A uniqueness criterion for measure-valued solutions of scalar hyperbolic conservation laws

We prove existence and uniqueness of Radon measure-valued solutions of the Cauchy problem $$\begin{cases} u_t+[\varphi(u)]_x=0 & \text{in } \mathbb{R}\times (0,T) \\ u=u_0\ge 0 &\text{in } \mathbb{R}\times \{0\}, \end{cases}$$ where $u_0$ a positive Radon measure whose singular part is a finite superposition of Dirac masses, and $\varphi\in C^2([0,\infty))$ is bounded. The novelty of the paper is the introduction of a compatibility condition which, combined with standard entropy conditions, guarantees uniqueness

Sobolev approximation for two-phase solutions of forward-backward parabolic problems

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Dolutegravir-based anti-retroviral therapy is effective and safe in HIV-infected paediatric patients

BACKGROUND: Treatment of HIV infection in adolescents is challenging due to long duration of therapy and poor adherence. Recently, the integrase strand transfer inhibitor dolutegravir (DTG) has been approved for the use in adolescents with HIV, but evidence in clinical practice is very limited. METHODS: We describe six cases of HIV-infected children/adolescents successfully treated with DTG-based regimen. Data relative to children/adolescents managed at the Referral Center for Pediatric HIV/AIDS of the University of Naples were reviewed. Patients were tested before introduction of DTG, after 1 month and every 3 months in the first 2 years to assess virologic and immunological response, tolerance and development of side effects. Families were asked to report any suspected adverse events. RESULTS: Six patients (2 male, median age 17 years, range 12-18) were started on DTG-based anti-retroviral regimen due to low adherence to anti-retroviral treatment (ART), multiple drug resistance mutations, or development of ART-related side effects. Within 4-8 weeks after DTG treatment onset, a complete viral suppression and a concomitant increase of CD4+ cell count was observed. Four patients showed a persistent suppression after 2 years of follow-up, and 2 patients at about 1 year. One month after the introduction of DTG, the patient enrolled because of severe dyslipidaemia and hyper-transaminasemia showed a complete normalization of laboratory values. During follow-up (median 24 months, range 9-24) no adverse events were reported and most patients demonstrated a good adherence to treatment. CONCLUSIONS: DTG-based treatments demonstrated efficacy and good safety profile in adolescents. All patients demonstrated a rapid virologic and immunological response within 4-8 weeks, with good adherence and absence of side effects

Radon measure-valued solutions of first order scalar conservation laws

Abstract We study nonnegative solutions of the Cauchy problem \left\{\begin{aligned} &\displaystyle\partial_{t}u+\partial_{x}[\varphi(u)]=0&% &\displaystyle\phantom{}\text{in }\mathbb{R}\times(0,T),\\ &\displaystyle u=u_{0}\geq 0&&\displaystyle\phantom{}\text{in }\mathbb{R}% \times\{0\},\end{aligned}\right. where {u_{0}} is a Radon measure and {\varphi\colon[0,\infty)\mapsto\mathbb{R}} is a globally Lipschitz continuous function. We construct suitably defined entropy solutions in the space of Radon measures. Under some additional conditions on φ, we prove their uniqueness if the singular part of {u_{0}} is a finite superposition of Dirac masses. Regarding the behavior of φ at infinity, we give criteria to distinguish two cases: either all solutions are function-valued for positive times (an instantaneous regularizing effect), or the singular parts of certain solutions persist until some positive waiting time (in the linear case {\varphi(u)=u} this happens for all times). In the latter case, we describe the evolution of the singular parts

A point-of-care test for facing the burden of undiagnosed celiac disease in the Mediterranean area: a pragmatic design study

BACKGROUND: We aimed at assessing the factors that can influence results of the dissemination of an already validated, new generation commercial Point-of-Care Test (POCT) for detecting celiac disease (CD), in the Mediterranean area, when used in settings where it was designed to be administered, especially in countries with poor resources. METHODS: Pragmatic study design. Family pediatricians at their offices in Italy, nurses and pediatricians in Slovenia and Turkey at pediatricians', schools and university primary care centers looked for CD in 3,559 (1-14 yrs), 1,480 (14-23 yrs) and 771 (1-18 yrs) asymptomatic subjects, respectively. A new generation POCT detecting IgA-tissue antitransglutaminase antibodies and IgA deficiency in a finger-tip blood drop was used. Subjects who tested positive and those suspected of having CD were referred to a Celiac Centre to undergo further investigations in order to confirm CD diagnosis. POCT Positive Predictive Value (PPV) at tertiary care (with Negative Predictive Value) and in primary care settings, and POCT and CD rates per thousand in primary care were estimated. RESULTS: At tertiary care setting, PPV of the POCT and 95% CI were 89.5 (81.3-94.3) and 90 (56-98.5) with Negative Predictive Value 98.5 (94.2-99.6) and 98.7% (92-99.8) in children and adults, respectively. In primary care settings of different countries where POCT was performed by a different number of personnel, PPV ranged from 16 to 33% and the CD and POCT rates per thousand ranged from 4.77 to 1.3 and from 31.18 to 2.59, respectively. CONCLUSIONS: Interpretation of POCT results by different personnel may influence the performance of POC but dissemination of POCT is an urgent priority to be implemented among people of countries with limited resources, such as rural populations and school children

