Optimal Szeg\"o-Weinberger type inequalities

Denote with $\mu_{1}(\Omega;e^{h\left(|x|\right)})$ the first nontrivial eigenvalue of the Neumann problem \begin{equation*} \left\{\begin{array}{lll} -\text{div}\left(e^{h\left(|x|\right)}\nabla u\right) =\mu e^{h\left(|x|\right)}u & \text{in} & \Omega & & \frac{\partial u}{\partial \nu}=0 & \text{on} & \partial \Omega , \end{array} \right. \end{equation*} where $\Omega$ is a bounded and Lipschitz domain in $\mathbb{R}^{N}$. Under suitable assumption on $h$ we prove that the ball centered at the origin is the unique set maximizing $\mu_{1}(\Omega;e^{h\left(|x|\right)})$ among all Lipschitz bounded domains $\Omega$ of $\mathbb{R}^{N}$ of prescribed $e^{h\left(|x|\right)}dx$-measure and symmetric about the origin. Moreover, an example in the model case $h\left(|x|\right) =|x|^{2},$ shows that, in general, the assumption on the symmetry of the domain cannot be dropped. In the one-dimensional case, i.e. when $\Omega$ reduces to an interval $(a,b),$ we consider a wide class of weights (including both Gaussian and anti-Gaussian). We then describe the behavior of the eigenvalue as the interval $(a,b)$ slides along the $x$-axis keeping fixed its weighted length

Uniformly bounded representations and completely bounded multipliers of SL(2,R)

We estimate the norms of many matrix coefficients of irreducible uniformly bounded representations of SL(2, R) as completely bounded multipliers of the Fourier algebra. Our results suggest that the known inequality relating the uniformly bounded norm of a representation and the completely bounded norm of its coefficients may not be optimal

In human retinoblastoma Y79 cells okadaic acid\u2013parthenolide co-treatment induces synergistic apoptotic effects, with PTEN as a key player.

Retinoblastoma is the most common intraocular malignancy of childhood. In developing countries, treatment is limited, long-term survival rates are low and current chemotherapy causes significant morbidity to pediatric patients and significantly limits dosing. Therefore there is an urgent need to identify new therapeutic strategies to improve the clinical outcome of patients with retinoblastoma. here, we investigated the effects of two natural compounds okadaic acid (OKa) and parthenolide (PN) on human retinoblastoma Y79 cells. For the first time we showed that OKa/PN combination at subtoxic doses induces potent synergistic apoptotic effects accompanied by lowering in p-akt levels, increasing in the stabilized forms of p53 and potent decrease in ps166-Mdm2. We also showed the key involvement of PTeN which, after OKa/PN treatment, potently increased before p53, thus suggesting that p53 activation was under PTeN action. Moreover, after PTEN-knockdown p-akt/ ps166Mdm2 increased over basal levels and p53 significantly lowered, while OKa/PN treatment failed both to lower p-akt and ps166-Mdm2 and to increase p53 below/over their basal levels respectively. OKa/PN treatment potently increased ROs levels whereas decreased those of Gsh. Reducing cellular Gsh by l-butathionine-[s,R]-sulfoximine treatment significantly anticipated the cytotoxic effect exerted by OKa/ PN. Furthermore, the effects of OKa/PN treatment on both Gsh content and cell viability were less pronounced in PTeN silenced cells than in control cells. The results provide strong suggestion for combining a treatment approach that targets the PTeN/akt/Mdm2/p53 pathway

Okadaic acid-Parthenolide combination at subtoxic doses induces potent synergistic apoptotic effects in human retinoblastoma Y79 cells by upregulating PTEN.

