Gibbs fragmentation trees

We study fragmentation trees of Gibbs type. In the binary case, we identify the most general Gibbs-type fragmentation tree with Aldous' beta-splitting model, which has an extended parameter range $\beta>-2$ with respect to the ${\rm beta}(\beta+1,\beta+1)$ probability distributions on which it is based. In the multifurcating case, we show that Gibbs fragmentation trees are associated with the two-parameter Poisson--Dirichlet models for exchangeable random partitions of $\mathbb {N}$, with an extended parameter range $0\le\alpha\le1$, $\theta\ge-2\alpha$ and $\alpha<0$, $\theta =-m\alpha$, $m\in \mathbb {N}$.Comment: Published in at http://dx.doi.org/10.3150/08-BEJ134 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Mitral and Tricuspid Transcatheter Interventions Current Indications and Future Directions.

Valvular heart disease is responsible for a high rate of morbidity and mortality, especially in the elderly population. With the emergence of new transcatheter treatment options, the therapeutic spectrum for patients with valvular heart disease has considerably expanded during the past years. Interventional treatment of the mitral and tricuspid valve requires an individualized and versatile approach owing to the different etiologies of valvular dysfunction and the complex anatomy of the atrioventricular valves. This article aims to review recent developments, summarize the evidence, indications and limitations of the available systems, and provide a glimpse into the future of transcatheter interventions for the treatment of mitral and tricuspid valve disease

Stopping Rules for Algebraic Iterative Reconstruction Methods in Computed Tomography

Algebraic models for the reconstruction problem in X-ray computed tomography (CT) provide a flexible framework that applies to many measurement geometries. For large-scale problems we need to use iterative solvers, and we need stopping rules for these methods that terminate the iterations when we have computed a satisfactory reconstruction that balances the reconstruction error and the influence of noise from the measurements. Many such stopping rules are developed in the inverse problems communities, but they have not attained much attention in the CT world. The goal of this paper is to describe and illustrate four stopping rules that are relevant for CT reconstructions.Comment: 11 pages, 10 figure