A remark on the sloshing frequencies for a half-space

The known sloshing frequencies of an incompressible and inviscid fluid in a half-space with circular or strip-like aperture are investigated in some detail, based on previous results [4]. The first two terms in the asymptotic expansion for large eigenvalues are determined and a conjecture is enunciated for the general structure of the next term. The asymptotic results are listed in Table 1 and compared with the known frequencies. Furthermore, the sum of the reciprocal squares of the eigenvalues is computed numerically for each symmetry class; the results suggest a conjecture about the exact value of these sums. Es werden die bekannten Eigenfrequenzen der Schwingungen einer idealen Flüssigkeit in einem Halbraum mit kreisförmiger oder streifenförmiger freier Oberfläche näher untersucht (siehe [4]). Die zwei ersten Glieder in der asymptotischen Entwicklung der Eigenfrequenzen werden hergeleitet und eine Vermutung über das nächste Glied aufgestellt (Abschnitt 2, 3). Die asymptotischen Ergebnisse werden mit den bekannten Frequenzen in Tabelle 1 verglichen.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43331/1/33_2005_Article_BF01593991.pd

Eigenvalue Problem in Two Dimension for An Irregular Boundary

An analytical perturbative method is suggested for solving the Helmholtz equation (\bigtriangledown^{2} + k^{2}){\psi} = 0 in two dimensions where {\psi} vanishes on an irregular closed curve. We can thus find the energy levels of a quantum mechanical particle confined in an infinitely deep potential well in two dimensions having an irregular boundary or the vibration frequencies of a membrane whose edge is an irregular closed curve. The method is tested by calculating the energy levels for an elliptical and a supercircular boundary and comparing with the results obtained numerically. Further, the phenomenon of level crossing due to shape variation is also discussed.Comment: 16 pages, 4 figures, v2 matches the journal versio

The effects of iron fortification on the gut microbiota in African children: a randomized controlled trial in Cote d'Ivoire.

BACKGROUND: Iron is essential for the growth and virulence of many pathogenic enterobacteria, whereas beneficial barrier bacteria, such as lactobacilli, do not require iron. Thus, increasing colonic iron could select gut microbiota for humans that are unfavorable to the host. OBJECTIVE: The objective was to determine the effect of iron fortification on gut microbiota and gut inflammation in African children. DESIGN: In a 6-mo, randomized, double-blind, controlled trial, 6-14-y-old Ivorian children (n = 139) received iron-fortified biscuits, which contained 20 mg Fe/d, 4 times/wk as electrolytic iron or nonfortifoed biscuits. We measured changes in hemoglobin concentrations, inflammation, iron status, helminths, diarrhea, fecal calprotectin concentrations, and microbiota diversity and composition (n = 60) and the prevalence of selected enteropathogens. RESULTS: At baseline, there were greater numbers of fecal enterobacteria than of lactobacilli and bifidobacteria (P < 0.02). Iron fortification was ineffective; there were no differences in iron status, anemia, or hookworm prevalence at 6 mo. The fecal microbiota was modified by iron fortification as shown by a significant increase in profile dissimilarity (P < 0.0001) in the iron group as compared with the control group. There was a significant increase in the number of enterobacteria (P < 0.005) and a decrease in lactobacilli (P < 0.0001) in the iron group after 6 mo. In the iron group, there was an increase in the mean fecal calprotectin concentration (P < 0.01), which is a marker of gut inflammation, that correlated with the increase in fecal enterobacteria (P < 0.05). CONCLUSIONS: Anemic African children carry an unfavorable ratio of fecal enterobacteria to bifidobacteria and lactobacilli, which is increased by iron fortification. Thus, iron fortification in this population produces a potentially more pathogenic gut microbiota profile, and this profile is associated with increased gut inflammation. This trial was registered at controlled-trials.com as ISRCTN21782274

Eigenvalue Problem in Two Dimensions for an Irregular Boundary II: Neumann Condition