Retinoblastoma is the most common intraocular malignancy afflicting children. The incidence is higher in developing countries, where treatment is limited and long-term survival rates are low. Vincristine, etoposide, and carboplatin -the agents commonly used in the treatment of retinoblastoma- determine side effects causing significant morbidity to pediatric patients and significantly limiting dosing. Thus, identifying new drugs and molecular targets to facilitate the development of novel therapeutics, and finding natural drug combinations to kill cancer cells by synergistically acting at subtoxic doses, may be a good goal. Here, we investigated the effects of two natural compounds, okadaic acid (OKA) and parthenolide (PN), in human retinoblastoma Y79 cells. We showed that OKA/PN combination at subtoxic doses induces potent synergistic apoptotic effects accompanied by decrease in p-Akt, increase in the stabilized p53 forms and potent decrease in pS166\u2013Mdm2. We also showed the key involvement of PTEN which, after OKA/PN treatment, potently increased before p53, suggesting that p53 activation was under PTEN action. PTEN-knockdown increased p-Akt/ pS166Mdm2 over basal levels and significantly lowered p53, while OKA/PN treatment failed both to lower p-Akt and pS166\u2013Mdm2 and to increase p53 below/over their basal levels respectively. OKA/PN treatment potently increased ROS levels while decreased those of GSH. Reducing cellular GSH by butathionine-sulfoximine treatment significantly anticipated the cytotoxic effect exerted by OKA/PN. The effects of OKA/PN treatment on both GSH content and cell viability were less pronounced in PTEN silenced cells than in control cells. Our study reports for the first time both a synergistic apoptotic action between OKA and PN and the involvement of PTEN as key player in the apoptotic mechanism in human retinoblastoma Y79 cells. The results provide strong suggestion for combined inhibition of the PTEN/Akt/Mdm2/p53 pathway

An eigenvalue problem for the anisotropic Φ\Phi-Laplacian

We study an eigenvalue problem involving a fully anisotropic elliptic differential operator in arbitrary Orlicz-Sobolev spaces. The relevant equations are associated with constrained minimization problems for integral functionals depending on the gradient of competing functions through general anisotropic $N$-functions. In particular, the latter need neither be radial, nor have a polynomial growth, and are not even assumed to satisfy the so called $\Delta_2$-condition. The resulting analysis requires the development of some new aspects of the theory of anisotropic Orlicz-Sobolev spaces

On the asymptotic behaviour of solutions to the fractional porous medium equation with variable density

We are concerned with the long time behaviour of solutions to the fractional porous medium equation with a variable spatial density. We prove that if the density decays slowly at infinity, then the solution approaches the Barenblatt-type solution of a proper singular fractional problem. If, on the contrary, the density decays rapidly at infinity, we show that the minimal solution multiplied by a suitable power of the time variable converges to the minimal solution of a certain fractional sublinear elliptic equation.Comment: To appear in DCDS-

Feasibility and acceptability of expressive writing with postpartum women: a randomised controlled trial

Abstract Background: Pregnancy, birth and adjusting to a new baby is a potentially stressful time that can negatively affect women’s mental and physical health. Expressive writing, where people write about a stressful event for at least 15 minutes on three consecutive days, has been associated with improved health in some groups but it is not clear whether it is feasible and acceptable for use with postpartum women. This study therefore examined the feasibility and acceptability of expressive writing for postpartum women as part of a randomised controlled trial (RCT). Methods: The Health After Birth Trial (HABiT) was an RCT evaluating expressive writing for postpartum women which included measures of feasibility and acceptability. At 6 to 12 weeks after birth 854 women were randomised to expressive writing, a control writing task or normal care, and outcome measures of health were measured at baseline, one month later and six months later. Feasibility was measured by recruitment, attrition, and adherence to the intervention. Quantitative and qualitative measures of acceptability of the materials and the task were completed six months after the intervention. Results: Recruitment was low (10.7% of those invited to participate) and the recruited sample was from a restricted sociodemographic range. Attrition was high, increased as the study progressed (35.8% at baseline, 57.5% at one month, and 68.1% at six months) and was higher in the writing groups than in the normal care group. Women complied with instructions to write expressively or not, but adherence to the instruction to write for 15 minutes per day for three days was low (Expressive writing: 29.3%; Control writing: 23.5%). Acceptability measures showed that women who wrote expressively rated the materials/task both more positively and more negatively than those in the control writing group, and qualitative comments revealed that women enjoyed the writing and/or found it helpful even when it was upsetting. Conclusions: The feasibility of offering expressive writing as a universal self-help intervention to all postpartum women 6 to 12 weeks after birth in the HABiT trial was low, but the expressive writing intervention was acceptable to the majority of women who completed it

Genetic and molecular characterization of the human osteosarcoma 3AB-OS cancer stem cell line: a possible model for studying osteosarcoma origin and stemness.

