The Hijazi inequality on conformally parabolic manifolds

We prove the Hijazi inequality, an estimate for Dirac eigenvalues, for complete manifolds of finite volume. Under some additional assumptions on the dimension and the scalar curvature, this inequality is also valid for elements of the essential spectrum. This allows to prove the conformal version of the Hijazi inequality on conformally parabolic manifolds if the spin analog to the Yamabe invariant is positive.     

OH�� Radical Production Induces Direct Enhancement of the Amylo?d �� Protein/Chondroitin Sulfate Binding: Inhibition by Potentially Radical Scavengers, a Biochromatographic and Thermodynamic Model

??-Amyloid (A??) is a major component of the senile plaques characteristic of Alzheimer disease (AD). Chondroitin sulfate (CS) and glycoaminoglycan (GAG) are also localized throughout the senile plaques in AD. In previous studies, the interaction of the A?? protein with CS immobilized on a chromatographic support and the role of aluminum and copper cations was studied using a molecular chromatographic approach [1, 2]. Here, we demonstrated the direct implication of OH· radical formation on this binding via a novel analytical procedure. The binding of A?? amyloid on CS was accompanied by an OH· radical uptake. The A?¨CCS complex was stabilized by the OH· radical via the creation of about one to two hydrogen bonds. The addition in the medium of a radical scavenger allowed decreasing the A??/CS association and thus confirmed the positive role of these compounds in amyloidosis.     

Quantitative and sensitive detection of rare mutations using droplet-based microfluidics

Somatic mutations within tumoral DNA can be used as highly specific biomarkers to distinguish cancer cells from their normal counterparts. These DNA biomarkers are potentially useful for the diagnosis, prognosis, treatment and follow-up of patients. In order to have the required sensitivity and specificity to detect rare tumoral DNA in stool, blood, lymph and other patient samples, a simple, sensitive and quantitative procedure to measure the ratio of mutant to wild-type genes is required. However, techniques such as dual probe TaqMan(?) assays and pyrosequencing, while quantitative, cannot detect less than ～1% mutant genes in a background of non-mutated DNA from normal cells. Here we describe a procedure allowing the highly sensitive detection of mutated DNA in a quantitative manner within complex mixtures of DNA. The method is based on using a droplet-based microfluidic system to perform digital PCR in millions of picolitre droplets. Genomic DNA (gDNA) is compartmentalized in droplets at a concentration of less than one genome equivalent per droplet together with two TaqMan(?) probes, one specific for the mutant and the other for the wild-type DNA, which generate green and red fluorescent signals, respectively. After thermocycling, the ratio of mutant to wild-type genes is determined by counting the ratio of green to red droplets. We demonstrate the accurate and sensitive quantification of mutated KRAS oncogene in gDNA. The technique enabled the determination of mutant allelic specific imbalance (MASI) in several cancer cell-lines and the precise quantification of a mutated KRAS gene in the presence of a 200,000-fold excess of unmutated KRAS genes. The sensitivity is only limited by the number of droplets analyzed. Furthermore, by one-to-one fusion of drops containing gDNA with any one of seven different types of droplets, each containing a TaqMan(?) probe specific for a different KRAS mutation, or wild-type KRAS, and an optical code, it was possible to screen the six common mutations in KRAS codon 12 in parallel in a single experiment.     

Γ-Convergence of 2D Ginzburg-Landau functionals with vortex concentration along curves

We study the variational convergence of a family of twodimensional Ginzburg-Landau functionals arising in the study of superfluidity or thin-film superconductivity as the Ginzburg-Landau parameter ε tends to 0. In this regime and for large enough applied rotations (for superfluids) or magnetic fields (for superconductors), the minimizers acquire quantized point singularities (vortices). We focus on situations in which an unbounded number of vortices accumulate along a prescribed Jordan curve or a simple arc in the domain. This is known to occur in a circular annulus under uniform rotation, or in a simply connected domain with an appropriately chosen rotational vector field. We prove that if suitably normalized, the energy functionals Γ-converge to a classical energy from potential theory. Applied to global minimizers, our results describe the limiting distribution of vortices along the curve in terms of Green equilibrium measures.     

