Strichartz Estimates for the Vibrating Plate Equation

We study the dispersive properties of the linear vibrating plate (LVP) equation. Splitting it into two Schr\"odinger-type equations we show its close relation with the Schr\"odinger equation. Then, the homogeneous Sobolev spaces appear to be the natural setting to show Strichartz-type estimates for the LVP equation. By showing a Kato-Ponce inequality for homogeneous Sobolev spaces we prove the well-posedness of the Cauchy problem for the LVP equation with time-dependent potentials. Finally, we exhibit the sharpness of our results. This is achieved by finding a suitable solution for the stationary homogeneous vibrating plate equation.Comment: 18 pages, 4 figures, some misprints correcte

Quantum enhanced correlated interferometry for quantum gravity tests: the experimental set-up and the locking scheme

Abstract The search for Planck scale scale effect is one of holy grails of physics. In Fermilab a double Michelson interferometer was built for this purpose: the holometer. In this proceedings we review our effort to build a quantum enhanced holometer

Twin beam quantum-enhanced correlated interferometry for testing fundamental physics

Quantum metrology deals with improving the resolution of instruments that are otherwise limited by shot noise and it is therefore a promising avenue for enabling scientific breakthroughs. The advantage can be even more striking when quantum enhancement is combined with correlation techniques among several devices. Here, we present and realize a correlation interferometry scheme exploiting bipartite quantum correlated states injected in two independent interferometers. The scheme outperforms classical analogues in detecting a faint signal that may be correlated/uncorrelated between the two devices. We also compare its sensitivity with that obtained for a pair of two independent squeezed modes, each addressed to one interferometer, for detecting a correlated stochastic signal in the MHz frequency band. Being the simpler solution, it may eventually find application to fundamental physics tests, e.g., searching for the effects predicted by some Planck scale theories

Fasting Plasma C-Peptide and Micro- and Macrovascular Complications in a Large Clinic-Based Cohort of Type 1 Diabetic Patients

OBJECTIVE—A protective effect of residual β-cell function on microvascular complications of type 1 diabetes has been suggested. Our aim was to retrospectively evaluate the association of fasting plasma C-peptide values with micro- and macrovascular complications

Clone-specific expression, transcriptional regulation, and action of interleukin-6 in human colon carcinoma cells

<p>Abstract</p> <p>Background</p> <p>Many cancer cells produce interleukin-6 (IL-6), a cytokine that plays a role in growth stimulation, metastasis, and angiogenesis of secondary tumours in a variety of malignancies, including colorectal cancer. Effectiveness of IL-6 in this respect may depend on the quantity of basal and inducible IL-6 expressed as the tumour progresses through stages of malignancy. We therefore have evaluated the effect of <it>IL-6 </it>modulators, i.e. IL-1β, prostaglandin E₂, 17β-estradiol, and 1,25-dihydroxyvitamin D₃, on expression and synthesis of the cytokine at different stages of tumour progression.</p> <p>Methods</p> <p>We utilized cultures of the human colon carcinoma cell clones Caco-2/AQ, COGA-1A and COGA-13, all of which expressed differentiation and proliferation markers typical of distinct stages of tumour progression. IL-6 mRNA and protein levels were assayed by RT-PCR and ELISA, respectively. DNA sequencing was utilized to detect polymorphisms in the <it>IL-6 </it>gene promoter.</p> <p>Results</p> <p><it>IL-6 </it>mRNA and protein concentrations were low in well and moderately differentiated Caco-2/AQ and COGA-1A cells, but were high in poorly differentiated COGA-13 cells. Addition of IL-1β (5 ng/ml) to a COGA-13 culture raised IL-6 production approximately thousandfold via a prostaglandin-independent mechanism. Addition of 17β-estradiol (10^-7M) reduced basal IL-6 production by one-third, but IL-1β-inducible IL-6 was unaffected. Search for polymorphisms in the <it>IL-6 </it>promoter revealed the presence of a single haplotype, i.e., -597A/-572G/-174C, in COGA-13 cells, which is associated with a high degree of transcriptional activity of the <it>IL-6 </it>gene. IL-6 blocked differentiation only in Caco-2/AQ cells and stimulated mitosis through up-regulation of c-<it>myc </it>proto-oncogene expression. These effects were inhibited by 10^-8M 1,25-dihydroxyvitamin D₃.</p> <p>Conclusion</p> <p>In human colon carcinoma cells derived from well and moderately differentiated tumours, IL-6 expression is low and only marginally affected, if at all, by PGE₂, 1,25-dihydroxyvitamin D₃, and 17β-estradiol. However, IL-6 is highly abundant in undifferentiated tumour cells and is effectively stimulated by IL-1β. In case of overexpression of an <it>IL-6 </it>gene variant with extreme sensitivity to IL-1β, massive release of the cytokine from undifferentiated tumour cells may accelerate progression towards malignancy by paracrine action on more differentiated tumour cells with a still functioning proliferative IL-6 signalling pathway.</p

A Low-Cost GPS GSM/GPRS Telemetry System: Performance in Stationary Field Tests and Preliminary Data on Wild Otters (Lutra lutra)

Background: Despite the increasing worldwide use of global positioning system (GPS) telemetry in wildlife research, it has never been tested on any freshwater diving animal or in the peculiar conditions of the riparian habitat, despite this latter being one of the most important habitat types for many animal taxa. Moreover, in most cases, the GPS devices used have been commercial and expensive, limiting their use in low-budget projects. Methodology/Principal Findings: We have developed a low-cost, easily constructed GPS GSM/GPRS (Global System for Mobile Communications/General Packet Radio Service) and examined its performance in stationary tests, by assessing the influence of different habitat types, including the riparian, as well as water submersion and certain climatic and environmental variables on GPS fix-success rate and accuracy. We then tested the GPS on wild diving animals, applying it, for the first time, to an otter species (Lutra lutra). The rate of locations acquired during the stationary tests reached 63.2%, with an average location error of 8.94 m (SD = 8.55). GPS performance in riparian habitats was principally affected by water submersion and secondarily by GPS inclination and position within the riverbed. Temporal and spatial correlations of location estimates accounted for some variation in the data sets. GPS-tagged otters also provided accurate locations and an even higher GPS fix-success rate (68.2%). Conclusions/Significance: Our results suggest that GPS telemetry is reliably applicable to riparian and even divin