Factors Associated With Severe Gastrointestinal Diagnoses in Children With SARS-CoV-2 Infection or Multisystem Inflammatory Syndrome

Importance Severe gastrointestinal (GI) manifestations have been sporadically reported in children with COVID-19; however, their frequency and clinical outcome are unknown. Objective To describe the clinical, radiological, and histopathologic characteristics of children with COVID-19 presenting with severe GI manifestations to identify factors associated with a severe outcome. Design, Setting, and Participants A multicenter retrospective cohort study (February 25, 2020, to January 20, 2021) enrolled inpatient and outpatient children (aged <18 years) with acute SARS-CoV-2 infection, confirmed by positive real-time reverse-transcriptase–polymerase chain reaction on nasopharyngeal swab or fulfilling the US Centers for Disease Control and Prevention criteria for multisystem inflammatory syndrome in children (MIS-C). The study was conducted by pediatricians working in primary care or hospitals in Italy participating in the COVID-19 Registry of the Italian Society of Pediatric Infectious Diseases. Main Outcomes and Measures The occurrence of severe GI manifestations, defined by a medical and/or radiological diagnosis of acute abdomen, appendicitis (complicated or not by perforation and/or peritonitis), intussusception, pancreatitis, abdominal fluid collection, and diffuse adenomesenteritis requiring surgical consultation, occurring during or within 4 to 6 weeks after infection with SARS-CoV-2 infection. Logistic regression was used to estimate odds ratios (ORs) with 95% CIs of factors potentially associated with severe outcomes. Results Overall, 685 children (386 boys [56.4%]; median age, 7.3 [IQR, 1.6-12.4] years) were included. Of these children, 628 (91.7%) were diagnosed with acute SARS-CoV-2 infection and 57 (8.3%) with MIS-C. The presence of GI symptoms was associated with a higher chance of hospitalization (OR, 2.64; 95% CI, 1.89-3.69) and intensive care unit admission (OR, 3.90; 95% CI, 1.98–7.68). Overall, 65 children (9.5%) showed severe GI involvement, including disseminated adenomesenteritis (39.6%), appendicitis (33.5%), abdominal fluid collection (21.3%), pancreatitis (6.9%), or intussusception (4.6%). Twenty-seven of these 65 children (41.5%) underwent surgery. Severe GI manifestations were associated with the child’s age (5-10 years: OR, 8.33; 95% CI, 2.62-26.5; >10 years: OR, 6.37; 95% CI, 2.12-19.1, compared with preschool-age), abdominal pain (adjusted OR [aOR], 34.5; 95% CI, 10.1-118), lymphopenia (aOR, 8.93; 95% CI, 3.03-26.3), or MIS-C (aOR, 6.28; 95% CI, 1.92-20.5). Diarrhea was associated with a higher chance of adenomesenteritis (aOR, 3.13; 95% CI, 1.08-9.12) or abdominal fluid collection (aOR, 3.22; 95% CI, 1.03-10.0). Conclusions and Relevance In this multicenter cohort study of Italian children with SARS-CoV-2 infection or MIS-C, 9.5% of the children had severe GI involvement, frequently associated with MIS-C. These findings suggest that prompt identification may improve the management of serious complications

age variation in bitter taste perception in relation to the tas2r38 taste receptor phenotype

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Radon measure-valued solutions of first order scalar conservation laws

We study nonnegative solutions of the Cauchy problem ∂ t u + ∂ x [ φ (u) ] = 0 in × (0, T), u = u 0 ≥ 0 in × 0 , \left\\beginaligned &\displaystyle\partial-tu+\partial-x[\varphi(u)]=0&% &\displaystyle\phantom\textin \mathbbR\times(0,T),\\ &\displaystyle u=u-0\geq 0&&\displaystyle\phantom\textin \mathbbR% \times\0\,\endaligned\right. where u 0 u-0 is a Radon measure and φ: [ 0, ∞) → \varphi\colon[0,\infty)\mapsto\mathbbR is a globally Lipschitz continuous function. We construct suitably defined entropy solutions in the space of Radon measures. Under some additional conditions on φ, we prove their uniqueness if the singular part of u 0 u-0 is a finite superposition of Dirac masses. Regarding the behavior of φ at infinity, we give criteria to distinguish two cases: either all solutions are function-valued for positive times (an instantaneous regularizing effect), or the singular parts of certain solutions persist until some positive waiting time (in the linear case φ (u) = u \varphi(u)=u this happens for all times). In the latter case, we describe the evolution of the singular parts

Radon measure-valued solutions of first order scalar conservation laws

We study nonnegative solutions of the Cauchy proble