In this paper, we introduce a subclass of chordal graphs which contains $d$-trees and show that their complement are vertex decomposable and so is shellable and sequentially Cohen-Macaulay.

Fundamental limitations in decentralized control of systems with multivariable zeros are considered. It is shown that arbitrary bandwidth can be obtained with a stable block-diagonal controller, if certain subsystems of the open-loop system fail to have zeros in the right half-plane and a high-frequency condition holds. Implications on control structure design and sequential loop-closuring meth...

We develop a Bayesian Markov chain Monte Carlo (MCMC) algorithm for estimating divergence times using sequentially sampled molecular sequences. This type of data is commonly collected during viral epidemics and is sometimes available from different species in ancient DNA studies. We derive the distribution of ages of nodes in the tree under a birth-death-sequential-sampling (BDSS) model and use...

We introduce a novel methodology for sampling from a sequence of probability distributions of increasing dimension and estimating their normalizing constants. These problems are usually addressed using Sequential Monte Carlo (SMC) methods. The alternative Sequentially Interacting Markov Chain Monte Carlo (SIMCMC) scheme proposed here works by generating interacting non-Markovian sequences which...