A Generalization of Martin's Axiom

We define the $\aleph_{1.5}$ chain condition. The corresponding forcing axiom is a generalization of Martin's Axiom and implies certain uniform failures of club--guessing on $\omega_1$ that don't seem to have been considered in the literature before.Comment: 36 page

Derived categories of cubic fourfolds

We discuss the structure of the derived category of coherent sheaves on cubic fourfolds of three types: Pfaffian cubics, cubics containing a plane and singular cubics, and discuss its relation to the rationality of these cubics.Comment: 18 page

Outcomes of haematology/oncology patients admitted to intensive care unit at The Canberra Hospital

BACKGROUND: Outcomes for haematology/oncology patients have improved; however, determining their suitability for intensive care unit (ICU) admission remains challenging and controversial. AIM: Examine outcomes of patients admitted to an Australian tertiary hospital ICU and explore potential prognostic factors. METHODS: A retrospective review of patients with haematological and solid tumour malignancies non-electively admitted to The Canberra Hospital (TCH) ICU, between January 2008 and December 2012. Patient demographics, cancer details, reasons for ICU admission and Acute Physiologic and Chronic Health Evaluation (APACHE) II scores were collected, and survival rates calculated and correlated with potential prognostic factors. RESULTS Of 205 patients, 113 (55%) had haematological malignancies, and 92 (45%) had solid tumours: 58% male and mean age 60.3 years (standard deviation (SD) 13.4). Eighty-two per cent of solid tumour patients had metastatic disease and 55% received palliative chemotherapy. Primary reasons for ICU admission included sepsis (59%), respiratory distress (37%) and hypotension/shock (18%). Mean APACHE II score was 20.1(SD 0.55); mean length of stay in ICU, 4 days (SD 5.2); ICU survival was 76% with 62% and 41% alive at 30 days and 6 months respectively. Overall 1-year survival was 36%. High APACHE II scores and ≥2 organs failing were significant risk factors for 30-day mortality. CONCLUSION: Short-term outcomes were similar to contemporary studies from a general tertiary hospital setting and better than historical data. Sixty-two per cent of patients were alive 30 days post-ICU admission, with a significant minority alive at 12 months, confirming some patients achieved worthwhile outcomes. Further research is needed to ensure appropriate patient selection and to explore quality of life post ICU

Cohomological descent theory for a morphism of stacks and for equivariant derived categories

In the paper we answer the following question: for a morphism of varieties (or, more generally, stacks), when the derived category of the base can be recovered from the derived category of the covering variety by means of descent theory? As a corollary, we show that for an action of a reductive group on a scheme, the derived category of equivariant sheaves is equivalent to the category of objects, equipped with an action of the group, in the ordinary derived category.Comment: 28 page

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

The relationship of femoral neck shaft angle and adiposity to greater trochanteric pain syndrome in women. A case control morphology and anthropometric study

OBJECTIVE To evaluate if pelvic or hip width predisposed women to developing greater trochanteric pain syndrome (GTPS). DESIGN Prospective case control study. PARTICIPANTS Four groups were included in the study: those gluteal tendon reconstructions (n=31, GTR), those with conservatively managed GTPS (n=29), those with hip osteoarthritis (n=20, OA) and 22 asymptomatic participants (ASC). METHODS Anterior-posterior pelvic x-rays were evaluated for femoral neck shaft angle; acetabular index, and width at the lateral acetabulum, and the superior and lateral aspects of the greater trochanter. Body mass index, and waist, hip and greater trochanter girth were measured. Data were analysed using a one-way analysis of variance (ANOVA; posthoc Scheffe analysis), then multivariate analysis. RESULTS The GTR group had a lower femoral neck shaft angle than the other groups (p=0.007). The OR (95% CI) of having a neck shaft angle of less than 134°, relative to the ASC group: GTR=3.33 (1.26 to 8.85); GTPS=1.4 (0.52 to 3.75); OA=0.85 (0.28 to 2.61). The OR of GTR relative to GTPS was 2.4 (1.01 to 5.6). No group difference was found for acetabular or greater trochanter width. Greater trochanter girth produced the only anthropometric group difference (mean (95% CI) in cm) GTR=103.8 (100.3 to 107.3), GTPS=105.9 (100.2 to 111.6), OA=100.3 (97.7 to 103.9), ASC=99.1 (94.7 to 103.5), (ANOVA: p=0.036). Multivariate analysis confirmed adiposity is associated with GTPS. CONCLUSION A lower neck shaft angle is a risk factor for, and adiposity is associated with, GTPS in women

The Topology of Parabolic Character Varieties of Free Groups

Let G be a complex affine algebraic reductive group, and let K be a maximal compact subgroup of G. Fix elements h_1,...,h_m in K. For n greater than or equal to 0, let X (respectively, Y) be the space of equivalence classes of representations of the free group of m+n generators in G (respectively, K) such that for each i between 1 and m, the image of the i-th free generator is conjugate to h_i. These spaces are parabolic analogues of character varieties of free groups. We prove that Y is a strong deformation retraction of X. In particular, X and Y are homotopy equivalent. We also describe explicit examples relating X to relative character varieties.Comment: 16 pages, version 2 includes minor revisions and some modified proofs, accepted for publication in Geometriae Dedicat

Evidence for cervical muscle morphometric changes on magnetic resonance images after whiplash: A systematic review and meta-analysis

INTRODUCTION Morphometric changes to cervical musculature in whiplash associated disorder have been reported in several studies with varying results. However, the evidence is not clear because only a limited number of cohorts have been studied and one cohort has been reported in multiple publications. The aim of this study was to assess the evidence for cervical muscle morphometric changes on magnetic resonance (MR) images after whiplash using a systematic review with meta-analysis. MATERIALS AND METHODS PubMed, MEDLINE and Cochrane Library were searched without language restriction using combinations of the MeSH terms "muscles", "whiplash injuries", and "magnetic resonance imaging". Studies of acute and chronic whiplash were included if they compared whiplash and control cervical spine muscle morphometry measurements from MR images. The search identified 380 studies. After screening, eight studies describing five cohorts (one acute, three chronic, one both acute and chronic) met the inclusion criteria. Participant characteristics and outcome measures were extracted using a standard extraction format. Quality of eligible studies was assessed using the Newcastle-Ottawa Scale. Muscle cross-sectional area (CSA) and fat infiltrate (MFI) for acute and chronic whiplash cohorts were compared using mean difference and 95% confidence intervals. Meta-analysis models were created when data from more than two eligible cohorts was available, using inverse-variance random-effects models (RevMan5 version 5.3.5). RESULTS Quality assessment was uniformly good but only two studies blinded the assessor. Analysis of the acute cohorts revealed no consensus with respect to CSA. MFI was not measured in the acute cohorts. Analysis of the chronic cohorts revealed CSA is probably increased in some muscles after whiplash but there is insufficient evidence to confirm whether MFI is also increased. Because the available data were limited, meta-analyses of only multifidus were performed. In chronic whiplash multifidus CSA was significantly increased at C5 (Z = 3.51, p < 0.01) and C6 (Z = 2.66, p < 0.01); and MFI was significantly increased at C7 only (Z = 2.52, p < 0.01) but the heterogeneity was unacceptably high (I2 = 83%). CONCLUSIONS The strength of the evidence for cervical muscle morphometric changes on MR images after whiplash is inconsistent for CSA and MFI. Future study designs should be standardised with quantification of three-dimensional muscle morphometry