Continued Fractions with Multiple Limits

For integers $m \geq 2$, we study divergent continued fractions whose numerators and denominators in each of the $m$ arithmetic progressions modulo $m$ converge. Special cases give, among other things, an infinite sequence of divergence theorems, the first of which is the classical Stern-Stolz theorem. We give a theorem on a general class of Poincar{\'e} type recurrences which shows that they tend to limits when the limits are taken in residue classes and the roots of their characteristic polynomials are distinct roots of unity. We also generalize a curious $q$-continued fraction of Ramanujan's with three limits to a continued fraction with $k$ distinct limit points, $k\geq 2$. The $k$ limits are evaluated in terms of ratios of certain unusual $q$ series. Finally, we show how to use Daniel Bernoulli's continued fraction in an elementary way to create analytic continued fractions with $m$ limit points, for any positive integer $m \geq 2$.Comment: 29 pages. Updated/new conten

SUMO-Interacting Motifs of Human TRIM5α are Important for Antiviral Activity

Human TRIM5α potently restricts particular strains of murine leukemia viruses (the so-called N-tropic strains) but not others (the B- or NB-tropic strains) during early stages of infection. We show that overexpression of SUMO-1 in human 293T cells, but not in mouse MDTF cells, profoundly blocks N-MLV infection. This block is dependent on the tropism of the incoming virus, as neither B-, NB-, nor the mutant R110E of N-MLV CA (a B-tropic switch) are affected by SUMO-1 overexpression. The block occurred prior to reverse transcription and could be abrogated by large amounts of restricted virus. Knockdown of TRIM5α in 293T SUMO-1-overexpressing cells resulted in ablation of the SUMO-1 antiviral effects, and this loss of restriction could be restored by expression of a human TRIM5α shRNA-resistant plasmid. Amino acid sequence analysis of human TRIM5α revealed a consensus SUMO conjugation site at the N-terminus and three putative SUMO interacting motifs (SIMs) in the B30.2 domain. Mutations of the TRIM5α consensus SUMO conjugation site did not affect the antiviral activity of TRIM5α in any of the cell types tested. Mutation of the SIM consensus sequences, however, abolished TRIM5α antiviral activity against N-MLV. Mutation of lysines at a potential site of SUMOylation in the CA region of the Gag gene reduced the SUMO-1 block and the TRIM5α restriction of N-MLV. Our data suggest a novel aspect of TRIM5α-mediated restriction, in which the presence of intact SIMs in TRIM5α, and also the SUMO conjugation of CA, are required for restriction. We propose that at least a portion of the antiviral activity of TRIM5α is mediated through the binding of its SIMs to SUMO-conjugated CA

Express Attentional Re-Engagement but Delayed Entry into Consciousness Following Invalid Spatial Cues in Visual Search

Background: In predictive spatial cueing studies, reaction times (RT) are shorter for targets appearing at cued locations (valid trials) than at other locations (invalid trials). An increase in the amplitude of early P1 and/or N1 event-related potential (ERP) components is also present for items appearing at cued locations, reflecting early attentional sensory gain control mechanisms. However, it is still unknown at which stage in the processing stream these early amplitude effects are translated into latency effects. Methodology/Principal Findings: Here, we measured the latency of two ERP components, the N2pc and the sustained posterior contralateral negativity (SPCN), to evaluate whether visual selection (as indexed by the N2pc) and visual-short term memory processes (as indexed by the SPCN) are delayed in invalid trials compared to valid trials. The P1 was larger contralateral to the cued side, indicating that attention was deployed to the cued location prior to the target onset. Despite these early amplitude effects, the N2pc onset latency was unaffected by cue validity, indicating an express, quasiinstantaneous re-engagement of attention in invalid trials. In contrast, latency effects were observed for the SPCN, and these were correlated to the RT effect. Conclusions/Significance: Results show that latency differences that could explain the RT cueing effects must occur after visual selection processes giving rise to the N2pc, but at or before transfer in visual short-term memory, as reflected by th

Multilocus Sequence Typing as a Replacement for Serotyping in Salmonella enterica

Salmonella enterica subspecies enterica is traditionally subdivided into serovars by serological and nutritional characteristics. We used Multilocus Sequence Typing (MLST) to assign 4,257 isolates from 554 serovars to 1092 sequence types (STs). The majority of the isolates and many STs were grouped into 138 genetically closely related clusters called eBurstGroups (eBGs). Many eBGs correspond to a serovar, for example most Typhimurium are in eBG1 and most Enteritidis are in eBG4, but many eBGs contained more than one serovar. Furthermore, most serovars were polyphyletic and are distributed across multiple unrelated eBGs. Thus, serovar designations confounded genetically unrelated isolates and failed to recognize natural evolutionary groupings. An inability of serotyping to correctly group isolates was most apparent for Paratyphi B and its variant Java. Most Paratyphi B were included within a sub-cluster of STs belonging to eBG5, which also encompasses a separate sub-cluster of Java STs. However, diphasic Java variants were also found in two other eBGs and monophasic Java variants were in four other eBGs or STs, one of which is in subspecies salamae and a second of which includes isolates assigned to Enteritidis, Dublin and monophasic Paratyphi B. Similarly, Choleraesuis was found in eBG6 and is closely related to Paratyphi C, which is in eBG20. However, Choleraesuis var. Decatur consists of isolates from seven other, unrelated eBGs or STs. The serological assignment of these Decatur isolates to Choleraesuis likely reflects lateral gene transfer of flagellar genes between unrelated bacteria plus purifying selection. By confounding multiple evolutionary groups, serotyping can be misleading about the disease potential of S. enterica. Unlike serotyping, MLST recognizes evolutionary groupings and we recommend that Salmonella classification by serotyping should be replaced by MLST or its equivalents

