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Covid-19 causedhospitalizations, severe disease and deaths in any age, including in the youngest children. The aim of this multicenter national study is to characterize the clinical and the prognostic role of lung ultrasound (LUS) in children with Covid-19. We enrolled children between 1 month and 18 years of age diagnosed with SARS-CoV2 infection and whounderwenta lung ultrasound within 6 hours from firstmedical evaluation. A total of 213 children were enrolled, 51.6%were male, median age was2 years and 5 months (IQR 4mm- 11 yearsand4 months).One hundred and fortyeight (69.4%) children were admitted in hospital, 9 (6.1%) in pediatric intensive care unit.We found an inverse correlation between the LUS score and the oxygen saturationatthe clinical evaluation (r = −0.16; p = 0.019). Moreover, LUS scores were significantly higher in patients requiring oxygen supplementation (8 (IQR 3 - 19) vs 2 (IQR 0 - 4); p= 0.001). Among LUS pathological findings, irregular pleural line, sub-pleural consolidations and pleural effusions were significantly more frequentin patients whoneeded oxygen supplementation (p = 0.007; p = 0.006 andp = 0.001, respectively). This multicentric study confirmed that LUS is able to detect Covid-19 low respiratory tract involvement, which is characterized by pleural line irregularities, vertical artifacts and subpleural consolidations. Notably, children with higher LUS score have an higher risk of hospitalization or need for oxygen supplementation, supporting LUS as a valid and safe point-of-care first level tool for the clinical evaluation of children with Covid-19.

There is increasing recognition of the role of lung ultrasound (LUS) to assess bronchiolitis severity in children. However, available studies are limited to small, single-center cohorts. We aimed to assess a qualitative and quantitative LUS protocol to evaluate the course of bronchiolitis at diagnosis and during follow-up. This is a prospective, multicenter study. Children with bronchiolitis were stratified according to clinical severity and underwent four LUS evaluations at set intervals. LUS was classified according to four models: (1) positive/negative; (2) main LUS pattern (normal/interstitial/consolidative/mixed) (3) LUS score; (4) LUS score with cutoff. Two hundred and thirty-three children were enrolled. The baseline LUS was significantly associated with bronchiolitis severity, using both the qualitative (positive/negative LUS p < 0.001; consolidated/normal LUS pattern or mixed/normal LUS p < 0.001) and quantitative models (cutoff score > 9 p < 0.001; LUS mean score p < 0.001). During follow-up, all LUS results according to all LUS models improved (p < 0.001). Better cut off value was declared at a value of >9 points. Conclusions: Our study supports the role of a comprehensive qualitative and quantitative LUS protocol for the identification of severe cases of bronchiolitis and provides data on the evolution of lung aeration during follow-up.

With the emergence of the Covid-19 pandemic, pleuropulmonary ultrasound has become a very common tool in clinical practice, even in the pediatric field. Therefore, the clinicians' need to speak a common ultrasound language becomes increasingly necessary. The Italian scientific society AdET (Academy of Thoracic Ultrasound) has been carrying out the study and dissemination of pulmonary ultrasound in medical practice in Italy for years. With this article, the pediatric AdET group wants to propose a report model of pediatric pulmonary ultrasound as a useful tool in daily clinical practice to interpret the images and reach a diagnostic conclusion, aiming to share a standardized approach that may also support the sharing of research findings.

We construct a new class of approximating functions that are M-refinable and provide shape preserving approximations. The refinable functions in the class are smooth, compactly supported, centrally symmetric and totally positive. Moreover, their refinable masks are associated with convergent subdivision schemes. The presence of one or more shape parameters gives a great flexibility in the applications. Some examples for dilation M = 4 and M = 5 are also given.

This paper concerns the construction of quadrature rules based on the use of suitable refinable quasi-interpolatory operators, for the numerical evaluation of Hadamard finite-part integrals. Convergence analysis of the obtained rules is developed and numerical examples are included.

We study integral refinable operators of integral type exact on polynomials of even degree constructed by using refinable B-bases of GP type. We prove a general theorem of existence and uniqueness. Then we study the Lp-norm of these operators and we give error bounds in approximating functions and their derivatives belonging to suitable classes. Numerical results and comparisons with other quasi-interpolatory operators having the same order of exactness on polynomial reproduction are presented.

This paper concerns with iterative schemes for the perfect reconstruction from nonuniform sampling of functions belonging to multiresolution spaces on bounded manifolds. Since the iterations converge uniformly, we can produce the corresponding iterative integration schemes that allow to recover the integral of functions belonging to multiresolution spaces from nonuniform sampling. We present also an error analysis and, in particular, we estimate the L^2-error we produce in recovering smooth functions in H^s, but not necessarily in any multiresolution space. The error analysis extends to integrals. Our results hold regardless of the dimension of the domain and for a variety of multiresolution spaces constructed from certain refinable bases formed by the so-called GP-functions.

