Representations and KK-theory of Discrete Groups

Let $\Gamma$ be a discrete group of finite virtual cohomological dimension with certain finiteness conditions of the type satisfied by arithmetic groups. We define a representation ring for $\Gamma$, determined on its elements of finite order, which is of finite type. Then we determine the contribution of this ring to the topological $K$-theory $K^*(B\Gamma)$, obtaining an exact formula for the difference in terms of the cohomology of the centralizers of elements of finite order in $\Gamma$.Comment: 4 page

Severe malaria - a case of fatal Plasmodium knowlesi infection with post-mortem findings: a case report.

BACKGROUND: Zoonotic malaria caused by Plasmodium knowlesi is an important, but newly recognized, human pathogen. For the first time, post-mortem findings from a fatal case of knowlesi malaria are reported here. CASE PRESENTATION: A formerly healthy 40 year-old male became symptomatic 10 days after spending time in the jungle of North Borneo. Four days later, he presented to hospital in a state of collapse and died within two hours. He was hyponatraemic and had elevated blood urea, potassium, lactate dehydrogenase and amino transferase values; he was also thrombocytopenic and eosinophilic. Dengue haemorrhagic shock was suspected and a post-mortem examination performed. Investigations for dengue virus were negative. Blood for malaria parasites indicated hyperparasitaemia and single species P. knowlesi infection was confirmed by nested-PCR. Macroscopic pathology of the brain and endocardium showed multiple petechial haemorrhages, the liver and spleen were enlarged and lungs had features consistent with ARDS. Microscopic pathology showed sequestration of pigmented parasitized red blood cells in the vessels of the cerebrum, cerebellum, heart and kidney without evidence of chronic inflammatory reaction in the brain or any other organ examined. Brain sections were negative for intracellular adhesion molecule-1. The spleen and liver had abundant pigment containing macrophages and parasitized red blood cells. The kidney had evidence of acute tubular necrosis and endothelial cells in heart sections were prominent. CONCLUSIONS: The overall picture in this case was one of systemic malaria infection that fit the WHO classification for severe malaria. Post-mortem findings in this case were unexpectedly similar to those that define fatal falciparum malaria, including cerebral pathology. There were important differences including the absence of coma despite petechial haemorrhages and parasite sequestration in the brain. These results suggest that further study of knowlesi malaria will aid the interpretation of, often conflicting, information on malaria pathophysiology in humans

Λr -sets and separation axioms

Separation axioms are among the most common and important and interesting concepts in topology as well as in bitopologies. In this paper, we introduce Λr-sets and some weak separation axioms using Λr -open sets and Λr -closure operator

Morphology of the ultraviolet Io footprint emission and its control by Io's location

[1] A total of 74 images of the ultraviolet footprint of the Io flux tube (IFT) on Jupiter's upper atmosphere made with the Space Telescope Imaging Spectrograph on board the Hubble Space Telescope have been analyzed to characterize their location, morphology, and brightness distribution. The observations cover a wide range of central meridian Jovian longitudes and Io orbital positions and include north and south footprint emissions. Comparing the location of the IFT with that expected from the VIP4 model of the Jovian magnetic field, we find that the lead angle is generally not significantly different from zero in the System III longitude sector 125 degrees - 195 degrees. Instead, the lead angles reach about 8 degrees in the 50 degrees sector, coinciding with a region of possible magnetic anomaly. We observe that the brightness of the main footprint shows intrinsic intensity changes that appear to be controlled by the system III longitude of Io and its position above or below the center of the torus. The size of the primary spot magnetically maps into a region varying from 1 to over 10 Io diameters in Io's orbital plane. Multiple footprints are observed with varying brightness relative to the mean spot. The number of spots is found to increase as Io gets closer to the torus outer edge facing the spots. The separation between the first and second spots is typically 1 degrees-3 degrees of longitude and increases when Io is displaced from the torus center in the direction of the IFT signature. These features confirm that Alfven waves play an important role and generate energization of precipitated electrons. However, the observed variation of the FUV spot structure with Io's position appears inconsistent with models where reflections of Alfven wings occur between the torus boundary and Jupiter's ionosphere. Instead, the multiple spots apparently correspond to electron precipitation generated by Alfven waves reflected inside the plasma torus

