The Ubiquity of Sidon Sets That Are Not I0I_0

We prove that every infinite, discrete abelian group admits a pair of $I_0$ sets whose union is not $I_0$. In particular, this implies that every such group contains a Sidon set that is not $I_{0}$

Cardiac Depression Scale: Mokken scaling in heart failure patients

Background: There is a high prevalence of depression in patients with heart failure (HF) that is associated with worsening prognosis. The value of using a reliable and valid instrument to measure depression in this population is therefore essential. We validated the Cardiac Depression Scale (CDS) in heart failure patients using a model of ordinal unidimensional measurement known as Mokken scaling. Findings: We administered in face-to-face interviews the CDS to 603 patients with HF. Data were analysed using Mokken scale analysis. Items of the CDS formed a statistically significant unidimensional Mokken scale of low strength (H<0.40) and high reliability (Rho>0.8). Conclusions: The CDS has a hierarchy of items which can be interpreted in terms of the increasingly serious effects of depression occurring as a result of HF. Identifying an appropriate instrument to measure depression in patients with HF allows for early identification and better medical management. Keywords: Cardiac Depression Scale, Heart failure, Depression, Mokken scalin

Choosing a calcium supplement for sheep fed cereal grains

Sheep fed cereal grains as an energy source over summer usually need added calcium because cereal grains are generally low in calcium (for example, 0.03 per cent calcium compared to 0.26 per cent phosphorus), and there may not be a natural source such as clover, weeds, leafy stubble or edible bush in the paddock. The safestt and most effective calcium supplement is finely ground limestone added to the feed, but some farmers have used other sources of calcium such as gypsum and superphosphate in this manner

Identifying Active Manifolds

Determining the "active manifold'' for a minimization problem is a large step towards solving the problem. Many researchers have studied under what conditions certain algorithms identify active manifolds in a finite number of iterations. In this work we outline a unifying framework encompassing many earlier results on identification via the Subgradient (Gradient) Projection Method, Newton-like Methods, and the Proximal Point Algorithm. This framework, prox-regular partial smoothness, has the advantage of not requiring convexity for its conclusions, and therefore extends many of these earlier results

Movement disorders and syndromic autism: a systematic review

Movement disorders are reported in idiopathic autism but the extent to which comparable movement disorders are found in syndromic/co-morbid autism is unknown. A systematic search of Medline, Embase, PsychINFO and CINAHL on the prevalence of specific movement disorder in syndromic autism associated with specific genetic syndromes identified 16 papers, all relating to Angelman syndrome or Rett syndrome. Prevalence rates of 72.7–100% and 25.0–27.3% were reported for ataxia and tremor, respectively, in Angelman syndrome. In Rett syndrome, prevalence rates of 43.6–50% were reported for ataxia and 27.3–48.3% for tremor with additional reports of dystonia, rigidity and pyramidal signs. However, reliable assessment measures were rarely used and recruitment was often not described in sufficient detail