Restricted volumes of effective divisors

We study the restricted volume of effective divisors, its properties and the relationship with the related notion of reduced volume, defined via multiplier ideals, and with the asymptotic intersection number. We build upon the fundamental work of Lazarsfeld and Mustata relating the restricted volume of big divisors to the volume of the associated Okounkov body. We extend their constructions and results to the case of effective divisors, recovering some results of Kaveh and Khovanskii, proving a Fujita-type approximation in this larger setting and studying the restricted volume function. In order to relate the reduced volume and the asymptotic intersection number we investigate a boundedness property of asymptotic multiplier ideals and prove it holds, for instance, for finitely generated divisors. In this way we obtain also a complete picture for the canonical divisor of an arbitrary smooth projective variety and for nef divisors on varieties of dimension at most 3.Comment: 32 page

Euler pseudoprimes for half of the bases

We prove that an odd number is an Euler pseudoprime for exactly one half of the admissible bases if and only if it is a special Carmichael number.Comment: 4 pages. To appear in Integer

Pluricanonical systems for 3-folds and 4-folds of general type

We explicitly find lower bounds on the volume of threefolds and fourfolds of general type in order to have nonvanishing of pluricanonical systems and birationality of pluricanonical maps. In the case of threefolds of large volume, we also give necessary and sufficient conditions for the fourth canonical map to be birational.Comment: 25 pages. Minor corrections and improved exposition. To appear in Mathematical Proceedings of the Cambridge Philosophical Societ

Indicatori comuni del PNRR e framework SDGs: una proposta di indicatore composito

The main component of the NextGeneration EU (NGEU) program is the Recovery and Resilience Facility (RRF), spanning an implementation period between 2021 and 2026. The RRF also includes a monitoring system: every six months, each country is required to send an update on the progress of the plan against 14 common indicators, measured on specific quantitative scales. The aim of this paper is to present the first empirical evidence on this system, while, at the same time, emphasizing the potential of its integration with the sustainable development framework (SDGs). We propose to develop a first linkage between the 14 common indicators and the SDGs which allows us to produce a composite index (SDGs-RRF) for France, Germany, Italy, and Spain for the period 2014-2021. Over this time, widespread improvements in the composite index across the four countries led to a partial reduction of the divergence. The proposed approach represents a first step towards a wider use of the SDGs for the assessment of the RRF, in line with their use in the European Semester documents prepared by the European Commission.Comment: 30 pages, in Italian, 10 figures, 13 table

The Evolution of the Italian Framework to Measure Well-Being

Abstract Recently, a new approach for measuring well-being was developed by eighteen European countries in the wake of the "Beyond GDP movement" started in the 1990 and continued by the Stiglitz Commission. Among these European economies, eleven of them use measures of well-being for monitoring public policy. The Italian Statistical Institute (Istat) jointly with the National Council for Economics and Labor (CNEL) developed a multi-dimensional framework for measuring "equitable and sustainable well-being" (Bes) and since 2013 Istat publishes an annual report on well-being. The Bes framework is continuously updated to take into account new challenges: the exploitation of new data sources, to produce better indicators; new ways for making the communication more effective and foster public awareness; the inclusion of well-being indicators in the budget documents, as established by law. Especially for the latter, the Italian Bes can be considered a forerunner and, more generally, the Italian experience is one of the most relevant at the European level, showing potential of become a benchmark for other countries. This article illustrates the development of the Italian Bes, focusing on its recent progresses and challenges

Apolarity, Hessian and Macaulay polynomials

A result by Macaulay states that an Artinian graded Gorenstein ring R of socle dimension one and socle degree b can be realized as the apolar ring of a homogeneous polynomial f of degree b. If R is the Jacobian ring of a smooth hypersurface g=0, then b is just equal to the degree of the Hessian polynomial of g. In this paper we investigate the relationship between f and the Hessian polynomial of g.Comment: 12 pages. Improved exposition, minor correction

Persistence of Unintegrated HIV DNA Associates With Ongoing NK Cell Activation and CD34+DNAM-1brightCXCR4+ Precursor Turnover in Vertically Infected Patients Despite Successful Antiretroviral Treatment