Bilinear forms on Grothendieck groups of triangulated categories

We extend the theory of bilinear forms on the Green ring of a finite group developed by Benson and Parker to the context of the Grothendieck group of a triangulated category with Auslander-Reiten triangles, taking only relations given by direct sum decompositions. We examine the non-degeneracy of the bilinear form given by dimensions of homomorphisms, and show that the form may be modified to give a Hermitian form for which the standard basis given by indecomposable objects has a dual basis given by Auslander-Reiten triangles. An application is given to the homotopy category of perfect complexes over a symmetric algebra, with a consequence analogous to a result of Erdmann and Kerner.Comment: arXiv admin note: substantial text overlap with arXiv:1301.470

Extending structures I: the level of groups

Let $H$ be a group and $E$ a set such that $H \subseteq E$. We shall describe and classify up to an isomorphism of groups that stabilizes $H$ the set of all group structures that can be defined on $E$ such that $H$ is a subgroup of $E$. A general product, which we call the unified product, is constructed such that both the crossed product and the bicrossed product of two groups are special cases of it. It is associated to $H$ and to a system $\bigl((S, 1_S,\ast), \triangleleft, \, \triangleright, \, f \bigl)$ called a group extending structure and we denote it by $H \ltimes S$. There exists a group structure on $E$ containing $H$ as a subgroup if and only if there exists an isomorphism of groups $(E, \cdot) \cong H \ltimes S$, for some group extending structure $\bigl((S, 1_S,\ast), \triangleleft, \, \triangleright, \, f \bigl)$. All such group structures on $E$ are classified up to an isomorphism of groups that stabilizes $H$ by a cohomological type set ${\mathcal K}^{2}_{\ltimes} (H, (S, 1_S))$. A Schreier type theorem is proved and an explicit example is given: it classifies up to an isomorphism that stabilizes $H$ all groups that contain $H$ as a subgroup of index 2.Comment: 17 pages; to appear in Algebras and Representation Theor

Weight variability and cardiovascular outcomes:a systematic review and meta-analysis

Abstract The association between body weight variability and the risk of cardiovascular disease (CVD) has been investigated previously with mixed findings. However, there has been no extensive study which systematically evaluates the current evidence. Furthermore, the impact of ethnicity and type 2 diabetes on this phenomena has not yet been investigated. Therefore, the aim of this study was to comprehensively evaluate the effect of weight variability on risk of CVD (any cardiovascular (CV) event, composite CV outcome, CV death, Stroke, Myocardial Infarction) and the influence of ethnicity and type 2 diabetes status on the observed association. A systematic review and meta-analysis was performed according to the meta-analyses of observational studies in epidemiology (MOOSE) guidelines. The electronic databases PubMed, Web of Science, and the Cochrane Library were searched for studies that investigated the relationship between body weight or BMI variability and CV diseases using Medical Subject Headings (MeSH) terms and keywords. The relative risks (RRs) for the outcomes were collected from studies, pooled, and analysed using a random-effects model to estimate the overall relative risk. Of 5645 articles screened, 23 studies with a total population of 15,382,537 fulfilled the prespecified criteria and were included. Individuals in the highest strata of body weight variability were found to have significantly increased risk of any CV event (RR = 1.27; 95% Confidence Interval (CI) 1.17–1.38; P < 0.0001; I2 = 97.28%), cardiovascular death (RR = 1.29; 95% CI 1.03–1.60; P < 0.0001; I2 = 55.16%), myocardial infarction (RR = 1.32; 95% CI 1.09–1.59; P = 0.0037; I2 = 97.14%), stroke (RR = 1.21; 95% CI 1.19–1.24; P < 0.0001; I2 = 0.06%), and compound CVD outcomes (RR = 1.36; 95% CI 1.08–1.73; P = 0.01; I2 = 92.41%). Similar RRs were observed regarding BMI variability and per unit standard deviation (SD) increase in body weight variability. Comparable effects were seen in people with and without diabetes, in White Europeans and Asians. In conclusion, body weight variability is associated with increased risk of CV diseases regardless of ethnicity or diabetes status. Future research is needed to prove a causative link between weight variability and CVD risk, as appropriate interventions to maintain stable weight could positively influence CVD