The structure of equivalent 3-separations in a 3-connected matroid

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The structure of 3-connected matroids of path width three

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Fork-decompositions of matroids

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On matroids of branch-width three

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Statin therapy, myopathy and exercise--a case report

In a bid to reduce the morbidity and mortality associated with coronary artery disease, statin therapy has become a cornerstone treatment for patients with dyslipideamia. Statins, or HMG-CoA reductase inhibitors, are effective in blocking hepatic synthesis of cholesterol and are generally regarded as safe. Although rare, severe adverse side effects such as rhabdomyolysis have been reported, however, the more common complaint from patients is that related to myopathy. There is also mounting evidence that exercise may exacerbate these side effects, however the mechanisms are yet to be fully defined and there is controversy regarding the role that inflammation may play in the myopathy. This paper reports a patients experience during 6 months of simvastatin therapy and provides some insight into the white cell count (inflammation) following two bouts of moderate intensity exercise before and during statin therapy. It also highlights the need for rehabilitation practitioners to be aware of the adverse effects of statins in exercising patients

The law of brevity in macaque vocal communication is not an artifact of analyzing mean call durations

Words follow the law of brevity, i.e. more frequent words tend to be shorter. From a statistical point of view, this qualitative definition of the law states that word length and word frequency are negatively correlated. Here the recent finding of patterning consistent with the law of brevity in Formosan macaque vocal communication (Semple et al., 2010) is revisited. It is shown that the negative correlation between mean duration and frequency of use in the vocalizations of Formosan macaques is not an artifact of the use of a mean duration for each call type instead of the customary 'word' length of studies of the law in human language. The key point demonstrated is that the total duration of calls of a particular type increases with the number of calls of that type. The finding of the law of brevity in the vocalizations of these macaques therefore defies a trivial explanation.Comment: Little improvements of the statistical argument

The structure of 3-connected matroids of path-width three

A 3-connected matroid M is sequential or has path width 3 if its ground set E(M) has a sequential ordering, that is, an ordering (e₁,e₂,...,en) such that ({e₁,e₂,...,ek},{ek+1,ek+2,...,en}) is a 3-separation for all k in {3,4,...,n-3}. In this paper, we consider the possible sequential orderings that such a matroid can have. In particular, we prove that M essentially has two fixed ends, each of which is a maximal segment, a maximal cosegment, or a maximal fan. We also identify the possible structures in M that account for different sequential orderings of E(M). These results rely on an earlier paper of the authors that describes the structure of equivalent non-sequential 3-separations in a 3-connected matroid. Those results are extended here to describe the structure of equivalent sequential 3-separations

The structure of the 3-separations of 3-connected matroids II

The authors showed in an earlier paper that there is a tree that displays, up to a natural equivalence, all non-trivial 3-separations of a 3-connected matroid. The purpose of this paper is to show that if certain natural conditions are imposed on the tree, then it has a uniqueness property. In particular; suppose that, from every pair of edges that meet at a degree-2 vertex and have their other ends of degree at least three, one edge is contracted. Then the resulting tree is unique

Adventures in Invariant Theory

We provide an introduction to enumerating and constructing invariants of group representations via character methods. The problem is contextualised via two case studies arising from our recent work: entanglement measures, for characterising the structure of state spaces for composite quantum systems; and Markov invariants, a robust alternative to parameter-estimation intensive methods of statistical inference in molecular phylogenetics.Comment: 12 pp, includes supplementary discussion of example