Immune function biomarkers in children exposed to lead and organochlorine compounds: a cross-sectional study

BACKGROUND: Different organochlorines and lead (Pb) have been shown to have immunomodulating properties. Children are at greater risk for exposure to these environmental toxicants, but very little data exist on simultaneous exposures to these substances. METHODS: We investigated whether the organochlorine compounds (OC) dichlorodiphenylethylene (DDE), hexachlorobenzene (HCB), hexachlorocyclohexane (γ-HCH), the sum of polychlorinated biphenyls (ΣPCBs) and Pb were associated with immune markers such as immunoglobulin (Ig) levels, white blood cell (WBC), counts of lymphocytes; eosinophils and their eosinophilic granula as well as IgE count on basophils. The investigation was part of a cross-sectional environmental study in Hesse, Germany. In 1995, exposure to OC and Pb were determined, questionnaire data collected and immune markers quantified in 331 children. For the analyses, exposure (OC and Pb) concentrations were grouped in quartiles (γ-HCH into tertiles). Using linear regression, controlling for age, gender, passive smoking, serum lipids, and infections in the previous 12 months, we assessed the association between exposures and immune markers. Adjusted geometric means are provided for the different exposure levels. RESULTS: Geometric means were: DDE 0.32 μg/L, ΣPCBs 0.50 μg/L, HCB 0.22 μg/L, γ-HCH 0.02 μg/L and Pb 26.8 μg/L. The ΣPCBs was significantly associated with increased IgM levels, whereas HCB was inversely related to IgM. There was a higher number of NK cells (CD56+) with increased γ-HCH concentrations. At higher lead concentrations we saw increased IgE levels. DDE showed the most associations with significant increases in WBC count, in IgE count on basophils, IgE, IgG, and IgA levels. DDE was also found to significantly decrease eosinophilic granula content. CONCLUSION: Low-level exposures to OC and lead (Pb) in children may have immunomodulating effects. The increased IgE levels, IgE count on basophils, and the reduction of eosinophilic granula at higher DDE concentrations showed a most consistent pattern, which could be of clinical importance in the etiology of allergic diseases

A coalgebraic view of bar recursion and bar induction

We reformulate the bar recursion and induction principles in terms of recursive and wellfounded coalgebras. Bar induction was originally proposed by Brouwer as an axiom to recover certain classically valid theorems in a constructive setting. It is a form of induction on non- wellfounded trees satisfying certain properties. Bar recursion, introduced later by Spector, is the corresponding function defnition principle. We give a generalization of these principles, by introducing the notion of barred coalgebra: a process with a branching behaviour given by a functor, such that all possible computations terminate. Coalgebraic bar recursion is the statement that every barred coalgebra is recursive; a recursive coalgebra is one that allows defnition of functions by a coalgebra-to-algebra morphism. It is a framework to characterize valid forms of recursion for terminating functional programs. One application of the principle is the tabulation of continuous functions: Ghani, Hancock and Pattinson defned a type of wellfounded trees that represent continuous functions on streams. Bar recursion allows us to prove that every stably continuous function can be tabulated to such a tree where by stability we mean that the modulus of continuity is also continuous. Coalgebraic bar induction states that every barred coalgebra is well-founded; a wellfounded coalgebra is one that admits proof by induction

Set Theory and Structures

Set-theoretic and category-theoretic foundations represent different perspectives on mathematical subject matter. In particular, category-theoretic language focusses on properties that can be determined up to isomorphism within a category, whereas set theory admits of properties determined by the internal structure of the membership relation. Various objections have been raised against this aspect of set theory in the category-theoretic literature. In this article, we advocate a methodological pluralism concerning the two foundational languages, and provide a theory that fruitfully interrelates a `structural' perspective to a set-theoretic one. We present a set-theoretic system that is able to talk about structures more naturally, and argue that it provides an important perspective on plausibly structural properties such as cardinality. We conclude the language of set theory can provide useful information about the notion of mathematical structure