Asymptotic base loci on singular varieties

We prove that the non-nef locus and the restricted base locus of a pseudoeffective divisor coincide on KLT pairs. We also extend to KLT pairs F. Russo's characterization of nef and abundant divisors by means of asymptotic multiplier ideals.Comment: Improved exposition. To appear in "Math. Z.

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

The evolution of composite indices of well-being: An application to Italy

Abstract Prompted by the work of the Stiglitz's Commission, the growing attention to the beyond-GDP measures has led to the inclusion of well-being indicators in the policy agenda. This innovation asks for an improvement of the existing methodology to produce composite indices, in order to correctly address spatial and temporal comparisons as well as tackling for unbalances. Following a short review of the main international experiences, this paper will investigate these issues considering the methodology currently adopted to normalize and aggregate the selected individual indicators included in the Italian well-being. We study the properties of this methodology looking at different normalization and aggregation approaches and underlining some drawbacks, mostly due to the way in which time dimension, normalization, aggregation and unbalance adjustment interplay with each other. We illustrate our findings by means of examples related also to the ecological side. We argue that new efforts should be done to overcome these drawbacks extending the research agenda toward new non-compensatory approaches. Testing for time series methods, such as dynamic factor models could represent another important step forward. Meanwhile the introduction of a more traditional framework for the composite indicators for Italian well-being could be considered

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

Simulating the development and progression of Chronic Kidney Disease and osteoporosis in people living with HIV

The "chronicization" of HIV infection brings about a growing necessity to attentively evaluate current and potential complications when prescribing the individual therapeutic regimen. Starting from this need, we developed two HIV-comorbidity simulators that, basing on the evidence available in medical literature and starting from the current clinical and demographic features of the individual patient, project and compare the risks of developing and worsening of nephropathy and osteopathy associated with possible ARV regimens. These simulators are embedded in a desktop, user-friendly software thought to be used by the treating physician during prescription discussion with his/her patients, in order to highlight expected clinical outcomes and healthcare resource consumption that may differ according to the therapeutic strategy selected. In this article we present the sources and methods used in developing the mathematical models, alongside a set of examples and the results of cohort-level validation runs

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