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

Pain in cancer. An outcome research project to evaluate the epidemiology, the quality and the effects of pain treatment in cancer patients

BACKGROUND: Management of pain related to advanced or metastatic cancer, although the availability of several pharmacological and non-pharmacological interventions and the existence of well-known guidelines and protocols, is often difficult and inadequate. Evidence of the relative effectiveness of current options for treating cancer pain from comparative randomized studies is scanty. METHODS: In the context of a wider project, a multicenter, open label, prospective Outcome Research study will be launched in Italy in 2006 to investigate the epidemiology of cancer pain and of its treatments, the quality of analgesic-drug therapy and the effectiveness of alternative analgesic strategies in a large, prospective, unselected cohort of cancer patients using the state-of-the art of patient-reported-outcomes. About 100 Italian centers will recruit 2500 patients with advanced/progressive/metastatic cancer with pain (related to the cancer disease) requiring analgesic treatments. Each center is expected to recruit 25 consecutive and eligible patients during the study inception period. Approximately two months will be allowed for subject recruitment and enrollment. Subject evaluation and follow-up will be for 3 months. The effect on outcomes of various therapeutic analgesic options administered by physicians, given the observational approach where patients are not assigned at random to different treatments, will be compared using the propensity score approach, allowing the adjustment for treatment selection bias. Later, after the launch of the observational study and on the basis of results, in specific subsamples of patients and in select centers of the network, a Randomized Controlled Trial will be carried out to formally compare the efficacy of alternative analgesic strategies, with particular emphasis on oral morphine (as comparator) and buprenorphine patch (as experimental arm). Results from the outcome (cohort) and experimental (Randomized Controlled Trial) studies will ensure both the external and internal validity

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

Geodesy and metrology with a transportable optical clock

partially_open24openGrotti, Jacopo; Koller, Silvio; Vogt, Stefan; Häfner, Sebastian; Sterr, Uwe; Lisdat, Christian; Denker, Heiner; Voigt, Christian; Timmen, Ludger; Rolland, Antoine; Baynes, Fred N.; Margolis, Helen S.; Zampaolo, Michel; Thoumany, Pierre; Pizzocaro, Marco; Rauf, Benjamin; Bregolin, Filippo; Tampellini, Anna; Barbieri, Piero; Zucco, Massimo; Costanzo, Giovanni A.; Clivati, Cecilia; Levi, Filippo; Calonico, DavideGrotti, Jacopo; Koller, Silvio; Vogt, Stefan; Häfner, Sebastian; Sterr, Uwe; Lisdat, Christian; Denker, Heiner; Voigt, Christian; Timmen, Ludger; Rolland, Antoine; Baynes, Fred N.; Margolis, Helen S.; Zampaolo, Michel; Thoumany, Pierre; Pizzocaro, Marco; Rauf, Benjamin; Bregolin, Filippo; Tampellini, Anna; Barbieri, Piero; Zucco, Massimo; Costanzo, Giovanni A.; Clivati, Cecilia; Levi, Filippo; Calonico, David

Sensing of Dietary Lipids by Enterocytes: A New Role for SR-BI/CLA-1

BACKGROUND: The intestine is responsible for absorbing dietary lipids and delivering them to the organism as triglyceride-rich lipoproteins (TRL). It is important to determine how this process is regulated in enterocytes, the absorptive cells of the intestine, as prolonged postprandial hypertriglyceridemia is a known risk factor for atherosclerosis. During the postprandial period, dietary lipids, mostly triglycerides (TG) hydrolyzed by pancreatic enzymes, are combined with bile products and reach the apical membrane of enterocytes as postprandial micelles (PPM). Our aim was to determine whether these micelles induce, in enterocytes, specific early cell signaling events that could control the processes leading to TRL secretion. METHODOLOGY/PRINCIPAL FINDINGS: The effects of supplying PPM to the apex of Caco-2/TC7 enterocytes were analyzed. Micelles devoid of TG hydrolysis products, like those present in the intestinal lumen in the interprandial period, were used as controls. The apical delivery of PPM specifically induced a number of cellular events that are not induced by interprandial micelles. These early events included the trafficking of apolipoprotein B, a structural component of TRL, from apical towards secretory domains, and the rapid, dose-dependent activation of ERK and p38MAPK. PPM supply induced the scavenger receptor SR-BI/CLA-1 to cluster at the apical brush border membrane and to move from non-raft to raft domains. Competition, inhibition or knockdown of SR-BI/CLA-1 impaired the PPM-dependent apoB trafficking and ERK activation. CONCLUSIONS/SIGNIFICANCE: These results are the first evidence that enterocytes specifically sense postprandial dietary lipid-containing micelles. SR-BI/CLA-1 is involved in this process and could be a target for further study with a view to modifying intestinal TRL secretion early in the control pathway