Weighed scalar averaging in LTB dust models, part I: statistical fluctuations and gravitational entropy

We introduce a weighed scalar average formalism ("q-average") for the study of the theoretical properties and the dynamics of spherically symmetric Lemaitre-Tolman-Bondi (LTB) dust models models. The "q-scalars" that emerge by applying the q-averages to the density, Hubble expansion and spatial curvature (which are common to FLRW models) are directly expressible in terms of curvature and kinematic invariants and identically satisfy FLRW evolution laws without the back-reaction terms that characterize Buchert's average. The local and non-local fluctuations and perturbations with respect to the q-average convey the effects of inhomogeneity through the ratio of curvature and kinematic invariants and the magnitude of radial gradients. All curvature and kinematic proper tensors that characterize the models are expressible as irreducible algebraic expansions on the metric and 4-velocity, whose coefficients are the q-scalars and their linear and quadratic local fluctuations. All invariant contractions of these tensors are quadratic fluctuations, whose q-averages are directly and exactly related to statistical correlation moments of the density and Hubble expansion scalar. We explore the application of this formalism to a definition of a gravitational entropy functional proposed by Hosoya et al (2004 Phys. Rev. Lett. 92 141302). We show that a positive entropy production follows from a negative correlation between fluctuations of the density and Hubble scalar, providing a brief outline on its fulfillment in various LTB models and regions. While the q-average formalism is specially suited for LTB and Szekeres models, it may provide a valuable theoretical insight on the properties of scalar averaging in inhomogeneous spacetimes in general.Comment: 27 pages in IOP format, 1 figure. Matches version accepted for publication in Classical and Quantum Gravit

Apresentação clínica da alergia ao leite de vaca com sintomatologia respiratória Clinical presentation of cow milk allergy symptoms

Os alérgenos do leite de vaca são os primeiros antígenos a entrar em contato com a criança. A sintomatologia, em geral multissistêmica, pode estar relacionada ao trato gastrointestinal, à pele e, raramente, ao aparelho respiratório. Objetivo: Descrever algumas características clínicas e epidemiológicas de crianças com alergia ao leite de vaca com sintomas respiratórios. Casuística e método: Foram avaliadas retrospectivamente 17 crianças com acometimento do trato respiratório imediato à ingestão de leite de vaca que, com a exclusão deste tipo de alimento por quatro a seis semanas, se tornaram assintomáticas e, posteriormente, voltaram a apresentar sintomas respiratórios com a reintrodução, em ambiente hospitalar, do leite de vaca. Resultados: Não houve diferença quanto ao sexo e 14 das 17 crianças tinham antecedentes atópicos familiares. O tempo médio do aleitamento materno exclusivo foi de 2,9 meses e o do início dos sintomas, de 3,6 meses. Oito dos dez testes de hipersensibilidade cutânea imediata ao leite de vaca foram positivos. As manifestações clínicas foram: lactente chiador (nove), asma (cinco), otite de repetição (duas), deficiência seletiva de IgA associada com broncoespasmo (duas), rinoconjuntivite alérgica (uma). Conclusão: Em lactentes chiadores a alergia ao leite de vaca deve ser incluída no diagnóstico diferencial e em pacientes com antecedentes familiares atópicos deve ser estimulado o aleitamento materno exclusivo. Entretanto, o diagnóstico preciso é importante para evitar privações alimentares desnecessárias.<br>Cow milk allergens are the first antigens children have contact with. The symptoms, which are frequently multi-systemic, may be related to the gastrointestinal tract, to the skin and, more rarely, to the respiratory tract. Objective: To describe some clinic and epidemiological characteristics of children who have cow milk allergy and present respiratory symptoms. Patients and method: This retrospective study included 17 children who presented respiratory problems immediately after ingesting cow milk, showed no symptoms as cow milk was excluded from their diets for a period of 4 to 6 weeks, and presented recurrent symptoms as cow milk was reintroduced into their diet in a hospital environment. Results: No difference was observed between genders. Family atopic antecedents were present in 14 of the 17 children. Mean exclusive breast-feeding period was 2.9 months and the onset of symptoms occurred at an average of 3.6 months. Eight of the ten tests conducted to evaluate immediate cutaneous hypersensitivity to cow milk were positive. Clinical manifestations observed were: wheezing infants (9), asthma (5), repetition otitis (2), selective IgA deficiency related to wheezing and allergic rhinoconjunctivitis (1). Conclusion: Regarding wheezing infants, cow milk allergy should be included as a differential diagnosis and exclusive breast-feeding should be stimulated in cases of atopic family antecedents. However, a precise diagnosis is vital to prevent unnecessary food deprivation