How real are real numbers?

We discuss mathematical and physical arguments against continuity and in favor of discreteness, with particular emphasis on the ideas of Émile Borel (1871-1956).

Daily birth numbers in Passo Fundo, South Brazil, 1997-1999: trends and periodicities

Between October 6, 1997 and April 30, 1999, 5011 births (mean: 8.76 per day) were registered in the city of Passo Fundo, South Brazil. The sequence of 572 daily birth numbers was not random (iteration test). Neyman distribution (m = ¥) showed the best fit. Clusters of days with higher birth numbers alternated with days with low numbers of births. Periodogram analysis revealed a significant periodicity of 6.98 days. The cosinor regression, testing 10 a priori supposed period lengths, found significant seasonality peaking in August-September and significantly highest birth numbers on Thursdays. Among the lunar and solar rotation cycles, the tropic lunar cycle and its 4th harmonic were most pronounced, in agreement with results concerning natality in Germany obtained by Svante Arrhenius in the 19th century. These findings confirm Derer-Halberg's concept of multiseptans. In addition to cycling, a significantly increasing linear trend with a daily increase of 0.0045 births was encountered. This documents a growth of the population in agreement with national statistical data.

Normal skin of HIV-infected individuals contains increased numbers of dermal CD8 T cells and normal numbers of Langerhans cells

Dysregulation of the skin immune system (SIS) could explain the high prevalence of skin disorders in HIV+ individuals. The present study was carried out to determine whether alterations in the cell population of SIS and epidermal immunoactivation occur in the normal skin of HIV+ individuals. Forty-five biopsies were taken from the normal upper arm skin of 45 HIV+ patients and of 15 healthy controls. HIV+ individuals were divided into three categories according to their CD4 cell blood count (<200, 200-499 and ³500/µl). Hematoxylin-eosin was used to stain tissue sections for morphological analysis and immunohistochemistry was used for the evaluation of the frequency of macrophages, Langerhans cells, and CD lymphocyte subsets. In addition, semiquantitative analysis of LFA-1, ICAM-1 and HLA-DR was determined in epidermal cells. Macrophages, Langerhans cells, and CD lymphocyte subsets did not differ significantly between any of the patient categories and the control group. When all HIV+ individuals were compared as a group to the control group, a significant increase in dermal CD8+ T lymphocytes (P < 0.01) and lower CD4-CD8 ratios (P < 0.01) were observed in the HIV+ individuals. Epidermal ICAM-1 and HLA-DR expression was negative in both HIV+ and normal skin biopsies. No evidence of a depletion of the SIS population or of epidermal immunoactivation in normal skin from HIV+ individuals was demonstrable, suggesting that alterations in the central immune system are not necessarily reflected in the SIS of HIV-infected patients.

Genetic variability of hepatitis A virus isolates in Rio de Janeiro: implications for the vaccination of school children

The epidemiology of hepatitis A virus (HAV) infection is shifting from high to intermediate endemicity in Brazil, resulting in increased numbers of susceptible individuals and a greater potential for the emergence of outbreaks. Universal vaccination against HAV has been recommended for children, but updated sero-epidemiological data are necessary to analyze the level of natural immunity and to identify candidates for preventive measures. In addition, more molecular studies are necessary to characterize the genotypes involved in HAV infections and outbreaks. Sera from 299 school children (5-15 years old) and 25 school staff members, collected during an outbreak of HAV at a rural public school in June 2000, were tested for IgM and total anti-HAV antibodies (ELISA). Viral RNA was amplified by RT-PCR from anti-HAV IgM-positive sera and from 19 fecal samples. Direct nucleotide sequencing of the VP1/2A region was carried out on 18 PCR-positive samples. Acute HAV infection was detected by anti-HAV IgM in 93/299 children and in 3/25 adult staff members. The prevalence of total anti-HAV antibodies in IgM-negative children under 5 years of age was only 10.5%. HAV-RNA was detected in 46% IgM-positive serum samples and in 16% stool samples. Sequence analysis showed that half the isolates belonged to subgenotype IA and the other half to IB. On the basis of these data, mass vaccination against HAV is recommended without prevaccination screening, especially for children before they enter school, since nearly 90% of the children under 5 years were susceptible. Molecular characterization indicated the endemic circulation of specific HAV strains belonging to subgenotypes IA and IB.