Relaying Simultaneous Multicast Messages

The problem of multicasting multiple messages with the help of a relay, which may also have an independent message of its own to multicast, is considered. As a first step to address this general model, referred to as the compound multiple access channel with a relay (cMACr), the capacity region of the multiple access channel with a "cognitive" relay is characterized, including the cases of partial and rate-limited cognition. Achievable rate regions for the cMACr model are then presented based on decode-and-forward (DF) and compress-and-forward (CF) relaying strategies. Moreover, an outer bound is derived for the special case in which each transmitter has a direct link to one of the receivers while the connection to the other receiver is enabled only through the relay terminal. Numerical results for the Gaussian channel are also provided.Comment: This paper was presented at the IEEE Information Theory Workshop, Volos, Greece, June 200

On Cosmall Abelian Groups

It is a well-known homological fact that every Abelian groupGhas the property that Hom(G,−)com-mutes with direct products. Here we investigate the ‘dual’ property: an Abelian groupGis said to be cosmallif Hom(−,G)commutes with direct products. We show that cosmall groups are cotorsion-free and that nogroup of cardinality less than a strongly compact cardinal can be cosmall. In particular, if there is a properclass of strongly compact cardinals, then there are no cosmall grou

On Cosmall Abelian Groups

It is a well-known homological fact that every Abelian group G has the property that Hom(G,−) commutes with direct products. Here we investigate the ‘dual’ property: an Abelian group G is said to be cosmall if Hom(−,G) commutes with direct products. We show that cosmall groups are cotorsion-free and that no group of cardinality less than a strongly compact cardinal can be cosmall. In particular, if there is a proper class of strongly compact cardinals, then there are no cosmall groups

If the world were a village of 100 people...

Some last-minute statistics to make you think

Association of anaemia in primary care patients with chronic kidney disease: cross sectional study of quality improvement in chronic kidney disease (QICKD) trial data.

BACKGROUND: Anaemia is a known risk factor for cardiovascular disease and treating anaemia in chronic kidney disease (CKD) may improve outcomes. However, little is known about the scope to improve primary care management of anaemia in CKD. METHODS: An observational study (N = 1,099,292) with a nationally representative sample using anonymised routine primary care data from 127 Quality Improvement in CKD trial practices (ISRCTN5631023731). We explored variables associated with anaemia in CKD: eGFR, haemoglobin (Hb), mean corpuscular volume (MCV), iron status, cardiovascular comorbidities, and use of therapy which associated with gastrointestinal bleeding, oral iron and deprivation score. We developed a linear regression model to identify variables amenable to improved primary care management. RESULTS: The prevalence of Stage 3-5 CKD was 6.76%. Hb was lower in CKD (13.2 g/dl) than without (13.7 g/dl). 22.2% of people with CKD had World Health Organization defined anaemia; 8.6% had Hb ≤ 11 g/dl; 3% Hb ≤ 10 g/dl; and 1% Hb ≤ 9 g/dl. Normocytic anaemia was present in 80.5% with Hb ≤ 11; 72.7% with Hb ≤ 10 g/dl; and 67.6% with Hb ≤ 9 g/dl; microcytic anaemia in 13.4% with Hb ≤ 11 g/dl; 20.8% with Hb ≤ 10 g/dl; and 24.9% where Hb ≤ 9 g/dl. 82.7% of people with microcytic and 58.8% with normocytic anaemia (Hb ≤ 11 g/dl) had a low ferritin (<100 ug/mL). Hypertension (67.2% vs. 54%) and diabetes (30.7% vs. 15.4%) were more prevalent in CKD and anaemia; 61% had been prescribed aspirin; 73% non-steroidal anti-inflammatory drugs (NSAIDs); 14.1% warfarin 12.4% clopidogrel; and 53.1% aspirin and NSAID. 56.3% of people with CKD and anaemia had been prescribed oral iron. The main limitations of the study are that routine data are inevitably incomplete and definitions of anaemia have not been standardised. CONCLUSIONS: Medication review is needed in people with CKD and anaemia prior to considering erythropoietin or parenteral iron. Iron stores may be depleted in over >60% of people with normocytic anaemia. Prescribing oral iron has not corrected anaemia

Correlation between the Extraordinary Hall Effect and Resistivity

We study the contribution of different types of scattering sources to the extraordinary Hall effect. Scattering by magnetic nano-particles embedded in normal-metal matrix, insulating impurities in magnetic matrix, surface scattering and temperature dependent scattering are experimentally tested. Our new data, as well as previously published results on a variety of materials, are fairly interpreted by a simple modification of the skew scattering model