An extension of Laplace's method

Asymptotic expansions are obtained for contour integrals of the form $$\int_a^b \exp \left( - zp(t) + z^{\nu /\mu } r(t) \right)q(t)dt,$$ in which $z$ is a large real or complex parameter, $p(t)$, $q(t)$ and $r(t)$ are analytic functions of $t$, and the positive constants $\mu$ and $\nu$ are related to the local behaviour of the functions $p(t)$ and $r(t)$ near the endpoint $a$. Our main theorem includes as special cases several important asymptotic methods for integrals such as those of Laplace, Watson, Erd\'elyi and Olver. Asymptotic expansions similar to ours were derived earlier by Dingle using formal, non-rigorous methods. The results of the paper also serve to place Dingle's investigations on a rigorous mathematical foundation. The new results have potential applications in the asymptotic theory of special functions in transition regions, and we illustrate this by two examples.Comment: 19 pages, 2 figures, revised version, accepted for publication in Constructive Approximatio

The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects

We study the dynamics of four dimensional gauge theories with adjoint fermions for all gauge groups, both in perturbation theory and non-perturbatively, by using circle compactification with periodic boundary conditions for the fermions. There are new gauge phenomena. We show that, to all orders in perturbation theory, many gauge groups are Higgsed by the gauge holonomy around the circle to a product of both abelian and nonabelian gauge group factors. Non-perturbatively there are monopole-instantons with fermion zero modes and two types of monopole-anti-monopole molecules, called bions. One type are "magnetic bions" which carry net magnetic charge and induce a mass gap for gauge fluctuations. Another type are "neutral bions" which are magnetically neutral, and their understanding requires a generalization of multi-instanton techniques in quantum mechanics - which we refer to as the Bogomolny-Zinn-Justin (BZJ) prescription - to compactified field theory. The BZJ prescription applied to bion-anti-bion topological molecules predicts a singularity on the positive real axis of the Borel plane (i.e., a divergence from summing large orders in peturbation theory) which is of order N times closer to the origin than the leading 4-d BPST instanton-anti-instanton singularity, where N is the rank of the gauge group. The position of the bion--anti-bion singularity is thus qualitatively similar to that of the 4-d IR renormalon singularity, and we conjecture that they are continuously related as the compactification radius is changed. By making use of transseries and Ecalle's resurgence theory we argue that a non-perturbative continuum definition of a class of field theories which admit semi-classical expansions may be possible.Comment: 112 pages, 7 figures; v2: typos corrected, discussion of supersymmetric models added at the end of section 8.1, reference adde

Identification of a novel zinc metalloprotease through a global analysis of clostridium difficile extracellular proteins

Clostridium difficile is a major cause of infectious diarrhea worldwide. Although the cell surface proteins are recognized to be important in clostridial pathogenesis, biological functions of only a few are known. Also, apart from the toxins, proteins exported by C. difficile into the extracellular milieu have been poorly studied. In order to identify novel extracellular factors of C. difficile, we analyzed bacterial culture supernatants prepared from clinical isolates, 630 and R20291, using liquid chromatography-tandem mass spectrometry. The majority of the proteins identified were non-canonical extracellular proteins. These could be largely classified into proteins associated to the cell wall (including CWPs and extracellular hydrolases), transporters and flagellar proteins. Seven unknown hypothetical proteins were also identified. One of these proteins, CD630_28300, shared sequence similarity with the anthrax lethal factor, a known zinc metallopeptidase. We demonstrated that CD630_28300 (named Zmp1) binds zinc and is able to cleave fibronectin and fibrinogen in vitro in a zinc-dependent manner. Using site-directed mutagenesis, we identified residues important in zinc binding and enzymatic activity. Furthermore, we demonstrated that Zmp1 destabilizes the fibronectin network produced by human fibroblasts. Thus, by analyzing the exoproteome of C. difficile, we identified a novel extracellular metalloprotease that may be important in key steps of clostridial pathogenesis

Evidence of Latitudinal Migration in Tri-colored Bats, Perimyotis subflavus

Background: Annual movements of tri-colored bats (Perimyotis subflavus) are poorly understood. While this species has been considered a regional migrant, some evidence suggests that it may undertake annual latitudinal migrations, similar to other long distance North American migratory bat species. Methodology/Principal Findings: We investigated migration in P. subflavus by conducting stable hydrogen isotope analyses of 184 museum specimen fur samples and comparing these results (dDfur) to published interpolated dD values of collection site growing season precipitation (dDprecip). Results suggest that the male molt period occurred between June 23 and October 16 and 33 % of males collected during the presumed non-molt period were south of their location of fur growth. For the same time period, 16 % of females were south of their location of fur growth and in general, had not travelled as far as migratory males. There were strong correlations between dDfur from the presumed molt period and both growing season dD precip (males – r 2 = 0.86; p,0.01; females – r 2 = 0.75; p,0.01), and latitude of collection (males – r 2 = 0.85; p,0.01; females – r 2 = 0.73; p,0.01). Most migrants were collected at the northern (.40uN; males and females) and southern (,35uN; males only) extents of the species ’ range. Conclusions/Significance: These results indicate a different pattern of migration for this species than previously documented, suggesting that some P. subflavus engage in annual latitudinal migrations and that migratory tendency varie

Predominance and high antibiotic resistance of the emerging Clostridium difficile genotypes NAPCR1 and NAP9 in a Costa Rican hospital over a 2-year period without outbreaks

