Gorenstein homological algebra and universal coefficient theorems

We study criteria for a ring—or more generally, for a small category—to be Gorenstein and for a module over it to be of finite projective dimension. The goal is to unify the universal coefficient theorems found in the literature and to develop machinery for proving new ones. Among the universal coefficient theorems covered by our methods we find, besides all the classic examples, several exotic examples arising from the KK-theory of C*-algebras and also Neeman’s Brown–Adams representability theorem for compactly generated categories

Brown representability for space-valued functors

In this paper we prove two theorems which resemble the classical cohomological and homological Brown representability theorems. The main difference is that our results classify small contravariant functors from spaces to spaces up to weak equivalence of functors. In more detail, we show that every small contravariant functor from spaces to spaces which takes coproducts to products up to homotopy and takes homotopy pushouts to homotopy pullbacks is naturally weekly equivalent to a representable functor. The second representability theorem states: every contravariant continuous functor from the category of finite simplicial sets to simplicial sets taking homotopy pushouts to homotopy pullbacks is equivalent to the restriction of a representable functor. This theorem may be considered as a contravariant analog of Goodwillie's classification of linear functors.Comment: 19 pages, final version, accepted by the Israel Journal of Mathematic

HARP/ACSIS: A submillimetre spectral imaging system on the James Clerk Maxwell Telescope

This paper describes a new Heterodyne Array Receiver Programme (HARP) and Auto-Correlation Spectral Imaging System (ACSIS) that have recently been installed and commissioned on the James Clerk Maxwell Telescope (JCMT). The 16-element focal-plane array receiver, operating in the submillimetre from 325 to 375 GHz, offers high (three-dimensional) mapping speeds, along with significant improvements over single-detector counterparts in calibration and image quality. Receiver temperatures are $\sim$120 K across the whole band and system temperatures of $\sim$300K are reached routinely under good weather conditions. The system includes a single-sideband filter so these are SSB figures. Used in conjunction with ACSIS, the system can produce large-scale maps rapidly, in one or more frequency settings, at high spatial and spectral resolution. Fully-sampled maps of size 1 square degree can be observed in under 1 hour. The scientific need for array receivers arises from the requirement for programmes to study samples of objects of statistically significant size, in large-scale unbiased surveys of galactic and extra-galactic regions. Along with morphological information, the new spectral imaging system can be used to study the physical and chemical properties of regions of interest. Its three-dimensional imaging capabilities are critical for research into turbulence and dynamics. In addition, HARP/ACSIS will provide highly complementary science programmes to wide-field continuum studies, and produce the essential preparatory work for submillimetre interferometers such as the SMA and ALMA.Comment: MNRAS Accepted 2009 July 2. 18 pages, 25 figures and 6 table

Multidisciplinary teams, and parents, negotiating common ground in shared-care of children with long-term conditions: A mixed methods study

Background: Limited negotiation around care decisions is believed to undermine collaborative working between parents of children with long-term conditions and professionals, but there is little evidence of how they actually negotiate their respective roles. Using chronic kidney disease as an exemplar this paper reports on a multi-method study of social interaction between multidisciplinary teams and parents as they shared clinical care. Methods. Phases 1 and 2: a telephone survey mapping multidisciplinary teams' parent-educative activities, and qualitative interviews with 112 professionals (Clinical-psychologists, Dietitians, Doctors, Nurses, Play-specialists, Pharmacists, Therapists and Social-workers) exploring their accounts of parent-teaching in the 12 British children's kidney units. Phase 3: six ethnographic case studies in two units involving observations of professional/parent interactions during shared-care, and individual interviews. We used an analytical framework based on concepts drawn from Communities of Practice and Activity Theory. Results: Professionals spoke of the challenge of explaining to each other how they are aware of parents' understanding of clinical knowledge, and described three patterns of parent-educative activity that were common across MDTs: Engaging parents in shared practice; Knowledge exchange and role negotiation, and Promoting common ground. Over time, professionals had developed a shared repertoire of tools to support their negotiations with parents that helped them accomplish common ground during the practice of shared-care. We observed mutual engagement between professionals and parents where a common understanding of the joint enterprise of clinical caring was negotiated. Conclusions: For professionals, making implicit knowledge explicit is important as it can provide them with a language through which to articulate more clearly to each other what is the basis of their intuition-based hunches about parents' support needs, and may help them to negotiate with parents and accelerate parents' learning about shared caring. Our methodology and results are potentially transferrable to shared management of other conditions. © 2013 Swallow et al.; licensee BioMed Central Ltd

Climate-driven regime shift of a temperate marine ecosystem.

