Formalising Mathematics in Simple Type Theory

Despite the considerable interest in new dependent type theories, simple type theory (which dates from 1940) is sufficient to formalise serious topics in mathematics. This point is seen by examining formal proofs of a theorem about stereographic projections. A formalisation using the HOL Light proof assistant is contrasted with one using Isabelle/HOL. Harrison's technique for formalising Euclidean spaces is contrasted with an approach using Isabelle/HOL's axiomatic type classes. However, every formal system can be outgrown, and mathematics should be formalised with a view that it will eventually migrate to a new formalism

Watching a superfluid untwist itself: Recurrence of Rabi oscillations in a Bose-Einstein condensate

The order parameter of a condensate with two internal states can continuously distort in such a way as to remove twists that have been imposed along its length. We observe this effect experimentally in the collapse and recurrence of Rabi oscillations in a magnetically trapped, two-component Bose-Einstein condensate of ^87Rb

Magnesium isotope ratios in Hyades stars

Using classical model atmospheres and an LTE analysis, Mg isotope ratios 24Mg:25Mg:26Mg are measured in 32 Hyades dwarfs covering 4000K < Teff < 5000K. We find no significant trend in any isotope ratio versus Teff and the mean isotope ratio is in excellent agreement with the solar value. We determine stellar parameters and Fe abundances for 56 Hyades dwarfs covering 4000K < Teff < 6200K. For stars warmer than 4700K, we derive a cluster mean value of [Fe/H] = 0.16 +/- 0.02 (sigma=0.1), in good agreement with previous studies. For stars cooler than 4700K, we find that the abundance of Fe from ionized lines exceeds the abundance of Fe from neutral lines. At 4700K [Fe/H]_II - [Fe/H]_I = 0.3 dex while at 4000K [Fe/H]_II - [Fe/H]_I = 1.2 dex. This discrepancy between the Fe abundance from neutral and ionized lines likely reflects inadequacies in the model atmospheres and the presence of Non-LTE or other effects. Despite the inability of the models to reproduce ionization equilibrium for Fe, the Mg isotope ratios appear immune to these problems and remain a powerful tool for studying Galactic chemical evolution.Comment: ApJ in press (March 10 2004

Diarrhea in young children from low-income countries leads to large-scale alterations in intestinal microbiota composition

Acknowledgments This work was funded in part by the William and Melinda Gates Foundation, award 42917 to JPN and OCS; US National Institutes of Health grants 5R01HG005220 to HCB, 5R01HG004885 to MP; US National Science Foundation Graduate Research Fellowship award DGE0750616 to JNP; AWW and JP are funded by The Wellcome Trust (Grant No. WT098051).Peer reviewedPublisher PD

Transkingdom Networks: A Systems Biology Approach to Identify Causal Members of Host-Microbiota Interactions

Improvements in sequencing technologies and reduced experimental costs have resulted in a vast number of studies generating high-throughput data. Although the number of methods to analyze these "omics" data has also increased, computational complexity and lack of documentation hinder researchers from analyzing their high-throughput data to its true potential. In this chapter we detail our data-driven, transkingdom network (TransNet) analysis protocol to integrate and interrogate multi-omics data. This systems biology approach has allowed us to successfully identify important causal relationships between different taxonomic kingdoms (e.g. mammals and microbes) using diverse types of data

Vulnerable warriors: the atmospheric marketing of military and policing equipment before and after 9/11

In this article, we analyse changes in the circulation of advertisements of policing products at security expos between 1995 and 2013. While the initial aim of the research was to evidence shifts in terrorist frames in the marketing of policing equipment before and after 9/11, our findings instead suggested that what we are seeing is the rise of marketing to police as “vulnerable warriors”, law enforcement officers in need of military weapons both for their offensive capabilities and for the protection they can offer to a police force that is always under threat

Electron ionization mass spectral fragmentation study of sulfation derivatives of polychlorinated biphenyls

<p>Abstract</p> <p>Background</p> <p>Polychlorinated biphenyls are persistent organic pollutants that can be metabolized via hydroxylated PCBs to PCB sulfate metabolites. The sensitive and selective analysis of PCB sulfate monoesters by gas chromatography-mass spectrometry (GC-MS) requires their derivatization, for example, as PCB 2,2,2-trichloroethyl (TCE) sulfate monoesters. To aid in the identification of unknown PCB sulfate metabolites isolated from biological samples, the electron impact MS fragmentation pathways of selected PCB TCE sulfate diesters were analyzed and compared to the fragmentation pathways of the corresponding methoxylated PCBs.</p> <p>Results</p> <p>The most abundant and characteristic fragment ions of PCB TCE sulfate diesters were formed by releasing CHCCl₃, SO₃, HCl₂and/or CCl₃from the TCE sulfate moiety and Cl₂, HCl, ethyne and chloroethyne from an intermediate phenylcyclopentadienyl cation. The fragmentation pattern depended on the degree of chlorination and the position of the TCE sulfate moiety (i.e., <it>ortho </it>vs. <it>meta/para </it>to the second phenyl ring), but were independent of the chlorine substitution pattern. These fragmentation pathways are similar to the fragmentation pathways of structurally related methoxylated PCBs.</p> <p>Conclusion</p> <p>Knowledge of the fragmentation patterns of PCB TCE sulfate diesters will greatly aid in determining the position of sulfate moiety (<it>ortho </it>vs. <it>meta/para</it>) of unknown PCB sulfate metabolites isolated from environmental or laboratory samples.</p

Listening to the voices of women suffering perinatal psychological distress

This article suggests that transactional analysis can be an effective treatment approach for women suffering from mental health conditions and the emotional and life disturbances that may occur during the perinatal period. It offers a brief introduction to perinatal psychological distress followed by a description of the use of transactional analysis psychotherapy for this condition. The article outlines a new model for a research project that aims to ascertain women’s views on the helpfulness of the treatment and to gain a better understanding of the stigma often associated with perinatal mental health issues. The author argues for the necessity of qualitative research to assess the efficacy of transactional-analysis-based treatment and to increase our knowledge about the change process in transactional analysis psychotherapy with this client population as well as to inform future transactional analysis treatment protocols