Splitting monoidal stable model categories

If C is a stable model category with a monoidal product then the set of homotopy classes of self-maps of the unit forms a commutative ring, [S,S]C. An idempotent e of this ring will split the homotopy category: [X,Y]C≅e[X,Y]C⊕(1−e)[X,Y]C. We prove that provided the localised model structures exist, this splitting of the homotopy category comes from a splitting of the model category, that is, C is Quillen equivalent to LeSC×L(1−e)SC and [X,Y]LeSC≅e[X,Y]C. This Quillen equivalence is strong monoidal and is symmetric when the monoidal product of C is.

Classifying Rational G-Spectra for Finite G

We give a new proof that for a finite group G, the category of rational G-equivariant spectra is Quillen equivalent to the product of the model categories of chain complexes of modules over the rational group ring of the Weyl group of H in G, as H runs over the conjugacy classes of subgroups of G. Furthermore, the Quillen equivalences of our proof are all symmetric monoidal. Thus we can understand categories of algebras or modules over a ring spectrum in terms of the algebraic model.

A monoidal algebraic model for rational SO(2)-spectra

The category of rational SO(2)--equivariant spectra admits an algebraic model. That is, there is an abelian category A(SO(2)) whose derived category is equivalent to the homotopy category of rational$SO(2)--equivariant spectra. An important question is: does this algebraic model capture the smash product of spectra? The category A(SO(2)) is known as Greenlees' standard model, it is an abelian category that has no projective objects and is constructed from modules over a non--Noetherian ring. As a consequence, the standard techniques for constructing a monoidal model structure cannot be applied. In this paper a monoidal model structure on A(SO(2)) is constructed and the derived tensor product on the homotopy category is shown to be compatible with the smash product of spectra. The method used is related to techniques developed by the author in earlier joint work with Roitzheim. That work constructed a monoidal model structure on Franke's exotic model for the K_(p)--local stable homotopy category. A monoidal Quillen equivalence to a simpler monoidal model category that has explicit generating sets is also given. Having monoidal model structures on the two categories removes a serious obstruction to constructing a series of monoidal Quillen equivalences between the algebraic model and rational SO(2)--equivariant spectra.

Turning the categories inside-out: Complex identifications and multiple interactions in religious ethnography

This paper challenges the fixed boundaries that ethnographers have often constructed between religious insiders and outsiders. Drawing on Neitz's observations, it argues that the main task of reflexive fieldwork is locating the self in relation to ambiguous and shifting boundaries. We offer a comparative analysis of the experiences of two differently socially located researchers to illustrate how religious identity emerges as a continuum, on which one's place is negotiated with one's research participants. We also examine the importance of intersecting multiple identities. Finally, the paper questions whether social identity categories are the primary way that we relate with our respondents. It explores the spiritual and emotional dimensions of research relationships and argues that these may transform, reinforce and generally interact with social identities. Comparing our experiences, we outline the consequences of these reflections for data gathering and analysis.

Tight junctional abnormality in multiple sclerosis white matter affects all calibres of vessel and is associated with blood-brain barrier leakage and active demyelination

Blood-brain barrier (BBB) hyperpermeability in multiple sclerosis (MS) is associated with lesion pathogenesis and has been linked to pathology in microvascular tight junctions (TJs). This study quantifies the uneven distribution of TJ pathology and its association with BBB leakage. Frozen sections from plaque and normal-appearing white matter (NAWM) in 14 cases were studied together with white matter from six neurological and five normal controls. Using single and double immunofluorescence and confocal microscopy, the TJ-associated protein zonula occludens-1 (ZO-1) was examined across lesion types and tissue categories, and in relation to fibrinogen leakage. Confocal image data sets were analysed for 2198 MS and 1062 control vessels. Significant differences in the incidence of TJ abnormalities were detected between the different lesion types in MS and between MS and control white matter. These were frequent in oil-red O (ORO)+ active plaques, affecting 42% of vessel segments, but less frequent in ORO- inactive plaques (23%), NAWM (13%), and normal (3.7%) and neurological controls (8%). A similar pattern was found irrespective of the vessel size, supporting a causal role for diffusible inflammatory mediators. In both NAWM and inactive lesions, dual labelling showed that vessels with the most TJ abnormality also showed most fibrinogen leakage. This was even more pronounced in active lesions, where 41% of vessels in the highest grade for TJ alteration showed severe leakage. It is concluded that disruption of TJs in MS, affecting both paracellular and transcellular paths, contributes to BBB leakage. TJ abnormality and BBB leakage in inactive lesions suggests either failure of TJ repair or a continuing pathological process. In NAWM, it suggests either pre-lesional change or secondary damage. Clinically inapparent TJ pathology has prognostic implications and should be considered when planning disease-modifying therapy

Recombinant alpha 2(IV)NC1 domain of type IV collagen is an effective regulator of retinal capillary endothelial cell proliferation and inhibits pre-retinal neovascularisation

Background A recombinant form of the alpha 2(IV)NC1 domain of type IV collagen has been shown to have potent anti-angiogenic activity although this peptide has not been studied in the context of proliferative retinopathies. In the current investigation we examined the potential for alpha 2(IV) NC1 to regulate retinal microvascular endothelial cell function using a range of in vitro and in vivo assay systems.