Ecosystem reconfigurations arising from climate-driven changes in species distributions are expected to have profound ecological, social, and economic implications. Here we reveal a rapid climate-driven regime shift of Australian temperate reef communities, which lost their defining kelp forests and became dominated by persistent seaweed turfs. After decades of ocean warming, extreme marine heat waves forced a 100-kilometer range contraction of extensive kelp forests and saw temperate species replaced by seaweeds, invertebrates, corals, and fishes characteristic of subtropical and tropical waters. This community-wide tropicalization fundamentally altered key ecological processes, suppressing the recovery of kelp forests

On the algebraic K-theory of the complex K-theory spectrum

Let p>3 be a prime, let ku be the connective complex K-theory spectrum, and let K(ku) be the algebraic K-theory spectrum of ku. We study the p-primary homotopy type of the spectrum K(ku) by computing its mod (p,v_1) homotopy groups. We show that up to a finite summand, these groups form a finitely generated free module over a polynomial algebra F_p[b], where b is a class of degree 2p+2 defined as a higher Bott element.Comment: Revised and expanded version, 42 pages

On the Whitehead spectrum of the circle

The seminal work of Waldhausen, Farrell and Jones, Igusa, and Weiss and Williams shows that the homotopy groups in low degrees of the space of homeomorphisms of a closed Riemannian manifold of negative sectional curvature can be expressed as a functor of the fundamental group of the manifold. To determine this functor, however, it remains to determine the homotopy groups of the topological Whitehead spectrum of the circle. The cyclotomic trace of B okstedt, Hsiang, and Madsen and a theorem of Dundas, in turn, lead to an expression for these homotopy groups in terms of the equivariant homotopy groups of the homotopy fiber of the map from the topological Hochschild T-spectrum of the sphere spectrum to that of the ring of integers induced by the Hurewicz map. We evaluate the latter homotopy groups, and hence, the homotopy groups of the topological Whitehead spectrum of the circle in low degrees. The result extends earlier work by Anderson and Hsiang and by Igusa and complements recent work by Grunewald, Klein, and Macko.Comment: 52 page

Understanding the small object argument

The small object argument is a transfinite construction which, starting from a set of maps in a category, generates a weak factorisation system on that category. As useful as it is, the small object argument has some problematic aspects: it possesses no universal property; it does not converge; and it does not seem to be related to other transfinite constructions occurring in categorical algebra. In this paper, we give an "algebraic" refinement of the small object argument, cast in terms of Grandis and Tholen's natural weak factorisation systems, which rectifies each of these three deficiencies.Comment: 42 pages; supersedes the earlier arXiv preprint math/0702290; v2: final journal version, minor corrections onl

Ethnic Inequalities in Mortality: The Case of Arab-Americans

BACKGROUND: Although nearly 112 million residents of the United States belong to a non-white ethnic group, the literature about differences in health indicators across ethnic groups is limited almost exclusively to Hispanics. Features of the social experience of many ethnic groups including immigration, discrimination, and acculturation may plausibly influence mortality risk. We explored life expectancy and age-adjusted mortality risk of Arab-Americans (AAs), relative to non-Arab and non-Hispanic Whites in Michigan, the state with the largest per capita population of AAs in the US. METHODOLOGY/PRINCIPAL FINDINGS: Data were collected about all deaths to AAs and non-Arab and non-Hispanic Whites in Michigan between 1990 and 2007, and year 2000 census data were collected for population denominators. We calculated life expectancy, age-adjusted all-cause, cause-specific, and age-specific mortality rates stratified by ethnicity and gender among AAs and non-Arab and non-Hispanic Whites. Among AAs, life expectancies among men and women were 2.0 and 1.4 years lower than among non-Arab and non-Hispanic White men and women, respectively. AA men had higher mortality than non-Arab and non-Hispanic White men due to infectious diseases, chronic diseases, and homicide. AA women had higher mortality than non-Arab and non-Hispanic White women due to chronic diseases. CONCLUSIONS/SIGNIFICANCE: Despite better education and higher income, AAs have higher age-adjusted mortality risk than non-Arab and non-Hispanic Whites, particularly due to chronic diseases. Features specific to AA culture may explain some of these findings