Distorted Copulas: Constructions and Tail Dependence

Given a copula C, we examine under which conditions on an order isomorphism ψ of [0, 1] the distortion C ψ: [0, 1]2 → [0, 1], C ψ(x, y) = ψ{C[ψ−1(x), ψ−1(y)]} is again a copula. In particular, when the copula C is totally positive of order 2, we give a sufficient condition on ψ that ensures that any distortion of C by means of ψ is again a copula. The presented results allow us to introduce in a more flexible way families of copulas exhibiting different behavior in the tails

A sharp condition for scattering of the radial 3d cubic nonlinear Schroedinger equation

We consider the problem of identifying sharp criteria under which radial $H^1$ (finite energy) solutions to the focusing 3d cubic nonlinear Schr\"odinger equation (NLS) $i\partial_t u + \Delta u + |u|^2u=0$ scatter, i.e. approach the solution to a linear Schr\"odinger equation as $t\to \pm \infty$. The criteria is expressed in terms of the scale-invariant quantities $\|u_0\|_{L^2}\|\nabla u_0\|_{L^2}$ and $M[u]E[u]$, where $u_0$ denotes the initial data, and $M[u]$ and $E[u]$ denote the (conserved in time) mass and energy of the corresponding solution $u(t)$. The focusing NLS possesses a soliton solution $e^{it}Q(x)$, where $Q$ is the ground-state solution to a nonlinear elliptic equation, and we prove that if $M[u]E[u]<M[Q]E[Q]$ and $\|u_0\|_{L^2}\|\nabla u_0\|_{L^2} < \|Q\|_{L^2}\|\nabla Q\|_{L^2}$, then the solution $u(t)$ is globally well-posed and scatters. This condition is sharp in the sense that the soliton solution $e^{it}Q(x)$, for which equality in these conditions is obtained, is global but does not scatter. We further show that if $M[u]E[u] \|Q\|_{L^2}\|\nabla Q\|_{L^2}$, then the solution blows-up in finite time. The technique employed is parallel to that employed by Kenig-Merle \cite{KM06a} in their study of the energy-critical NLS

The dynamics of the 3D radial NLS with the combined terms

In this paper, we show the scattering and blow-up result of the radial solution with the energy below the threshold for the nonlinear Schr\"{o}dinger equation (NLS) with the combined terms iu_t + \Delta u = -|u|^4u + |u|^2u \tag{CNLS} in the energy space $H^1(\R^3)$. The threshold is given by the ground state $W$ for the energy-critical NLS: $iu_t + \Delta u = -|u|^4u$. This problem was proposed by Tao, Visan and Zhang in \cite{TaoVZ:NLS:combined}. The main difficulty is the lack of the scaling invariance. Illuminated by \cite{IbrMN:f:NLKG}, we need give the new radial profile decomposition with the scaling parameter, then apply it into the scattering theory. Our result shows that the defocusing, $\dot H^1$-subcritical perturbation $|u|^2u$ does not affect the determination of the threshold of the scattering solution of (CNLS) in the energy space.Comment: 46page

Stable self-similar blow-up dynamics for slightly L2L^2-supercritical generalized KdV equations

In this paper we consider the slightly $L^2$-supercritical gKdV equations $\partial_t u+(u_{xx}+u|u|^{p-1})_x=0$, with the nonlinearity $5<p<5+\varepsilon$ and $0<\varepsilon\ll 1$ . We will prove the existence and stability of a blow-up dynamic with self-similar blow-up rate in the energy space $H^1$ and give a specific description of the formation of the singularity near the blow-up time.Comment: 38 page

On non-local variational problems with lack of compactness related to non-linear optics

We give a simple proof of existence of solutions of the dispersion manage- ment and diffraction management equations for zero average dispersion, respectively diffraction. These solutions are found as maximizers of non-linear and non-local vari- ational problems which are invariant under a large non-compact group. Our proof of existence of maximizer is rather direct and avoids the use of Lions' concentration compactness argument or Ekeland's variational principle.Comment: 30 page

Years of life that could be saved from prevention of hepatocellular carcinoma

BACKGROUND: Hepatocellular carcinoma (HCC) causes premature death and loss of life expectancy worldwide. Its primary and secondary prevention can result in a significant number of years of life saved. AIM: To assess how many years of life are lost after HCC diagnosis. METHODS: Data from 5346 patients with first HCC diagnosis were used to estimate lifespan and number of years of life lost after tumour onset, using a semi-parametric extrapolation having as reference an age-, sex- and year-of-onset-matched population derived from national life tables. RESULTS: Between 1986 and 2014, HCC lead to an average of 11.5 years-of-life lost for each patient. The youngest age-quartile group (18-61 years) had the highest number of years-of-life lost, representing approximately 41% of the overall benefit obtainable from prevention. Advancements in HCC management have progressively reduced the number of years-of-life lost from 12.6 years in 1986-1999, to 10.7 in 2000-2006 and 7.4 years in 2007-2014. Currently, an HCC diagnosis when a single tumour <2 cm results in 3.7 years-of-life lost while the diagnosis when a single tumour 65 2 cm or 2/3 nodules still within the Milan criteria, results in 5.0 years-of-life lost, representing the loss of only approximately 5.5% and 7.2%, respectively, of the entire lifespan from birth. CONCLUSIONS: Hepatocellular carcinoma occurrence results in the loss of a considerable number of years-of-life, especially for younger patients. In recent years, the increased possibility of effectively treating this tumour has improved life expectancy, thus reducing years-of-life lost