In this paper, we present a new class of operators, which are refinable, quasi-interpolatory and satisfy some interpolation conditions. The refinability is achieved by using as functional bases the B-bases corresponding to totally positive refinable functions. We analyze the main properties of the constructed refinable operators and give some convergence results. Some examples are also displayed.

In this paper a new class of nonstationary subdivision schemes is proposed to construct functions having all the main properties of B-splines, namely compact support, central symmetry and total positivity. We show that the constructed nonstationary subdivision schemes are asympotically equivalent to the stationary subdivision scheme associated with a B-spline of suitable degree, but the resulting limit function has smaller support than the B-spline although keeping its regularity.

The convergence of a class of operators, both refinable and quasi-interpolatory, is analyzed and some examples are provided.

The aim of this paper is to study the shape preserving properties of some positive operators constructed by means of B-bases on a finite interval. These bases are obtained by the integer translates of totally positive compactly supported refinable functions. We shall prove that the constructed B-bases generate, on the interval, multiresolution analyses which reproduce polynomials up to a certain degree.

Recently, linear positive operators of Bernstein–Schoenberg type, relative to B-splines bases, have been considered. The properties of these operators are derived mainly from the total positivity of normalized B-spline bases. In this paper we shall construct a generalization of the operator considered in [15] by means of normalized totally positive bases generated by a particular class of totally positive scaling functions. Next, we shall study its approximation properties. Our results can be established also for more general sequences of normalized totally positive bases.

The aim of this paper is to provide a large class of scaling functions for which the convergence analysis for the Galerkin method developed in [9] is applicable, whereas in that paper the only scaling functions considered for practical applications are B-splines and a few of the orthonormal Daubechies scaling functions. The functions considered here, were recently introduced in [12] where it was proved that they satisfy many properties making them interesting for the applications. In particular, here we show that the use of these functions has some advantages with respect to other basis functions.

Summary. It is shown how recent ideas on rational Gauss-type quadrature rules can be extended to Gauss-Kronrod, Gauss-Turan, and Cauchy principal value quadrature rules. Numerical examples illustrate the advantages in accuracy thus achievable.

A two-parameter class of refinable functions is considered and Gaussian quadrature rules having these functions as weight functions. A discretization method is described for generating the recursion coefficients of the required orthogonal polynomials. Numerical results are also presented.

In 3 children with chronic liver disease, although multiple studies of copper metabolism were normal, which made the diagnosis of Wilson disease unlikely, analysis of ATP7B gene showed disease causing mutations in all. Molecular diagnosis should be considered in children with enigmatic liver disease, especially those with features of nonalcoholic fatty liver disease.

We analyze the properties of a class of shape-preserving refinable functions with dilation M=3. We give an algorithm to construct totally positive bases with optimal shape-preserving properties on a finite interval. Bernstein-type bases on [0,1] are also treated. Moreover, semiorthogonal wavelets associated with these refinable functions are constructed. Finally, a detailed example is described.

The main purpose of this paper is the construction of explicit Gauss-Turan quadrature formulas: they are relative to some classes of weight functions, which have the peculiarity that the corresponding s-orthogonal polynomials, of the same degree, are independent of s. These weights too are introduced and discussed here. Moreover, highest-precision quadratures for evaluating Fourier-Chebyshev coefficients are given.

Viene presentata una breve rassegna di alcuni metodi per la soluzione numerica di equazioni integrali singolari di tipo Cauchy; alcuni di essi sono su basi polinomiali, altri su basi di splines. In particolare, e esposto, in grandi linee, un recente metodo che fa uso di splines di tipo proiettore. Alcuni esempi numerici, tratti dalla letteratura, completano la panoramica.

The presence of antibiotic resistant bacteria was revealed among bacteria isolated from non carbonated mineral waters bottled in plastic (PVC) and in glass containers. Heterotrophic plate count values ranged between < 10 and 4.3 x 10(3) and between < 10 and 1.2 x 10(4) colony forming units/ml for the waters bottled in PVC and glass, respectively. The greatest resistance to a single antibiotic, 39.1% of 320 isolates from mineral waters, was found for nalidixic acid. Resistance to the other antibiotics was as follows: ampicillin (26.2%), bacitracin (19.7%), cotrimoxazole (18.7%), streptomycin (15.0%), tetracycline (14.4%), gentamycin (11.6%), chloramphenicol and rifampin (9.7%). The strains resistant to two or more antibiotics (multiple antibiotic resistant, MAR) provided 51% of the total isolates. Identification of 127 MAR strains showed that in the mineral waters gram-positive cocci dominated. The second, third and fourth group of identified MAR phenotypes were, in order to importance, gram-negative non-fermentative rods, gram-positive rods and gram-negative fermentative rods. The importance of the antibiotic resistant bacteria in mineral water is discussed.