Comparative genomics of Pseudomonas fluorescens subclade III strains from human lungs

Abstract Background While the taxonomy and genomics of environmental strains from the P. fluorescens species-complex has been reported, little is known about P. fluorescens strains from clinical samples. In this report, we provide the first genomic analysis of P. fluorescens strains in which human vs. environmental isolates are compared. Results Seven P. fluorescens strains were isolated from respiratory samples from cystic fibrosis (CF) patients. The clinical strains could grow at a higher temperature (>34 °C) than has been reported for environmental strains. Draft genomes were generated for all of the clinical strains, and multi-locus sequence analysis placed them within subclade III of the P. fluorescens species-complex. All strains encoded type- II, −III, −IV, and -VI secretion systems, as well as the widespread colonization island (WCI). This is the first description of a WCI in P. fluorescens strains. All strains also encoded a complete I2/PfiT locus and showed evidence of horizontal gene transfer. The clinical strains were found to differ from the environmental strains in the number of genes involved in metal resistance, which may be a possible adaptation to chronic antibiotic exposure in the CF lung. Conclusions This is the largest comparative genomics analysis of P. fluorescens subclade III strains to date and includes the first clinical isolates. At a global level, the clinical P. fluorescens subclade III strains were largely indistinguishable from environmental P. fluorescens subclade III strains, supporting the idea that identifying strains as ‘environmental’ vs ‘clinical’ is not a phenotypic trait. Rather, strains within P. fluorescens subclade III will colonize and persist in any niche that provides the requirements necessary for growth.http://deepblue.lib.umich.edu/bitstream/2027.42/116129/1/12864_2015_Article_2261.pd

Integrating multiple lines of evidence to assess the effects of maternal BMI on pregnancy and perinatal outcomes

This is the final version. Available from BMC via the DOI in this record. Availability of data and materials: In order to protect participant confdentiality, supporting data cannot be made openly available. Bona fide researchers can apply for access to study specifc executive committees. Summary association data for FinnGen is publicly available at https://www.fnngen.f/en/access_results. Researchers can apply for access to the UK Biobank data via the Access Management System (AMS) (https://www.ukbiobank.ac.uk/enable-your-research/apply-for-access).BACKGROUND: Higher maternal pre-pregnancy body mass index (BMI) is associated with adverse pregnancy and perinatal outcomes. However, whether these associations are causal remains unclear. METHODS: We explored the relation of maternal pre-/early-pregnancy BMI with 20 pregnancy and perinatal outcomes by integrating evidence from three different approaches (i.e. multivariable regression, Mendelian randomisation, and paternal negative control analyses), including data from over 400,000 women. RESULTS: All three analytical approaches supported associations of higher maternal BMI with lower odds of maternal anaemia, delivering a small-for-gestational-age baby and initiating breastfeeding, but higher odds of hypertensive disorders of pregnancy, gestational hypertension, preeclampsia, gestational diabetes, pre-labour membrane rupture, induction of labour, caesarean section, large-for-gestational age, high birthweight, low Apgar score at 1 min, and neonatal intensive care unit admission. For example, higher maternal BMI was associated with higher risk of gestational hypertension in multivariable regression (OR = 1.67; 95% CI = 1.63, 1.70 per standard unit in BMI) and Mendelian randomisation (OR = 1.59; 95% CI = 1.38, 1.83), which was not seen for paternal BMI (OR = 1.01; 95% CI = 0.98, 1.04). Findings did not support a relation between maternal BMI and perinatal depression. For other outcomes, evidence was inconclusive due to inconsistencies across the applied approaches or substantial imprecision in effect estimates from Mendelian randomisation. CONCLUSIONS: Our findings support a causal role for maternal pre-/early-pregnancy BMI on 14 out of 20 adverse pregnancy and perinatal outcomes. Pre-conception interventions to support women maintaining a healthy BMI may reduce the burden of obstetric and neonatal complications. FUNDING: Medical Research Council, British Heart Foundation, European Research Council, National Institutes of Health, National Institute for Health Research, Research Council of Norway, Wellcome Trust.Medical Research CouncilBritish Heart FoundationEuropean Research CouncilEuropean Research CouncilEuropean Union’s Horizon 2020National Institutes of HealthNational Institutes of HealthResearch Council of NorwayWellcome Trus

Fractional Integration Versus Structural Change: Testing the Convergence of CO2 Emissions

This paper assesses the stochastic convergence of relative CO₂ emissions within 28 OECD countries over the period 1950–2013. Using the local Whittle estimator and some of its variants we assess whether relative per capita CO₂ emissions are long memory processes which, although highly persistent, may revert to their mean/trend in the long run thereby indicating evidence of stochastic convergence. Furthermore, we test whether (possibly) slow convergence or the complete lack of it may be the result of structural changes to the deterministics of each of the relative per-capita emissions series by means of the tests of Berkes et al. (Ann Stat 1140–1165, 2006) and Mayoral (Oxford Bull Econ Stat 74(2):278–305, 2012). Our results show relatively weak support for stochastic convergence of CO₂ emissions, indicating that only between 30 and 40% of the countries converge to the OECD average in a stochastic sense. This weak evidence disappears if we enlarge the sample to include 4 out of the 5 BRICS, indicating that our results are not robust to the inclusion of countries which are experiencing rates of growth which are far larger than those of the OECD members. Our results also decisively indicate that a slow or lack of convergence is not the results of a structural break in the relative CO₂ emissions series