Steiner symmetry in the minimization of the first eigenvalue in problems involving the p-Laplacian

Let Ω ⊂ ℝN be an open bounded connected set. We consider the eigenvalue problem −Δpu = λρ|u|p−2u in Ω with homogeneous Dirichlet boundary condition, where Δp is the p-Laplacian operator and ρ is an arbitrary function that takes only two given values 0 < α < β and that is subject to the constraint ∫Ω ρdx = αγ +β(|Ω|−γ) for a fixed 0 < γ < |Ω|. The optimization of the map ρ ↦ λ1(ρ), where λ1 is the first eigenvalue, has been studied by Cuccu, Emamizadeh and Porru. In this paper we consider a Steiner symmetric domain Ω and we show that the minimizers inherit the same symmetry

Symmetry and regularity of an optimization problem related to a nonlinear BVP

We consider the functional where uf is the unique nontrivial weak solution of the boundary-value problem where Ω ⊂ Rn is a bounded smooth domain. We prove a result of Steiner symmetry preservation and, if n = 2, we show the regularity of the level sets of minimizers

Minimization of the first eigenvalue in problems involving the bi-laplacian

This paper concerns the minimization of the first eigenvalue in problems involvingthe bi-Laplacian under either homogeneous Navier boundary conditions or homogeneousDirichlet boundary conditions. Physically, in case of N = 2, our equation modelsthe vibration of a non homogeneous plate  which is either hinged or clamped alongthe boundary. Given several materials (with different densities) of total extension ||,we investigate the location of these materials inside  so to minimize the first modein the vibration of the corresponding plate.Keywords: bi-Laplacian, first eigenvalue, minimization.Este art´?culo trata de la minimizaci´on del primer autovalor en problemas relativosal bi-Laplaciano bajo condiciones de frontera homog´eneas de tipo Navier o Dirichlet.F´?sicamente, en el problema bi-dimensional, nuestra ecuacin modela la vibraci´on deuna placa inhomog´enea  fija con goznes a lo largo de su borde. Dados varios materiales(de diferentes densidades) y extensi´on total ||, investigamos cu´al debe serla localizaci´on de tales materiales en la placa para minimizar el primer modo de suvibraci´on.Palabras clave: bi-Laplaciano, primer autovalor, minimizaci´on

Boundary estimates for solutions to singular elliptic equations

We deal with the Dirichlet problem in a bounded smooth domain.[omissis

Acute Delta Hepatitis in Italy spanning three decades (1991–2019): Evidence for the effectiveness of the hepatitis B vaccination campaign

Updated incidence data of acute Delta virus hepatitis (HDV) are lacking worldwide. Our aim was to evaluate incidence of and risk factors for acute HDV in Italy after the introduction of the compulsory vaccination against hepatitis B virus (HBV) in 1991. Data were obtained from the National Surveillance System of acute viral hepatitis (SEIEVA). Independent predictors of HDV were assessed by logistic-regression analysis. The incidence of acute HDV per 1-million population declined from 3.2 cases in 1987 to 0.04 in 2019, parallel to that of acute HBV per 100,000 from 10.0 to 0.39 cases during the same period. The median age of cases increased from 27 years in the decade 1991-1999 to 44 years in the decade 2010-2019 (p &lt; .001). Over the same period, the male/female ratio decreased from 3.8 to 2.1, the proportion of coinfections increased from 55% to 75% (p = .003) and that of HBsAg positive acute hepatitis tested for by IgM anti-HDV linearly decreased from 50.1% to 34.1% (p &lt; .001). People born abroad accounted for 24.6% of cases in 2004-2010 and 32.1% in 2011-2019. In the period 2010-2019, risky sexual behaviour (O.R. 4.2; 95%CI: 1.4-12.8) was the sole independent predictor of acute HDV; conversely intravenous drug use was no longer associated (O.R. 1.25; 95%CI: 0.15-10.22) with this. In conclusion, HBV vaccination was an effective measure to control acute HDV. Intravenous drug use is no longer an efficient mode of HDV spread. Testing for IgM-anti HDV is a grey area requiring alert. Acute HDV in foreigners should be monitored in the years to come

Association of Variants in the SPTLC1 Gene With Juvenile Amyotrophic Lateral Sclerosis