Finding new treatments targeting cancer stem cells (CSCs) within a tumor seems to be critical to halt cancer and improve patient survival. Osteosarcoma is an aggressive tumor affecting adolescents, for which there is no second-line chemotherapy. Uncovering new molecular mechanisms underlying the development of osteosarcoma and origin of CSCs is crucial to identify new possible therapeutic strategies. Here, we aimed to characterize genetically and molecularly the human osteosarcoma 3AB-OS CSC line, previously selected from MG63 cells and which proved to have both in vitro and in vivo features of CSCs. Classic cytogenetic studies demonstrated that 3AB-OS cells have hypertriploid karyotype with 71–82 chromosomes. By comparing 3AB-OS CSCs to the parental cells, array CGH, Affymetrix microarray, and TaqMan1 Human MicroRNA array analyses identified 49 copy number variations (CNV), 3,512 dysregulated genes and 189 differentially expressed miRNAs. Some of the chromosomal abnormalities and mRNA/miRNA expression profiles appeared to be congruent with those reported in human osteosarcomas. Bioinformatic analyses selected 196 genes and 46 anticorrelated miRNAs involved in carcinogenesis and stemness. For the first time, a predictive network is also described for two miRNA family (let-7/98 and miR-29a,b,c) and their anticorrelated mRNAs (MSTN, CCND2, Lin28B, MEST, HMGA2, and GHR), which may represent new biomarkers for osteosarcoma and may pave the way for the identification of new potential therapeutic targets

Mutant p53 gain of function can be at the root of dedifferentiation of human osteosarcoma MG63 cells into 3AB-OS cancer stem cells.

Osteosarcoma is a highly metastatic tumor affecting adolescents, for which there is no second-line chemotherapy. As suggested for most tumors, its capability to overgrow is probably driven by cancer stem cells (CSCs), and finding new targets to kill CSCs may be critical for improving patient survival. TP53 is the most frequently mutated tumor suppressor gene in cancers and mutant p53 protein (mutp53) can acquire gain of function (GOF) strongly contributing to malignancy. Studies thus far have not shown p53-GOF in osteosarcoma. Here, we investigated TP53 gene status/role in 3AB-OS cells-a highly aggressive CSC line previously selected from human osteosarcoma MG63 cells-to evaluate its involvement in promoting proliferation, invasiveness, resistance to apoptosis and stemness. By RT-PCR, methylation-specific PCR, fluorescent in situ hybridization, DNA sequence, western blot and immunofluorescence analyses, we have shown that-in comparison with parental MG63 cells where TP53 gene is hypermethylated, rearranged and in single copy-in 3AB-OS cells, TP53 is unmethylated, rearranged and in multiple copies, and mutp53 (p53-R248W/P72R) is post-translationally modified and with nuclear localization. p53-R248W/P72R-knockdown by short-interfering RNA reduced the growth and replication rate of 3AB-OS cells, markedly increasing cell cycle inhibitor levels and sensitized 3AB-OS cells to TRAIL-induced apoptosis by DR5 up-regulation; moreover, it strongly decreased the levels of stemness and invasiveness genes. We have also found that the ectopic expression of p53-R248W/P72R in MG63 cells promoted cancer stem-like features, as high proliferation rate, sphere formation, clonogenic growth, high migration and invasive ability; furthermore, it strongly increased the levels of stemness proteins. Overall, the findings suggest the involvement of p53-R248W/P72R at the origin of the aberrant characters of the 3AB-OS cells with the hypothesis that its GOF can be at the root of the dedifferentiation of MG63 cells into CSCs