Problems for p-Monge-Ampère equations

We consider the homogeneous Dirichlet problem for a class of equations which generalize the p-Laplace equations as well as the Monge- Amp`ere equations in a strictly convex domain Ω ⊂ Rn, n ≥ 2. In the sub-linear case, we study the comparison between quantities involving the solution to this boundary value problem and the corresponding quantities involving the (radial) solution of a problem in a ball having the same η1- mean radius as Ω. Next, we consider the eigenvalue problem for such a p-Monge-Amp`ere equation and study a comparison between its principal eigenvalue (eigenfunction) and the principal eigenvalue (eigenfunction) of the corresponding problem in a ball having the same η1-mean radius as Ω. Symmetrization techniques and comparison principles are the main tools used to get our results

Best Possible Maximum Principles for Fully Nonlinear Elliptic Partial Differential Equations

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Hybrid lipid self-assembling nanoparticles for brain delivery of microRNA

Hybrid self-assembling nanoparticles (SANPs) have been previously designed as novel drug delivery system that overcomes stability issues following long-term storage and with an easy scale-up. This system has been successfully used to deliver anionic-charged agents, e.g. bisphosphonates, in different types of tumors, such glioblastoma (GBM). Here, SANPs were tested and optimized for the delivery of nucleic acids, in particular of a specific microRNA, e.g. miR603, used for its potential role in controlling the chemoresistance in different forms of cancer, e.g. (GBM). To this aim, SANPs with different lipids were prepared and characterized, in terms of size, polydispersity index, zeta potential, miRNA encapsulation, stability in BSA, serum and hemolytic activity. Then, SANPs were tested in vitro on two different cell lines of GBM. Finally, miRNA biodistribution was tested in vivo in an orthotopic model of GBM. The majority of the formulations showed good technological characteristics and were stable in BSA and serum with a low hemolytic activity. The intracellular uptake studies on GBM cell lines showed that SANPs allow to achieve a higher miRNA delivery compared to others transfection agents, e.g. lipofectamine. Finally, in vivo biodistribution studies in an orthotopic of GBM demonstrated that the optimized SANP formulations, were able to deliver miRNA in different organs, e.g. the brain

Shimura varieties in the Torelli locus via Galois coverings of elliptic curves

We study Shimura subvarieties of $\mathsf{A}_g$ obtained from families of Galois coverings $f: C \rightarrow C'$ where $C'$ is a smooth complex projective curve of genus $g' \geq 1$ and $g= g(C)$. We give the complete list of all such families that satisfy a simple sufficient condition that ensures that the closure of the image of the family via the Torelli map yields a Shimura subvariety of $\mathsf{A}_g$ for $g' =1,2$ and for all $g \geq 2,4$ and for $g' > 2$ and $g \leq 9$. In a previous work of the first and second author together with A. Ghigi [FGP] similar computations were done in the case $g'=0$. Here we find 6 families of Galois coverings, all with $g' = 1$ and $g=2,3,4$ and we show that these are the only families with $g'=1$ satisfying this sufficient condition. We show that among these examples two families yield new Shimura subvarieties of $\mathsf{A}_g$, while the other examples arise from certain Shimura subvarieties of $\mathsf{A}_g$ already obtained as families of Galois coverings of $\mathbb{P}^1$ in [FGP]. Finally we prove that if a family satisfies this sufficient condition with $g'\geq 1$, then $g \leq 6g'+1$.Comment: 18 pages, to appear in Geometriae Dedicat

Role of nucleus accumbens μ opioid receptors in the effects of morphine on ERK1/2 phosphorylation

Rationale: Despite the critical role attributed to phosphorylated extracellular signal regulated kinase (pERK1/2) in the nucleus accumbens (Acb) in the actions of addictive drugs, the effects of morphine on ERK1/2 phosphorylation in this area are still controversial. Objectives: In order to investigate further this issue, we studied (1) the ability of morphine to affect ERK1/2 phosphorylation in the shell (AcbSh) and core (AcbC) of Sprague-Dawley and Wistar rats and of CD-1 and C57BL/6J mice and (2) the role of dopamine D1 and μ-opioid receptors in Sprague-Dawley rats and CD-1 mice. Methods: The pERK1/2 expression was assessed by immunohistochemistry. Results: In rats, morphine decreased AcbSh and AcbC pERK1/2 expression, whereas in mice, increased it preferentially in the AcbSh compared with the AcbC. Systemic SCH 39166 decreased pERK1/2 expression on its own in the AcbSh and AcbC of Sprague-Dawley rats and CD-1 mice; furthermore, in rats, SCH 39166 disclosed the ability of morphine to stimulate pERK1/2 expression. Systemic (rats and mice) and intra-Acb (rats) naltrexone prevented both decreases, in rats, and increases, in mice. Conclusions: These findings confirm the differential effects of morphine in rats and mice Acb and that D1 receptors exert a facilitatory role on ERK1/2 phosphorylation; furthermore, they indicate that, in rats, removal of the D1-dependent pERK1/2 expression discloses the stimulatory influence of morphine on ERK1/2 phosphorylation and that the morphine’s ability to decrease pERK1/2 expression is mediated by Acb μ-opioid receptors. Future experiments may disentangle the psychopharmacological significance of the effects of morphine on pERK1/2 in the Acb

The probabilistic random forest applied to the QUBRICS survey: improving the selection of high-redshift quasars with synthetic data