Clostridium difficile is the major causative agent of nosocomial antibiotic-associated diarrhea. In a 2009 outbreak of C. difficileassociated diarrhea that was recorded in a major Costa Rican hospital, the hypervirulent NAP1 strain (45%) predominated together with a local genotype variant (NAPCR1, 31%). Both strains were fluoroquinolone-resistant and the NAPCR1 genotype, in addition, was resistant to clindamycin and rifampicin. We now report on the genotypes and antibiotic susceptibilities of 68C. difficile isolates from a major Costa Rican hospital over a 2-year period without outbreaks. In contrast to our previous findings, no NAP1 strains were detected, and for the first time in a Costa Rican hospital, a significant fraction of the isolates were NAP9 strains (n = 14, 21%). The local NAPCR1 genotype remained prevalent (n = 18, 26%) and coexisted with 14 strains (21%) of classic hospital NAP types (NAP2, NAP4, and NAP6), eight new genotypes (12%), four environmental strains classified as NAP10 or NAP11 (6%), three strains without NAP designation (4%) and seven non-toxigenic strains (10%). All 68 strains were resistant to ciprofloxacin, 88% were resistant to clindamycin and 50% were resistant to moxifloxacin and rifampicin. Metronidazole and vancomycin susceptibilities were universal. The NAPCR1 and NAP9 strains, which have been associated with more severe clinical infections, were more resistant to antibiotics than the other strains. Altogether, our results confirm that the epidemiology of C. difficile infection is dynamic and that A−B+ strains from the NAP9 type are on the rise not only in the developed world. Moreover, our results reveal that the local NAPCR1 strains still circulate in the country without causing outbreaks but with equally high antibiotic-resistance rates and levelsUCR::Vicerrectoría de Investigación::Unidades de Investigación::Ciencias de la Salud::Centro de Investigación en Enfermedades Tropicales (CIET)UCR::Vicerrectoría de Docencia::Salud::Facultad de Microbiologí

Biological Roles of the O-Methyl Phosphoramidate Capsule Modification in Campylobacter jejuni.

Campylobacter jejuni is a major cause of bacterial gastroenteritis worldwide, and the capsular polysaccharide (CPS) of this organism is required for persistence and disease. C. jejuni produces over 47 different capsular structures, including a unique O-methyl phosphoramidate (MeOPN) modification present on most C. jejuni isolates. Although the MeOPN structure is rare in nature it has structural similarity to some synthetic pesticides. In this study, we have demonstrated, by whole genome comparisons and high resolution magic angle spinning NMR, that MeOPN modifications are common to several Campylobacter species. Using MeOPN biosynthesis and transferase mutants generated in C. jejuni strain 81-176, we observed that loss of MeOPN from the cell surface correlated with increased invasion of Caco-2 epithelial cells and reduced resistance to killing by human serum. In C. jejuni, the observed serum mediated killing was determined to result primarily from activation of the classical complement pathway. The C. jejuni MeOPN transferase mutant showed similar levels of colonization relative to the wild-type in chickens, but showed a five-fold drop in colonization when co-infected with the wild-type in piglets. In Galleria mellonella waxmoth larvae, the MeOPN transferase mutant was able to kill the insects at wild-type levels. Furthermore, injection of the larvae with MeOPN-linked monosaccharides or CPS purified from the wild-type strain did not result in larval killing, indicating that MeOPN does not have inherent insecticidal activity

Multilocus sequence typing (MLST) for lineage assignment and high resolution diversity studies in Trypanosoma cruzi.

BACKGROUND: Multilocus sequence typing (MLST) is a powerful and highly discriminatory method for analysing pathogen population structure and epidemiology. Trypanosoma cruzi, the protozoan agent of American trypanosomiasis (Chagas disease), has remarkable genetic and ecological diversity. A standardised MLST protocol that is suitable for assignment of T. cruzi isolates to genetic lineage and for higher resolution diversity studies has not been developed. METHODOLOGY/PRINCIPAL FINDINGS: We have sequenced and diplotyped nine single copy housekeeping genes and assessed their value as part of a systematic MLST scheme for T. cruzi. A minimum panel of four MLST targets (Met-III, RB19, TcGPXII, and DHFR-TS) was shown to provide unambiguous assignment of isolates to the six known T. cruzi lineages (Discrete Typing Units, DTUs TcI-TcVI). In addition, we recommend six MLST targets (Met-II, Met-III, RB19, TcMPX, DHFR-TS, and TR) for more in depth diversity studies on the basis that diploid sequence typing (DST) with this expanded panel distinguished 38 out of 39 reference isolates. Phylogenetic analysis implies a subdivision between North and South American TcIV isolates. Single Nucleotide Polymorphism (SNP) data revealed high levels of heterozygosity among DTUs TcI, TcIII, TcIV and, for three targets, putative corresponding homozygous and heterozygous loci within DTUs TcI and TcIII. Furthermore, individual gene trees gave incongruent topologies at inter- and intra-DTU levels, inconsistent with a model of strict clonality. CONCLUSIONS/SIGNIFICANCE: We demonstrate the value of systematic MLST diplotyping for describing inter-DTU relationships and for higher resolution diversity studies of T. cruzi, including presence of recombination events. The high levels of heterozygosity will facilitate future population genetics analysis based on MLST haplotypes