Orders and partitions of integers induced by arithmetic functions

We pursue the question how integers can be ordered or partitioned according to their divisibility properties. Based on pseudometrics on $\mathbb{Z}$, we investigate induced preorders, associated equivalence relations, and quotient sets. The focus is on metrics or pseudometrics on $\mathbb{D}_n$, the set of divisors of a given modulus $n\in\mathbb{N}$, that can be extended to pseudometrics on $\mathbb{Z}$. Arithmetic functions can be used to generate such pseudometrics. We discuss several subsets of additive and multiplicative arithmetic functions and various combinations of their function values leading to binary metric functions that represent different divisibility properties of integers. We conclude this paper with numerous examples and review the most important results. As an additional result, we derive a necessary condition for the truth of the odd k-perfect number conjecture.Comment: 50 pages, 3 diagram

Rapid identification of Burkholderia mallei and Burkholderia pseudomallei by intact cell Matrix-assisted Laser Desorption/Ionisation mass spectrometric typing

BACKGROUND: Burkholderia (B.) pseudomallei and B. mallei are genetically closely related species. B. pseudomallei causes melioidosis in humans and animals, whereas B. mallei is the causative agent of glanders in equines and rarely also in humans. Both agents have been classified by the CDC as priority category B biological agents. Rapid identification is crucial, because both agents are intrinsically resistant to many antibiotics. Matrix-assisted laser desorption/ionisation mass spectrometry (MALDI-TOF MS) has the potential of rapid and reliable identification of pathogens, but is limited by the availability of a database containing validated reference spectra. The aim of this study was to evaluate the use of MALDI-TOF MS for the rapid and reliable identification and differentiation of B. pseudomallei and B. mallei and to build up a reliable reference database for both organisms. RESULTS: A collection of ten B. pseudomallei and seventeen B. mallei strains was used to generate a library of reference spectra. Samples of both species could be identified by MALDI-TOF MS, if a dedicated subset of the reference spectra library was used. In comparison with samples representing B. mallei, higher genetic diversity among B. pseudomallei was reflected in the higher average Eucledian distances between the mass spectra and a broader range of identification score values obtained with commercial software for the identification of microorganisms. The type strain of B. pseudomallei (ATCC 23343) was isolated decades ago and is outstanding in the spectrum-based dendrograms probably due to massive methylations as indicated by two intensive series of mass increments of 14 Da specifically and reproducibly found in the spectra of this strain. CONCLUSIONS: Handling of pathogens under BSL 3 conditions is dangerous and cumbersome but can be minimized by inactivation of bacteria with ethanol, subsequent protein extraction under BSL 1 conditions and MALDI-TOF MS analysis being faster than nucleic amplification methods. Our spectra demonstrated a higher homogeneity in B. mallei than in B. pseudomallei isolates. As expected for closely related species, the identification process with MALDI Biotyper software (Bruker Daltonik GmbH, Bremen, Germany) requires the careful selection of spectra from reference strains. When a dedicated reference set is used and spectra of high quality are acquired, it is possible to distinguish both species unambiguously. The need for a careful curation of reference spectra databases is stressed

Simultaneous detection and differentiation by multiplex real time RT-PCR of highly pathogenic avian influenza subtype H5N1 classic (clade 2.2.1 proper) and escape mutant (clade 2.2.1 variant) lineages in Egypt