A method for evaluating Hilbert transforms, by means of Turan quadrature rules with generalized Gegenbauer weights, is presented. The main feature of these integration formulas is the independence of the nodes of their multiplicity and thus of the precision degree. The error is analyzed both from a real and a complex perspective; in this context a new representation of the remainder term of the quadrature rules with multiple nodes for the evaluation of Hilbert transforms, valid not only for the particular class of weight functions here considered, is presented. A few numerical examples are provided.

We analyze the properties of a new class of totally positive refinable functions obtained from nonstationary subdivision schemes. We show that the corresponding system of the integer translates is linearly independent, satisfies a Whitney-Schoenberg condition, reproduces polynomials up to a certain degree and generates a multiresolution analysis. Finally, pre-wavelets and bases on the interval are constructed.

International audience; On a four-directional uniform mesh of the plane, we define and study C0 Gori–Pitolli (abbreviated as GP) quadratics and C1 GP quartics generated by integer translates of GP box-splines generalizing respectively the classical C1 quadratic box-spline and one of the C2 quartic box-splines. More specifically, we study the approximation of a bivariate function f by some quasi-interpolants and interpolants with values in these generalized spline spaces

This is the first report of Guillain-Barre syndrome (GBS) related to Bartonella henselae infection. A 10-year-old girl had difficulty walking and marked myalgia. The search for all causes known to trigger GBS was negative. She was treated with intravenous immunoglobulins and recovered. Because she lived in a rural area and had a history of kitten contact, a specific serology for B. henselae infection was performed and confirmed an ongoing infection. She did not show any clinical typical feature of cat-scratch disease. B. henselae infection should be considered in the wide etiologic spectrum of GBS.

Bartonella spp cause various clinical syndromes immunocompetent and immunocompromised hosts. Domestic cats are the natural reservoir, and vectors of B henselae. B henselae infection usually occurs early in childhood, is generally asymptomatic, and in most cases revolves spontaneously. It may, however, produce a wide spectrum of clinical symptoms, the most frequent feature being cat-scratch disease. Disseminated atypical B. henselae infection may follow cat-scratch disease alter a symptom-free period or may present de novo mimicking a wide range of clinical disorders. A careful clinical history researching an intimate contact with a kitten associated with a specific serology and an abdominal ultrasound for typical hepatosplenic involvement may follow a rapid and accurate diagnosis.

Few data are available on the seroprevalence of antibodies to Bartonella henselae among children. We retrospectively evaluated the presence of immunoglobulin G and M class antibodies to B. henselae in 508 children living in central Italy who were apparently free of any features suggesting B. henselae infection. We found that B. henselae infection is common among children in central Italy, occurs early in life, is in most cases asymptomatic, and resolves spontaneously.

Integrals defined by Cauchy principal values or by Hadamard finite parts are involved in many boundary integral equations; in this paper we present a method based on the use of Gauss-Turan quadrature formulas, that is, formulas with multiple nodes, for approximating these kinds of singular or hypersingular integrals. We show that the rules here proposed are particularly effective when the s-orthogonal polynomials involved in the construction of the method are invariant with respect to s. Finally, we introduce another type of integration rules, also with multiple nodes, for numerically evaluating hypersingular integrals.

Objective To assess the outcome of giant cell hepatitis combined with autoimmune hemolytic anemia in early childhood. Study design We report on 16 children with this disease evaluated over a 28-year period. Results Children (nine boys; median age, 6 months) presented with jaundice, hepatomegaly, elevated aminotransferases, a positive Coombs test, and diffuse giant-cell transformation of hepatocytes on histology. Treatment with prednisone and azathioprine, plus, in three children, cyclosporine, resulted in complete remission in eight, partial remission in six, and failure in two. Relapses of hepatitis and/or anemia occurred in 11 and 10 children, respectively, requiring prolonged high levels of immunosuppression, and splenectomy or Rituximab, respectively. Treatment was stopped after a mean duration of 6 years, with no relapse, in seven children, with a median follow-up of 14 years. One child is alive 9 years after liver transplantation. Four children died of sepsis or multiple organ failure. Conclusions Giant cell hepatitis combined with autoimmune hemolytic anemia requires rigorous treatment. Immunosuppressive therapy results in remission in most cases. A complete cure can be expected after several years of intensive treatment. Liver transplantation may be associated with prolonged survival.