An Immersive Haptic Experimentation for Dematerialized Textile Perception in Collaborative Design Processes

This experimentation arises in the context of the design process of digital tools in the fashion sector of Made in Italy. The contribution presents an overview of the main insights gained from the analysis of the state of the art and experimentation conducted in order to obtain a low-cost digital textile sampling and restitution process useful for possible new advanced modalities of collaborative remote design. This project is related to the extended MICS partnership of the PNRR project that researches at a low TRL level new scenarios for the integration of immersive technologies in traditional craft processes

Regenerative Endodontic Procedures for the Treatment of Necrotic Mature Teeth with Apical Periodontitis: A Systematic Review and Meta-analysis of Randomized Controlled Trials

Introduction: Regenerative endodontic procedures (REPs) are intended to repair and regenerate part of the pulp-dentin complex. The aim of this study was to systematically appraise the existing evidence on the effectiveness of REPs on mature teeth with pulp necrosis and apical periodontitis. Methods: Electronic database and hand searches were performed on 8 databases of published and unpublished literature from inception to January 3, 2021, for the identification of randomized controlled trials (RCTs) or prospective clinical trials. The related key words included “regenerative,” “pulp revascularization,” “revitalization procedure,” and “necrotic mature teeth.” A random effects meta-analysis was conducted assessing success as the main outcome treatment. Risk of bias was assessed through the Cochrane Risk of Bias 2.0 tool, and the quality of the evidence was assessed with the Grading of Recommendations Assessment, Development and Evaluation approach. Results: Of the 337 initial hits, 4 RCTs were eligible for inclusion, whereas 3 were included in the quantitative synthesis. Overall, there was no difference in the relative risk for a successful/unsuccessful treatment outcome between REPs or conventional treatment (3 studies, relative risk = 1.03; 95% confidence interval, 0.92–1.15; P =.61; heterogeneity I2 = 0.0%, P =.53; prediction interval = 0.51–2.09). Risk of bias ranged from low to raising some concerns, whereas the quality of the evidence was graded as moderate. Conclusions: Based on moderate-quality evidence, REPs appear as a viable treatment alternative for mature necrotic teeth with periapical lesions at present. Furthermore, well-designed RCTs might also provide confirmatory evidence in this respect while also framing a backbone for standardization of the therapeutic protocol of REPs

Design and Synthesis of Hsp90 Inhibitors with B-Raf and PDHK1 Multi-Target Activity

5noopenThe design of multi-target ligands has become an innovative approach for the identification of effective therapeutic treatments against complex diseases, such as cancer. Recent studies have demonstrated that the combined inhibition of Hsp90 and B-Raf provides synergistic effects against several types of cancers. Moreover, it has been reported that PDHK1, which presents an ATP-binding pocket similar to that of Hsp90, plays an important role in tumor initiation, maintenance and progression, participating also to the senescence process induced by B-Raf oncogenic proteins. Based on these premises, the simultaneous inhibition of these targets may provide several benefits for the treatment of cancer. In this work, we set up a design strategy including the assembly and integration of molecular fragments known to be important for binding to the Hsp90, PDHK1 and B-Raf targets, aided by molecular docking for the selection of a set of compounds potentially able to exert Hsp90-B-Raf-PDHK1 multi-target activities. The designed compounds were synthesized and experimentally validated in vitro. According to the in vitro assays, compounds 4 a, 4 d and 4 e potently inhibited Hsp90 and moderately inhibited the PDHK1 kinase. Finally, molecular dynamics simulations were performed to provide further insights into the structural basis of their multi-target activity.openPinzi L.; Foschi F.; Christodoulou M.S.; Passarella D.; Rastelli G.Pinzi, L.; Foschi, F.; Christodoulou, M. S.; Passarella, D.; Rastelli, G

Vincamine by synthesis and semi-synthesis

This review summarizes the main strategies aimed at the total synthesis of vincamine and congeners. Then, our contribution in this field is presented: we describe (+)-vincamine semi-synthesis using tabersonine as starting material. Characterization and quantification of the main impurities are discussed, and HPLC conditions, structural elucidation and NMR data of four of them are reported