Clades and clans: a comparison study of two evolutionary models

The Yule-Harding-Kingman (YHK) model and the proportional to distinguishable arrangements (PDA) model are two binary tree generating models that are widely used in evolutionary biology. Understanding the distributions of clade sizes under these two models provides valuable insights into macro-evolutionary processes, and is important in hypothesis testing and Bayesian analyses in phylogenetics. Here we show that these distributions are log-convex, which implies that very large clades or very small clades are more likely to occur under these two models. Moreover, we prove that there exists a critical value $\kappa(n)$ for each $n\geqslant 4$ such that for a given clade with size $k$, the probability that this clade is contained in a random tree with $n$ leaves generated under the YHK model is higher than that under the PDA model if $1<k<\kappa(n)$, and lower if $\kappa(n)<k<n$. Finally, we extend our results to binary unrooted trees, and obtain similar results for the distributions of clan sizes.Comment: 21page

Telomerase and breast cancer

Current therapies for breast cancer include treatments that are toxic and often result in drug resistance. Telomerase, a cellular reverse transcriptase that maintains the ends of chromosomes (telomeres), is activated in the vast majority of breast cancers (over 90% of breast carcinomas) but not in normal adjacent tissues. Telomerase is thus an attractive target for both diagnosis and therapy because of its distinct pattern of expression. We address the use of telomerase in the diagnostics of breast pathology, as well as the use of telomerase inhibitors in the treatment and prevention of breast cancer

Invariance principles for non-uniform random mappings and trees

In the context of uniform random mappings of an n-element set to itself, Aldous and Pitman (1994) established a functional invariance principle, showing that many n!1 limit distributions can be described as distributions of suitable functions of reflecting Brownian bridge. To study non-uniform cases, in this paper we formulate a sampling invariance principle in terms of iterates of a fixed number of random elements. We show that the sampling invariance principle implies many, but not all, of the distributional limits implied by the functional invariance principle. We give direct verifications of the sampling invariance principle in two successive generalizations of the uniform case, to p-mappings (where elements are mapped to i.i.d. non-uniform elements) and P-mappings (where elements are mapped according to a Markov matrix). We compare with parallel results in the simpler setting of random trees

Diagnostic and prognostic performance of the ratio between high-sensitivity cardiac troponin I and troponin T in patients with chest pain

10.1371/journal.pone.0276645PLoS ONE1711-Nove0276645