We formulate a systematic elegant perturbative scheme for determining the eigenvalues of the Helmholtz equation (\bigtriangledown^{2} + k^{2}){\psi} = 0 in two dimensions when the normal derivative of {\psi} vanishes on an irregular closed curve. Unique feature of this method, unlike other perturbation schemes, is that it does not require a separate formalism to treat degeneracies. Degenerate states are handled equally elegantly as the non-degenerate ones. A real parameter, extracted from the parameters defining the irregular boundary, serves as a perturbation parameter in this scheme as opposed to earlier schemes where the perturbation parameter is an artificial one. The efficacy of the proposed scheme is gauged by calculating the eigenvalues for elliptical and supercircular boundaries and comparing with the results obtained numerically. We also present a simple and interesting semi-empirical formula, determining the eigenspectrum of the 2D Helmholtz equation with the Dirichlet or the Neumann condition for a supercircular boundary. A comparison of the eigenspectrum for several low-lying modes obtained by employing the formula with the corresponding numerical estimates shows good agreement for a wide range of the supercircular exponent.Comment: 26 pages, 12 figure

A Meta-Analysis of the Existing Knowledge of Immunoreactivity against Hepatitis C Virus (HCV)

Approximately 3% of the world population is infected by HCV, which represents a major global health challenge. Almost 400 different scientific reports present immunological data related to T cell and antibody epitopes derived from HCV literature. Analysis of all HCV-related epitope hosted in the Immune Epitope Database (IEDB), a repository of freely accessible immune epitope data, revealed more than 1500 and 1900 distinct T cell and antibody epitopes, respectively. The inventory of all data revealed specific trends in terms of the host and the HCV genotypes from which sequences were derived. Upon further analysis we found that this large number of epitopes reflects overlapping structures, and homologous sequences derived from different HCV isolates. To access and visualize this information we developed a novel strategy that assembles large sets of epitope data, maps them onto reference genomes and displays the frequency of positive responses. Compilation of the HCV immune reactivity from hundreds of different studies, revealed a complex and thorough picture of HCV immune epitope data to date. The results pinpoint areas of more intense reactivity or research activities at the level of antibody, CD4 and CD8 responses for each of the individual HCV proteins. In general, the areas targeted by the different effector immune functions were distinct and antibody reactivity was positively correlated with hydrophilicity, while T cell reactivity correlated with hydrophobicity. At the sequence level, epitopes frequently recognized by both T cell and B cell correlated with low variability, and our analysis thus highlighted areas of potential interest for practical applications. The human reactivity was further analyzed to pinpoint differential patterns of reactivity associated with acute versus chronic infection, to reveal the apparent impact of glycosylation on T cell, but not antibody responses, and to highlight a paucity of studies involved antibody epitopes associated with virus neutralization

Effect of Supplementation with Zinc and Other Micronutrients on Malaria in Tanzanian Children: A Randomised Trial

Hans Verhoef and colleagues report findings from a randomized trial conducted among Tanzanian children at high risk for malaria. Children in the trial received either daily oral supplementation with either zinc alone, multi-nutrients without zinc, multi-nutrients with zinc, or placebo. The investigators did not find evidence from this study that zinc or multi-nutrients protected against malaria episodes

Genetic variability of hepatitis C virus before and after combined therapy of interferon plus ribavirin

We present an analysis of the selective forces acting on two hepatitis C virus genome regions previously postulated to be involved in the viral response to combined antiviral therapy. One includes the three hypervariable regions in the envelope E2 glycoprotein, and the other encompasses the PKR binding domain and the V3 domain in the NS5A region. We used a cohort of 22 non-responder patients to combined therapy (interferon alpha-2a plus ribavirin) for which samples were obtained before initiation of therapy and after 6 or/and 12 months of treatment. A range of 25-100 clones per patient, genome region and time sample were sequenced. These were used to detect general patterns of adaptation, to identify particular adaptation mechanisms and to analyze the patterns of evolutionary change in both genome regions. These analyses failed to detect a common adaptive mechanism for the lack of response to antiviral treatment in these patients. On the contrary, a wide range of situations were observed, from patients showing no positively selected sites to others with many, and with completely different topologies in the reconstructed phylogenetic trees. Altogether, these results suggest that viral strategies to evade selection pressure from the immune system and antiviral therapies do not result from a single mechanism and they are likely based on a range of different alternatives, in which several different changes, or their combination, along the HCV genome confer viruses the ability to overcome strong selective [email protected]; [email protected]; [email protected]; [email protected]; [email protected]; [email protected]; [email protected]; [email protected]