Quantitative Chevalley-Weil theorem for curves

The classical Chevalley-Weil theorem asserts that for an \'etale covering of projective varieties over a number field K, the discriminant of the field of definition of the fiber over a K-rational point is uniformly bounded. We obtain a fully explicit version of this theorem in dimension 1.Comment: version 4: minor inaccuracies in Lemma 3.4 and Proposition 5.2 correcte

'Designer atoms' for quantum metrology

Entanglement is recognized as a key resource for quantum computation and quantum cryptography. For quantum metrology, the use of entangled states has been discussed and demonstrated as a means of improving the signal-to-noise ratio. In addition, entangled states have been used in experiments for efficient quantum state detection and for the measurement of scattering lengths. In quantum information processing, manipulation of individual quantum bits allows for the tailored design of specific states that are insensitive to the detrimental influences of an environment. Such 'decoherence-free subspaces' protect quantum information and yield significantly enhanced coherence times. Here we use a decoherence-free subspace with specifically designed entangled states to demonstrate precision spectroscopy of a pair of trapped Ca+ ions; we obtain the electric quadrupole moment, which is of use for frequency standard applications. We find that entangled states are not only useful for enhancing the signal-to-noise ratio in frequency measurements - a suitably designed pair of atoms also allows clock measurements in the presence of strong technical noise. Our technique makes explicit use of non-locality as an entanglement property and provides an approach for 'designed' quantum metrology

Analysis of LIGO data for gravitational waves from binary neutron stars

We report on a search for gravitational waves from coalescing compact binary systems in the Milky Way and the Magellanic Clouds. The analysis uses data taken by two of the three LIGO interferometers during the first LIGO science run and illustrates a method of setting upper limits on inspiral event rates using interferometer data. The analysis pipeline is described with particular attention to data selection and coincidence between the two interferometers. We establish an observational upper limit of

Pulsed Molecular Optomechanics in Plasmonic Nanocavities: From Nonlinear Vibrational Instabilities to Bond-Breaking

Small numbers of surface-bound molecules are shown to behave as would be expected for opto-mechanical oscillators placed inside plasmonic nano-cavities that support extreme confinement of optical fields. Pulsed Raman scattering reveals superlinear Stokes emission above a threshold, arising from the stimulated vibrational pumping of molecular bonds under pulsed excitation shorter than the phonon decay time, and agreeing with pulsed optomechanical quantum theory. Reaching the parametric instability (equivalent to a phonon laser or ‘phaser’ regime) is however hindered by motion of gold atoms and molecular reconfiguration at phonon occupations approaching unity. We show how this irreversible bond breaking can ultimately limit the exploitation of molecules as quantum mechanical oscillators, but accesses optically-driven chemistry

Aggressiveness of human melanoma xenograft models is promoted by aneuploidy-driven gene expression deregulation.

Melanoma is a devastating skin cancer characterized by distinct biological subtypes. Besides frequent mutations in growth- and survival-promoting genes like BRAF and NRAS, melanomas additionally harbor complex non-random genomic alterations. Using an integrative approach, we have analysed genomic and gene expression changes in human melanoma cell lines (N=32) derived from primary tumors and various metastatic sites and investigated the relation to local growth aggressiveness as xenografts in immuno-compromised mice (N=22). Although the vast majority >90% of melanoma models harbored mutations in either BRAF or NRAS, significant differences in subcutaneous growth aggressiveness became obvious. Unsupervised clustering revealed that genomic alterations rather than gene expression data reflected this aggressive phenotype, while no association with histology, stage or metastatic site of the original melanoma was found. Genomic clustering allowed separation of melanoma models into two subgroups with differing local growth aggressiveness in vivo. Regarding genes expressed at significantly altered levels between these subgroups, a surprising correlation with the respective gene doses (>85% accordance) was found. Genes deregulated at the DNA and mRNA level included well-known cancer genes partly already linked to melanoma (RAS genes, PTEN, AURKA, MAPK inhibitors Sprouty/Spred), but also novel candidates like SIPA1 (a Rap1GAP). Pathway mining further supported deregulation of Rap1 signaling in the aggressive subgroup e.g. by additional repression of two Rap1GEFs. Accordingly, siRNA-mediated down-regulation of SIPA1 exerted significant effects on clonogenicity, adherence and migration in aggressive melanoma models. Together our data suggest that an aneuploidy-driven gene expression deregulation drives local aggressiveness in human melanoma

