</p> <p>Background</p> <p>Around 20% of breast cancers (BC) show <it>ERBB2 </it>gene amplification and overexpression of the ERBB2 tyrosine kinase receptor. They are associated with a poor prognosis but can benefit from targeted therapy. A better knowledge of these BCs, genomically and biologically heterogeneous, may help understand their behavior and design new therapeutic strategies.</p> <p>Methods</p> <p>We defined the high resolution genome and gene expression profiles of 54 <it>ERBB2</it>-amplified BCs using 244K oligonucleotide array-comparative genomic hybridization and whole-genome DNA microarrays. Expression of ERBB2, phosphorylated ERBB2, EGFR, IGF1R and FOXA1 proteins was assessed by immunohistochemistry to evaluate the functional ERBB2 status and identify co-expressions.</p> <p>Results</p> <p>First, we identified the <it>ERBB2</it>-<it>C17orf37</it>-<it>GRB7 </it>genomic segment as the minimal common 17q12-q21 amplicon, and <it>CRKRS </it>and <it>IKZF3 </it>as the most frequent centromeric and telomeric amplicon borders, respectively. Second, GISTIC analysis identified 17 other genome regions affected by copy number aberration (CNA) (amplifications, gains, losses). The expression of 37 genes of these regions was deregulated. Third, two types of heterogeneity were observed in <it>ERBB2</it>-amplified BCs. The genomic profiles of estrogen receptor-postive (ER+) and negative (ER-) <it>ERBB2</it>-amplified BCs were different. The WNT/β-catenin signaling pathway was involved in ER- <it>ERBB2</it>-amplified BCs, and <it>PVT1 </it>and <it>TRPS1 </it>were candidate oncogenes associated with ER+ <it>ERBB2</it>-amplified BCs. The size of the <it>ERBB2 </it>amplicon was different in inflammatory (IBC) and non-inflammatory BCs. <it>ERBB2</it>-amplified IBCs were characterized by the downregulated and upregulated mRNA expression of ten and two genes in proportion to CNA, respectively. IHC results showed (i) a linear relationship between <it>ERBB2 </it>gene amplification and its gene and protein expressions with a good correlation between ERBB2 expression and phosphorylation status; (ii) a potential signaling cross-talk between EGFR or IGF1R and ERBB2, which could influence response of <it>ERBB2</it>-positive BCs to inhibitors. FOXA1 was frequently coexpressed with ERBB2 but its expression did not impact on the outcome of patients with <it>ERBB2</it>-amplified tumors.</p> <p>Conclusion</p> <p>We have shown that ER+ and ER- <it>ERBB2</it>-amplified BCs are different, distinguished <it>ERBB2 </it>amplicons in IBC and non-IBC, and identified genomic features that may be useful in the design of alternative therapeutical strategies.</p