Were molecular data available for extinct taxa, questions regarding the origins of many groups could be settled in short order. As this is not the case, various strategies have been proposed to combine paleontological and neontological data sets. The use of fossil dates as node age calibrations for divergence time estimation from molecular phylogenies is commonplace. In addition, simulations su...

Background: The spatial genetic structuring of natural populations is mostly studied using neutral markers. Recently, morphometric methods have also been used to to study genetic divergence through adaptive processes. These methods provide better insights into the conservation needs of focal populations. However, all morphometric methods assume that samples obtained in different localities repr...

We derive sharp thresholds for exact recovery of communities in a weighted stochastic block model, where observations are collected in the form of a weighted adjacency matrix, and the weight of each edge is generated independently from a distribution determined by the community membership of its endpoints. Our main result, characterizing the precise boundary between success and failure of maxim...

Aris-Brosou, S., and Z. Yang. 2002. Effects of models of rate evolution on estimation of divergence dates with special reference to the metazoan 18S ribosomal RNA phylogeny. Syst. Biol. 51:703–714. Aris-Brosou, S., and Z. Yang. 2003. Bayesian models of episodic evolution support a late precambrian explosive diversification of the metazoa. Mol. Biol. Evol. 20:1947–1954. Ayala, F. J., A. Rzhetsky...

Adaptive systems rely on recursive estimation of a firmly bounded complexity. As a rule, they have to use an approximation of the posterior probability density function (pdf), which comprises unreduced information about the estimated parameter. In recursive setting, the latest approximate pdf is updated using the learnt system model and the newest data and then approximated. The fact that appro...

The theory developed by Takahata and colleagues for estimating the effective population size of ancestral species using homologous sequences from closely related extant species was extended to take account of variation of evolutionary rates among loci. Nuclear sequence data related to the evolution of modern humans were reanalysed and computer simulations were performed to examine the effect of...

We obtain a collection of multilinear Littlewood-Paley estimates, which we then apply to two problems in partial differential equations. The first problem is the estimation of the square root of an elliptic operator in divergence form, and the second is the estimation of solutions to the Cauchy problem for nondivergence-form parabolic equations.

Estimation of divergence times from sequence data has become increasingly feasible in recent years. Conflicts between fossil evidence and molecular dates have sparked the development of new methods for inferring divergence times, further encouraging these efforts. In this paper, available methods for estimating divergence times are reviewed, especially those geared toward handling the widesprea...

We develop and analyze an algorithm for nonparametric estimation of divergence functionals and the density ratio of two probability distributions. Our method is based on a variational characterization of f -divergences, which turns the estimation into a penalized convex risk minimization problem. We present a derivation of our kernel-based estimation algorithm and an analysis of convergence rat...