Integrality gaps of integer knapsack problems

We obtain optimal lower and upper bounds for the (additive) integrality gaps of integer knapsack problems. In a randomised setting, we show that the integrality gap of a “typical” knapsack problem is drastically smaller than the integrality gap that occurs in a worst case scenario

Distance Optimization and the Extremal Variety of the Grassmann Variety

The approximation of a multivector by a decomposable one is a distance-optimization problem between the multivector and the Grassmann variety of lines in a projective space. When the multivector diverges from the Grassmann variety, then the approximate solution sought is the worst possible. In this paper, it is shown that the worst solution of this problem is achieved, when the eigenvalues of the matrix representation of a related two-vector are all equal. Then, all these pathological points form a projective variety. We derive the equation describing this projective variety, as well as its maximum distance from the corresponding Grassmann variety. Several geometric and algebraic properties of this extremal variety are examined, providing a new aspect for the Grassmann varieties and the respective projective spaces

Analysis of acute vascular damage after photodynamic therapy using benzoporphyrin derivative (BPD)

Benzoporphyrin derivative monoacid ring A (BPD-MA, verteporfin) is currently under investigation as a photosensitizer for photodynamic therapy (PDT). Since BPD exhibits rapid pharmacokinetics in plasma and tissues, we assessed damage to tumour and muscle microvasculature when light treatment for PDT was given at short times after injection of photosensitizer. Groups of rats with chondrosarcoma were given 2 mg kg−1 of BPD intravenously 5 min to 180 min before light treatment of 150 J cm−2 690 nm. Vascular response was monitored using intravital microscopy and tumour cure was monitored by following regrowth over 42 days. For treatment at 5 or 30 min after BPD injection, blood flow stasis was limited to tumour microvasculature with lesser response in the surrounding normal microvasculature, indicating selective targeting for damage. No acute changes were observed in vessels when light was given 180 min after BPD injection. Tumour regression after light treatment occurred in all animals given PDT with BPD. Long-term tumour regression was greater in animals treated 5 min after BPD injection and least in animals given treatment 180 min after drug injection. The correlation between the timing for vascular damage and cure implies that blood flow stasis plays a significant role in PDT-induced tumour destruction. © 1999 Cancer Research Campaig

Genetic risk factors for ischaemic stroke and its subtypes (the METASTROKE Collaboration): a meta-analysis of genome-wide association studies

<p>Background - Various genome-wide association studies (GWAS) have been done in ischaemic stroke, identifying a few loci associated with the disease, but sample sizes have been 3500 cases or less. We established the METASTROKE collaboration with the aim of validating associations from previous GWAS and identifying novel genetic associations through meta-analysis of GWAS datasets for ischaemic stroke and its subtypes.</p> <p>Methods - We meta-analysed data from 15 ischaemic stroke cohorts with a total of 12 389 individuals with ischaemic stroke and 62 004 controls, all of European ancestry. For the associations reaching genome-wide significance in METASTROKE, we did a further analysis, conditioning on the lead single nucleotide polymorphism in every associated region. Replication of novel suggestive signals was done in 13 347 cases and 29 083 controls.</p> <p>Findings - We verified previous associations for cardioembolic stroke near PITX2 (p=2·8×10−16) and ZFHX3 (p=2·28×10−8), and for large-vessel stroke at a 9p21 locus (p=3·32×10−5) and HDAC9 (p=2·03×10−12). Additionally, we verified that all associations were subtype specific. Conditional analysis in the three regions for which the associations reached genome-wide significance (PITX2, ZFHX3, and HDAC9) indicated that all the signal in each region could be attributed to one risk haplotype. We also identified 12 potentially novel loci at p<5×10−6. However, we were unable to replicate any of these novel associations in the replication cohort.</p> <p>Interpretation - Our results show that, although genetic variants can be detected in patients with ischaemic stroke when compared with controls, all associations we were able to confirm are specific to a stroke subtype. This finding has two implications. First, to maximise success of genetic studies in ischaemic stroke, detailed stroke subtyping is required. Second, different genetic pathophysiological mechanisms seem to be associated with different stroke subtypes.</p&gt