Spatiotemporal and statistical symmetries

The notion of symmetries, either statistical or deterministic, can be useful for the characterization of complex systems and their bifurcations. In this paper, we investigate the connection between the (microscopic) spatiotemporal symmetries of a space-time functionu(x, t), on the one hand, and the (macroscopic) symmetries of statistical quantities such as the spatial (resp. temporal) two-point correlations and the spatial (resp. temporal) average, on the other hand. We show, how, under certain conditions, these symmetries are related to the symmetries of the orbits described byu(x, t) in the characteristic (phase) spaces. We also determine the largest group of spatiotemporal symmetries (in the sense introduced in our earlier work) satisfied by a given space-time functionu(x, t) and indicate how to extract the subgroups of point symmetries, namely those directly implemented on the space and time variables. Conversely, we determine all the functions invariant by a given space-time symmetry group. Finally, we illustrate all the previous points with specific examples.     

A new method for the study of thermomigration using a non isothermal electrolytic cell

An experimental device is described which is essentially a symmetrical electrolytic cell in a temperature gradient. It is composed of a thin solid electrolyte (ZrO₂-Y₂0₂) and two symmetric electrodes of the studied oxide.We show that the determination of Q1 is possible from the measurement of the Seebeck effects of the electrodes and electrolyte in two different stationary states. One corresponds to an imposed chemical potential gradient of oxygen by an oxydo reducing atmosphere (H₂-H₂O or CO-CO₂). The other is obtained by replacing this gas phase by an inert gas (Ar).The validity and the limitations of the method are discussed from an experimental study on CeO_2?x.     

Diastereoselective spiroannulation of phenolic substrates: synthesis of (+/-)-2-tert-butyl-6-methoxy-1-oxaspiro[4,5]deca-6,9-diene-8-one

The synthesis of a new spiroether is described. The title compound is obtained as a diastereomeric mixture in 45% yield.     

New 64Cu PET imaging agents for personalised medicine and drug development using the hexa-aza cage, SarAr

The success of positron emission tomography (PET) in personalised medicine and drug development requires radioisotopes that provide high quality images and flexible chemistry for a broad application. 64Cu is arguably one of the most suitable PET isotopes for imaging with the evolving target agents, but there are not many appropriate chelating agents for 64Cu and this has limited its wider application. The bi-functional chelator, SarAr is known to bind 64Cu2+ quantitatively (i.e. one metal per ligand present) and rapidly (<2 min) at 10(-6) M over a range of pH (4-9). In this paper the conjugation of SarAr to the whole and fragmented antibody is described. Conjugation of the SarAr to the protein does not impair its coordination of the 64Cu. It complexes the 64Cu2+ rapidly, quantitatively and essentially irreversibly at pH 5. Animal studies show that the 64Cu-SarAr-immunoconjugates maintain their specificity for the target and are stable in vivo. Also, SarAr is a platform technology, is easy to use in a kit formulation and is readily adaptable for the wider application in 64Cu PET imaging.     

Extended tunnelling states in the benzoic acid crystal: infrared and Raman spectra of the OH and OD stretching modes

We compare Raman and infrared spectra of the nuOH/OD modes in benzoic acid crystal powders at 7 K. The extremely sharp Raman bands contrast to the broad infrared profiles and suggest adiabatic separation of hydrogen (deuterium) dynamics from the crystal lattice. There is no evidence of any proton-proton coupling term. The assignment scheme is consistent with a quasisymmetric double-minimum potential, largely temperature independent. Tunnel splitting is a major band shaping mechanism, in addition to anharmonic coupling with lattice modes. The proton/deuteron dynamics are rationalized with nonlocal pseudoparticles and extended states. We propose a symmetry-related damping mechanism to account for the broad infrared profiles, as opposed to the sharp Raman bands. We assign spectral features to distinct interconversion mechanisms based on either pseudoparticle transfer or adiabatic pairwise transfer. We establish close contacts with theoretical models based on first-principles calculations.