Existence and multiplicity for elliptic problems with quadratic growth in the gradient

We show that a class of divergence-form elliptic problems with quadratic growth in the gradient and non-coercive zero order terms are solvable, under essentially optimal hypotheses on the coefficients in the equation. In addition, we prove that the solutions are in general not unique. The case where the zero order term has the opposite sign was already intensively studied and the uniqueness is the rule.Comment: To appear in Comm. PD

Diffeomorphism-invariant properties for quasi-linear elliptic operators

For quasi-linear elliptic equations we detect relevant properties which remain invariant under the action of a suitable class of diffeomorphisms. This yields a connection between existence theories for equations with degenerate and non-degenerate coerciveness.Comment: 16 page

Engineering of an Extreme Rainfall Detection System using Grid Computing

This paper describes a new approach for intensive rainfall data analysis. ITHACA's Extreme Rainfall Detection System (ERDS) is conceived to provide near real-time alerts related to potential exceptional rainfalls worldwide, which can be used by WFP or other humanitarian assistance organizations to evaluate the event and understand the potentially floodable areas where their assistance is needed. This system is based on precipitation analysis and it uses rainfall data from satellite at worldwide extent. This project uses the Tropical Rainfall Measuring Mission Multisatellite Precipitation Analysis dataset, a NASA-delivered near real-time product for current rainfall condition monitoring over the world. Considering the great deal of data to process, this paper presents an architectural solution based on Grid Computing techniques. Our focus is on the advantages of using a distributed architecture in terms of performances for this specific purpos

The prognostic value of stromal and epithelial periostin expression in human breast cancer: Correlation with clinical pathological features and mortality outcome

open6noBackground: PN is a secreted cell adhesion protein critical for carcinogenesis. In breast cancer, it is overexpressed compared to normal breast, and a few reports suggest that it has a potential role as a prognostic marker. Methods: Tumour samples obtained at the time of mastectomy from 200 women followed for a median time of 18.7 years (range 0.5-29.5 years) were investigated through IHC with a polyclonal anti-PN antibody using tissue microarrays. Epithelial and stromal PN expression were scored independently according to the percentage of coloured cells; the 60th percentile of PN epithelial expression, corresponding to 1 %, and the median value of PN stromal expression, corresponding to 90 %, were used as arbitrary cut-offs. The relationships between epithelial and stromal PN expression and clinicalpathological features, tumour phenotype and the risk of mortality following surgery were analysed. Appropriate statistics, including the Fine and Gray competing risk proportional hazard regression model, were used. Results: The expression of PN in tumour epithelial cells was significantly lower than that which was observed in stromal cells (p < 0.000). No specific association between epithelial or stromal PN expression and any of the clinicalpathological parameters analysed was found as it was observed in respect to mortality when these variables were analysed individually. However, when both variables were considered as a function of the other one, the expression of PN in the stromal cells maintained a statistically significant predictive value with respect to both all causes and cancerspecific mortality only in the presence of high epithelial expression levels. No significant differences in either all causes or BCa-specific mortality rates were shown according to epithelial expression for tumours displaying higher stromal PN expression rates. However, the trends were opposite for the higher stromal values and the patients with high epithelial expression levels denoted the group with the worst prognosis, while higher epithelial values in patients with lower stromal expression levels denoted the group with the best prognosis, suggesting that PN epithelial/stromal interactions play a crucial role in breast carcinogenesis, most likely due to functional cross-talk between the two compartments. On the basis of PN expression in both compartments, we defined 4 subgroups of patients with different mortality rates with the group of patients characterized by positive epithelial and low stromal PN expression cells showing the lowest mortality risk as opposed to the groups of patients identified by a high PN expression in both cell compartments or those identified by a low or absent PN expression in both cell compartments showing the worst mortality rates. The differences were highly statistically significant and were also retained after multiparametric analysis. Competing risk analysis demonstrated that PN expression patterns characterizing each of previous groups are specifically associated with cancer-specific mortality. Conclusions: Although they require further validation through larger studies, our findings suggest that the patterns of expression of PN in both compartments can allow for the development of IHC "signatures" that maintain a strong independent predictive value of both all causes and, namely, of cancer-specific mortality.openNuzzo, P.V.; Rubagotti, A.; Zinoli, L.; Salvi, S.; Boccardo, S.; Boccardo, F.Nuzzo, PIER VITALE; Rubagotti, Alessandra; Zinoli, Linda; Salvi, Sara; Boccardo, S.; Boccardo, F

On the limit of solutions of ut=Δum as m→∞

Let f∈L1(RN), N≥1, f≥0, and consider the Cauchy problem ut=Δum on ]0,∞[×RN, u(0,⋅)=f on RN. The authors prove that as m→∞, the corresponding solutions um(t)→u_=f+Δw in L1(RN), uniformly for t in a compact set in ]0,∞[, where 0≤w_∈L1(Rn) is the solution of the variational inequality Δw_∈L1(RN), 0≤f+Δw_≤1, w_(f+Δw_ −1)=0 a.e. The authors also show similar results for the same equation on a bounded open set Ω in RN with Dirichlet or Neumann boundary condition

Application of dissipative particle dynamics to interfacial systems: Parameterization and scaling

Dissipative Particle Dynamics (DPD) is a stochastic particle model that is able to simulate larger systems over longer time scales than atomistic modeling approaches by including the concept of coarse-graining. Whether standard DPD can cover the whole mesoscale by changing the level of coarse-graining is still an open issue. A scaling scheme originally developed by Füchslin et al. (2009) was here applied to interfacial systems as one of the most successful uses of the classical DPD method. In particular, equilibrium properties such as the interfacial tension were analyzed at different levels of coarse-graining for planar oil–water interfaces with and without surfactant. A scaling factor for the interfacial tension was found due to the combined effect of the scaling scheme and the coarse-graining parameterization. Although the level of molecular description was largely decreased, promising results showed that it is possible to conserve the interfacial tension trend at increasing surfactant concentrations, remarkably reducing modeling complexity. The same approach was also employed to simulate a droplet configuration. Both planar and droplet conformations were maintained, showing that typical domain formations of multi-component systems can be performed in DPD by means of the scaling procedure. Therefore, we explored the possibility of describing oil–water and oil–water–surfactant systems in standard DPD using a scaling scheme with the aim of highlighting its advantages and limitations