Importance: Juvenile amyotrophic lateral sclerosis (ALS) is a rare form of ALS characterized by age of symptom onset less than 25 years and a variable presentation.Objective: To identify the genetic variants associated with juvenile ALS.Design, Setting, and Participants: In this multicenter family-based genetic study, trio whole-exome sequencing was performed to identify the disease-associated gene in a case series of unrelated patients diagnosed with juvenile ALS and severe growth retardation. The patients and their family members were enrolled at academic hospitals and a government research facility between March 1, 2016, and March 13, 2020, and were observed until October 1, 2020. Whole-exome sequencing was also performed in a series of patients with juvenile ALS. A total of 66 patients with juvenile ALS and 6258 adult patients with ALS participated in the study. Patients were selected for the study based on their diagnosis, and all eligible participants were enrolled in the study. None of the participants had a family history of neurological disorders, suggesting de novo variants as the underlying genetic mechanism.Main Outcomes and Measures: De novo variants present only in the index case and not in unaffected family members.Results: Trio whole-exome sequencing was performed in 3 patients diagnosed with juvenile ALS and their parents. An additional 63 patients with juvenile ALS and 6258 adult patients with ALS were subsequently screened for variants in the SPTLC1 gene. De novo variants in SPTLC1 (p.Ala20Ser in 2 patients and p.Ser331Tyr in 1 patient) were identified in 3 unrelated patients diagnosed with juvenile ALS and failure to thrive. A fourth variant (p.Leu39del) was identified in a patient with juvenile ALS where parental DNA was unavailable. Variants in this gene have been previously shown to be associated with autosomal-dominant hereditary sensory autonomic neuropathy, type 1A, by disrupting an essential enzyme complex in the sphingolipid synthesis pathway.Conclusions and Relevance: These data broaden the phenotype associated with SPTLC1 and suggest that patients presenting with juvenile ALS should be screened for variants in this gene.</p

Genome-wide Analyses Identify KIF5A as a Novel ALS Gene

To identify novel genes associated with ALS, we undertook two lines of investigation. We carried out a genome-wide association study comparing 20,806 ALS cases and 59,804 controls. Independently, we performed a rare variant burden analysis comparing 1,138 index familial ALS cases and 19,494 controls. Through both approaches, we identified kinesin family member 5A (KIF5A) as a novel gene associated with ALS. Interestingly, mutations predominantly in the N-terminal motor domain of KIF5A are causative for two neurodegenerative diseases: hereditary spastic paraplegia (SPG10) and Charcot-Marie-Tooth type 2 (CMT2). In contrast, ALS-associated mutations are primarily located at the C-terminal cargo-binding tail domain and patients harboring loss-of-function mutations displayed an extended survival relative to typical ALS cases. Taken together, these results broaden the phenotype spectrum resulting from mutations in KIF5A and strengthen the role of cytoskeletal defects in the pathogenesis of ALS.Peer reviewe

Proprietà qualitative delle soluzioni di alcuni problemi di ottimizzazione

Sunto di Tesi di Dottorato

The securitisation of religion. Training imams to address violent extremism in post-revolutionary Tunisia

This dissertation analyses the development of Tunisia’s Preventing and Countering Violent Extremism (P/CVE) policies by examining two local programmes focusing on training imams in democratic discourses and values. Taking a genealogical approach, this thesis examines P/CVE measures as the latest iteration of a postcolonial enterprise and asks if these programmes result in the exclusion or marginalisation of specific social groups. Its objective is to analyse whether the opening of the political sphere due to the post-211 democratic transition has led to a democratisation of the security and surveillance apparatus, with a desecuritisation of religion and religious leaders’ public role, or whether the state’s control over the religious sphere has remained unchanged after 2011. I chose Tunisia as a case-study because of its long history of systematic control over Islamists and religious groups and movements. Scholars have studied the role of religion and the moderate vs radical Islam binary in maintaining and legitimising the ruling elite in power, while perpetuating the exclusion of disenfranchised social groups. However, the role of security policies and particularly P/CVE in shaping the mainstream discourse on religion has so far been neglected, despite being central to post-2011 transition and in consideration of the multiple terroristic attack in the past four years in Tunisia. Building on postcolonial scholarship and methodological approaches, I use critical discourse analysis, qualitative interviews, and ethnographic fieldwork to examine the implementation of P/CVE programmes in the country and their implications for the de-securitisation of religion. In particular, I have examined P/CVE at different levels. First, my work focuses on the role of Tunisian civil society organisations (CSOs) in training imams to prevent or address radicalisation processes leading to violent extremism. Second, on the donors – mostly international donors – that support such training programmes and the implementation of P/CVE and third, on imams, that is, the receiving end of the training programmes and crucial actors in preventative programmes as non-traditional security professionals. Through 3 interview with international donors, local CSOs and imams, I argue that Tunisian institutions used the P/CVE framework to legitimise the use of special security measures in the aftermath of the terroristic attacks of 2013 and 2015. Such institutional action, however, has not gone unchallenged. In fact, I have observed that local imams partly challenge the implementation of preventative programmes, by accepting their role as community leaders but rejecting their role as security professionals. In conclusion, the thesis argues that the role of religion in the public sphere has remined a highly securitised policy space where, in spite of larger political liberalisation, the state plays a securitarian role – paradoxically, even when its policy role is less central. The elaboration, implementation and assessment of P/CVE programmes is in fact in the hands of international donors and local CSOs, with Tunisian state institutions having a relatively small role in this policy cycle. In continuity with pre-2011 period, the state has not liberalised or de-securitised religion as a policy field