none11noThe quantification of proviral DNA is raising interest in view of clinical management and functional HIV eradication. Measures of all unintegrated HIV DNA (uDNA) forms in infected reservoir cells provides information on recent replication events that is not found from other proviral DNA assays. To evaluate its actual relevance in a cohort of perinatally-infected adult HIV patients (PHIV), we studied how peripheral blood mononuclear cell uDNA levels correlated with total HIV DNA (tDNA) and with overall replication or innate immune control parameters including NK cell activation/exhaustion and lymphoid turnover. Twenty-two PHIV were included, with successfully controlled HIV (HIV RNA <50 copies/mL) on combined antiretroviral therapy for mean of 8.7 ± 3.9 years. uDNA accounted for 16 [5.2-83.5] copies/µg and was strongly correlated with tDNA (ρ=0.700, p=0.001). Flow cytometric analysis of peripheral NK cells showed that CD69 expression was directly correlated uDNA (p=0.0412), but not with tDNA. Interestingly, CD56-CD16+NK cells which include newly described inflammatory precursors and terminally differentiated cells were directly correlated with uDNA levels (p<0.001), but not with tDNA, and an inverse association was observed between the proportion of NKG2D+ NK cells and uDNA (ρ=-0.548, p=0.015). In addition, CD34+DNAM-1brightCXCR4+ inflammatory precursor frequency correlated directly with uDNA levels (ρ=0.579, p=0.0075). The frequencies of CD56-CD16+ and CD34+DNAM-1brightCXCR4+ cells maintained association with uDNA levels in a multivariable analysis (p=0.045 and p=0.168, respectively). Thus, control of HIV-1 reservoir in aviremic patients on ART is an active process associated with continuous NK cell intervention and turnover, even after many years of treatment. Quantification of linear and circular uDNA provides relevant information on the requirement for ongoing innate immune control in addition to ART, on recent replication history and may help stratify patients for functional HIV eradication protocols with targeted options.openTaramasso, Lucia; Bozzano, Federica; Casabianca, Anna; Orlandi, Chiara; Bovis, Francesca; Mora, Sara; Giacomini, Mauro; Moretta, Lorenzo; Magnani, Mauro; Di Biagio, Antonio; De Maria, AndreaTaramasso, Lucia; Bozzano, Federica; Casabianca, Anna; Orlandi, Chiara; Bovis, Francesca; Mora, Sara; Giacomini, Mauro; Moretta, Lorenzo; Magnani, Mauro; Di Biagio, Antonio; De Maria, Andre

β-Arrestin-1 expression and epithelial-to-mesenchymal transition in laryngeal carcinoma.

Aim: The novel primary end-point of the present study was to ascertain β-arrestin-1 expression in a cohort of consecutive patients with laryngeal squamous cell carcinoma (LSCC) with information available on their cigarette-smoking habits. A secondary end-point was to conduct a preliminary clinical and pathological investigation into the possible role of β-arrestin-1 in the epithelial-to-mesenchymal transition (EMT), identified by testing for E-cadherin, Zeb1, and Zeb2 expression, in the setting of LSCC. Methods: The expression of β-arrestin-1, E-cadherin, zeb1, and zeb2 was ascertained in 20 consecutive LSCCs. Results: Statistical analysis showed no significant associations between β-arrestin-1 and EMT (based on the expression of E-cadherin, Zeb1, and Zeb2). The combined effect of nicotine and β-arrestin-1 was significantly associated with a shorter disease-free survival ( P=0.01) in our series of LSCC. This latter result was also confirmed in an independent, publicly available LSCC cohort ( P=0.047). Conclusions: Further investigations on larger series (ideally in prospective settings) are needed before we can consider closer follow-up protocols and/or more aggressive treatments for patients with LSCC and a combination of nicotine exposure and β-arrestin-1 positivity in tumor cells at the time of their diagnosis. Further studies on how β-arrestin functions in cancer via different signaling pathways might reveal potential targets for the treatment of even advanced laryngeal malignancies

Immune Checkpoint Inhibitors as a Neoadjuvant/Adjuvant Treatment of Muscle-Invasive Bladder Cancer: A Systematic Review

Bladder cancer is the ninth most common cancer worldwide. Over 75% of non-muscle invasive cancer patients require conservative local treatment, while the remaining 25% of patients undergo radical cystectomy or radiotherapy. Immune checkpoint inhibitors represent a novel class of immunotherapy drugs that restore natural antitumoral immune activity via the blockage of inhibitory receptors and ligands expressed on antigen-presenting cells, T lymphocytes and tumour cells. The use of immune checkpoint inhibitors in bladder cancer has been expanded from the neoadjuvant setting, i.e., after radical cystectomy, to the adjuvant setting, i.e., before the operative time or chemotherapy, in order to improve the overall survival and to reduce the morbidity and mortality of both the disease and its treatment. However, some patients do not respond to checkpoint inhibitors. As result, the capability for identifying patients that are eligible for this immunotherapy represent one of the efforts of ongoing studies. The aim of this systematic review is to summarize the most recent evidence regarding the use of immune checkpoint inhibitors, in a neoadjuvant and adjuvant setting, in the treatment of muscle-invasive bladder cancer