Related papers: The Bayesian `star paradox' persists for long fini…
Phylogenetic networks extend phylogenetic trees to allow for modeling reticulate evolutionary processes such as hybridization. They take the shape of a rooted, directed, acyclic graph, and when parameterized with evolutionary parameters,…
This paper gives a condensed review of the history of solutions to the Euler-Poisson equations modeling equilibrium states of rotating stars and galaxies, leading to a recent result of Walter Strauss and the author. This result constructs a…
Massive stars are able to pursue their evolution through the whole sequence of burning phases. They are born hot and luminous, and live a short life before exploding as a supernova or collapsing directly into a black hole. They have a…
In this chapter I give an overall description of the structure and evolution of stars of different masses, and review the main ingredients included in state-of-the-art calculations aiming at reproducing observational features. I give…
Biologists have long sought a way to explain how statistical properties of genetic sequences emerged and are maintained through evolution. On the one hand, non-random structures at different scales indicate a complex genome organisation. On…
The evolution of aligned DNA sequence sites is generally modeled by a Markov process operating along the edges of a phylogenetic tree. It is well known that the probability distribution on the site patterns at the tips of the tree…
Stellar multiplicity is an ubiquitous outcome of the star formation process. Characterizing the frequency and main characteristics of multiple systems and their dependencies on primary mass and environment is therefore a powerful tool to…
Multiple systems play an important role in the evolution of star clusters. First we discuss several formation mechanisms which depend on the presence of binaries, either primordial or of dynamical origin. Hierarchical configurations are…
A family of sets is intersecting if every pair of its sets intersect. A star is a family with some element (a center) in each of its sets. The classical 1961 result of Erd\H{o}s, Ko, and Rado states that every intersecting family of r-sets…
Suppose we have a set $X$ consisting of $n$ taxa and we are given information from $k$ loci from which to construct a phylogeny for $X$. Each locus offers information for only a fraction of the taxa. The question is whether this data…
The formation of massive stars is an outstanding problem in stellar evolution. However, it is expected that they are (predominantly) born in heirarchical environments within massive young clusters, which in turn are located within larger…
We derive ensembles of decision trees through a nonparametric Bayesian model, allowing us to view random forests as samples from a posterior distribution. This insight provides large gains in interpretability, and motivates a class of…
Generalised Probabilistic Theories (GPTs) provide a unifying framework encompassing classical theories, quantum theories, as well as hypothetical alternatives. We investigate the problem of extending a system with a finite set of…
Fry (1996) showed that galaxy bias has the tendency to evolve towards unity, i.e. in the long run, the galaxy distribution tends to trace that of matter. Generalizing slightly Fry's reasoning, we show that his conclusion remains valid in…
In 1957, Lindley published "A statistical paradox" in Biometrika, revealing a fundamental conflict between frequentist and Bayesian inference as sample size approaches infinity. We present a new paradox of a different kind: a conflict…
The realization that most stars form in clusters, raises the question of whether star/planet formation are influenced by the cluster environment. The stellar density in the most prevalent clusters is the key factor here. Whether dominant…
Phylogenetic mixture models are statistical models of character evolution allowing for heterogeneity. Each of the classes in some unknown partition of the characters may evolve by different processes, or even along different trees. The…
Massive stars play a major role in the evolution of their host galaxies, and serve as important probes of the distant Universe. It has been established that the majority of massive stars reside in close binaries and will interact with their…
Many classes of phylogenetic networks have been proposed in the literature. A feature of several of these classes is that if one restricts a network in the class to a subset of its leaves, then the resulting network may no longer lie within…
The present paper reviews massive star (initial mass smaller than 120 M0) and very massive star (initial mass larger than 120 M0) evolution. I will focus on evolutionary facts and questions that may critically affect predictions of…