Several recent works have focused on the search for bright, high-z quasars (QSOs) in the South. Among them, the QUasars as BRIght beacons for Cosmology in the Southern hemisphere (QUBRICS) survey has now delivered hundreds of new spectroscopically confirmed QSOs selected by means of machine learning algorithms. Building upon the results obtained by introducing the probabilistic random forest (PRF) for the QUBRICS selection, we explore in this work the feasibility of training the algorithm on synthetic data to improve the completeness in the higher redshift bins. We also compare the performances of the algorithm if colours are used as primary features instead of magnitudes. We generate synthetic data based on a composite QSO spectral energy distribution. We first train the PRF to identify QSOs among stars and galaxies, then separate high-z quasar from low-z contaminants. We apply the algorithm on an updated data set, based on SkyMapper DR3, combined with Gaia eDR3, 2MASS, and WISE magnitudes. We find that employing colours as features slightly improves the results with respect to the algorithm trained on magnitude data. Adding synthetic data to the training set provides significantly better results with respect to the PRF trained only on spectroscopically confirmed QSOs. We estimate, on a testing data set, a completeness of ∼ 86 per cent and a contamination of ∼ 36 per cent. Finally, 206 PRF-selected candidates were observed: 149/206 turned out to be genuine QSOs with z > 2.5, 41 with z < 2.5, 3 galaxies and 13 stars. The result confirms the ability of the PRF to select high-z quasars in large data sets

Influence of MLH1 on colon cancer sensitivity to poly(ADP-ribose) polymerase inhibitor combined with irinotecan

Poly(ADP-ribose) polymerase inhibitors (PARPi) are currently evaluated in clinical trials in combination with topoisomerase I (Top1) inhibitors against a variety of cancers, including colon carcinoma. Since the mismatch repair component MLH1 is defective in 10-15% of colorectal cancers we have investigated whether MLH1 affects response to the Top1 inhibitor irinotecan, alone or in combination with PARPi. To this end, the colon cancer cell lines HCT116, carrying MLH1 mutations on chromosome 3 and HCT116 in which the wildtype MLH1 gene was replaced via chromosomal transfer (HCT116+3) or by transfection of the corresponding MLH1 cDNA (HCT116 1-2) were used. HCT116 cells or HCT116+3 cells stably silenced for PARP-1 expression were also analysed. The results of in vitro and in vivo experiments indicated that MLH1, together with low levels of Top1, contributed to colon cancer resistance to irinotecan. In the MLH1-proficient cells SN-38, the active metabolite of irinotecan, induced lower levels of DNA damage than in MLH1-deficient cells, as shown by the weaker induction of γ-H2AX and p53 phosphorylation. The presence of MLH1 contributed to induce of prompt Chk1 phosphorylation, restoring G2/M cell cycle checkpoint and repair of DNA damage. On the contrary, in the absence of MLH1, HCT116 cells showed minor Chk1 phosphorylation and underwent apoptosis. Remarkably, inhibition of PARP function by PARPi or by PARP-1 gene silencing always increased the antitumor activity of irinotecan, even in the presence of low PARP-1 expression

Crossing the Rubicon of Reionization with z~5 QSOs

One of the key open questions in Cosmology is the nature of the sources that completed the cosmological hydrogen Reionization at z~5.2. High-z primeval galaxies have been long considered the main drivers for Reionization, with a minor role played by high-z AGN. However, in order to confirm this scenario, it is fundamental to measure the photo-ionization rate produced by active SMBHs close to the epoch of Reionization. Given the pivotal role played by spectroscopically complete observations of high-z QSOs, in this paper we present the first results of the RUBICON (Reionizing the Universe with BrIght COsmological Nuclei) survey. It consists of a color selected sample of bona-fide z~5 QSO candidates from the Hyper Suprime-Cam Subaru Strategic Survey. Our QSO candidates have been validated both by photometric redshifts based on SED fitting and by spectroscopic redshifts, confirming that they lie at 4.5<5.2. A relatively large space density of QSOs (Phi~1.4x10^-8 cMpc^-3) is thus confirmed at z~5 and M1450~-27, consistent with a pure density evolution of the AGN luminosity function from z=4 to z=5, with a mild density evolution rate of 0.25 dex. This indicates that AGN could play a non-negligible role in the cosmic Reionization. The Rubicon of Reionization has been crossed

Spectroscopy of QUBRICS quasar candidates: 1672 new redshifts and a golden sample for the Sandage test of the redshift drift

The QUBRICS (QUasars as BRIght beacons for Cosmology in the Southern hemisphere) survey aims at constructing a sample of the brightest quasars with z∼> 2.5, observable with facilities in the Southern Hemisphere. QUBRICS makes use of the available optical and IR wide-field surveys in the South and of Machine Learning techniques to produce thousands of bright quasar candidates of which only a few hundred have been confirmed with follow-up spectroscopy. Taking advantage of the recent Gaia Data Release 3, which contains 220 million low-resolution spectra, and of a newly developed spectral energy distribution fitting technique, designed to combine the photometric information with the Gaia spectroscopy, it has been possible to measure 1672 new secure redshifts of QUBRICS candidates, with a typical uncertainty of σz = 0.02. This significant progress of QUBRICS brings it closer to (one of) its primary goals: providing a sample of bright quasars at redshift 2.5 < z < 5 to perform the Sandage test of the cosmological redshift drift. A Golden Sample of seven quasars is presented that makes it possible to carry out this experiment in about 1500 h of observation in 25 yr, using the ANDES spectrograph at the 39m ELT, a significant improvement with respect to previous estimates