<p>Abstract</p> <p>Background</p> <p>The endemic status of highly pathogenic avian influenza virus (HPAIV) of subtype H5N1 in Egypt continues to devastate the local poultry industry and poses a permanent threat for human health. Several genetically and antigenically distinct H5N1 lineages co-circulate in Egypt: Strains of clade 2.2.1 proper replicate mainly in backyard birds causing the bulk of human infections, while a variant lineage within 2.2.1 (2.2.1v) appears to be perpetuated mainly in commercial poultry farms in Egypt. Viruses of the 2.2.1v lineage represent drift variants escaping from conventional vaccine-induced immunity and some of these strains also escaped detection by commercial real time reverse transcriptase PCR (RT-qPCR) protocols due to mismatches in the primers/probe binding sites.</p> <p>Results</p> <p>We developed therefore a versatile, sensitive and lineage-specific multiplex RT-qPCR for detection and typing of H5N1 viruses in Egypt. Analytical characterization was carried out using 50 Egyptian HPAIV H5N1 strains isolated since 2006 and 45 other avian influenza viruses (AIV). A detection limit of 400 cRNA copies per ml sample matrix was found. Higher diagnostic sensitivity of the multiplex assay in comparison to other generic H5 or M-gene based RT-qPCR assays were found by examination of 63 swab samples from experimentally infected chickens and 50 AIV-positive swab samples from different host species in the field in Egypt.</p> <p>Conclusions</p> <p>The new multiplex RT-qPCR assay could be useful for rapid high-throughput monitoring for the presence of HPAIV H5N1 in commercial poultry in Egypt. It may also aid in prospective epidemiological studies to further delineate and better control spread of HPAIV H5N1 in Egypt.</p

Impact of El Niño/Southern Oscillation on Visceral Leishmaniasis, Brazil

We used time-series analysis and linear regression to investigate the relationship between the annual Niño-3 index from 1980 to 1998 and the annual incidence of visceral leishmaniasis (VL) in the State of Bahia, Brazil, during 1985–1999. An increase in VL incidence was observed in the post-El Niño years 1989 (+38.7%) and 1995 (+33.5%). The regression model demonstrates that the previous year’s mean Niño-3 index and the temporal trend account for approximately 50% of the variance in the annual incidence of VL in Bahia. The model shows a robust agreement with the real data, as only the influence of El Niño on the cycle of VL was analyzed. The results suggest that this relationship could be used to predict high-risk years for VL and thus help reduce health impact in susceptible regions in Brazil

Chances and Limitations of Wild Bird Monitoring for the Avian Influenza Virus H5N1 — Detection of Pathogens Highly Mobile in Time and Space

Highly pathogenic influenza virus (HPAIV) H5N1 proved to be remarkably mobile in migratory bird populations where it has led to extensive outbreaks for which the true number of affected birds usually cannot be determined. For the evaluation of avian influenza monitoring and HPAIV early warning systems, we propose a time-series analysis that includes the estimation of confidence intervals for (i) the prevalence in outbreak situations or (ii) in the apparent absence of disease in time intervals for specified regional units. For the German outbreak regions in 2006 and 2007, the upper 95% confidence limit allowed the detection of prevalences below 1% only for certain time intervals. Although more than 25,000 birds were sampled in Germany per year, the upper 95% confidence limit did not fall below 5% in the outbreak regions for most of the time. The proposed analysis can be used to monitor water bodies and high risk areas, also as part of an early-warning system. Chances for an improved targeting of the monitoring system as part of a risk-based approach are discussed with the perspective of reducing sample sizes

Priority areas for surveillance and prevention of avian influenza during the water-bird migration season in Pakistan

Avian influenza viruses may be introduced into domestic poultry through migratory wild birds, particularly from Pakistan, which is situated across the migratory Indus flyway and holds more than 225 wetlands. To answer the question which areas should be given priority in surveillance and prevention with respect to notifiable avian influenza during the migratory season, a subset of Asian waterbird census data was reviewed. The dataset contains 535 local sites and available counts of waterbirds reported from 1987 to 2007. However, as the majority of the sites are not counted regularly gaps in data matrix appeared. The coordinates of 270 known sites completely fitted the administrative boundaries of the country. These coordinates were geo-processed with polygons of water-bodies and a raster map of predicted poultry density. Pixels representing the estimated number of poultry per km2 were found within a 3 to 9 km range of the census sites (or water-bodies) in their proximity. The coordinates were also used to map the maximum reported counts of waterbirds and local clusters of under-sampled sites. A retrospective case-series analysis of previous outbreaks (2006-2008) of influenza A virus, subtype H5N1 was performed, which revealed that 64% of outbreaks, reported to Office International des Epizooties, the World Organization for Animal Health, occurred during the migratory period. This paper highlights the potential use and limitations of the Asian waterbirds census data in the context of avian influenza. The proposed methodology may be used to prioritize districts for surveillance and economize prevention measures provided better data are generated in futur