An Internet Heartbeat

Obtaining sound inferences over remote networks via active or passive measurements is difficult. Active measurement campaigns face challenges of load, coverage, and visibility. Passive measurements require a privileged vantage point. Even networks under our own control too often remain poorly understood and hard to diagnose. As a step toward the democratization of Internet measurement, we consider the inferential power possible were the network to include a constant and predictable stream of dedicated lightweight measurement traffic. We posit an Internet "heartbeat," which nodes periodically send to random destinations, and show how aggregating heartbeats facilitates introspection into parts of the network that are today generally obtuse. We explore the design space of an Internet heartbeat, potential use cases, incentives, and paths to deployment

Breaking the chain

We consider the motion of a Brownian particle in $\mathbb{R}$, moving between a particle fixed at the origin and another moving deterministically away at slow speed $\epsilon>0$. The middle particle interacts with its neighbours via a potential of finite range $b>0$, with a unique minimum at $a>0$, where $b<2a$. We say that the chain of particles breaks on the left- or right-hand side when the middle particle is greater than a distance $b$ from its left or right neighbour, respectively. We study the asymptotic location of the first break of the chain in the limit of small noise, in the case where $\epsilon = \epsilon(\sigma)$ and $\sigma>0$ is the noise intensity.Comment: 13 pages, 2 figures. v2: Corrected a mistake in proof of second part of main theore

The identifiability of tree topology for phylogenetic models, including covarion and mixture models

For a model of molecular evolution to be useful for phylogenetic inference, the topology of evolutionary trees must be identifiable. That is, from a joint distribution the model predicts, it must be possible to recover the tree parameter. We establish tree identifiability for a number of phylogenetic models, including a covarion model and a variety of mixture models with a limited number of classes. The proof is based on the introduction of a more general model, allowing more states at internal nodes of the tree than at leaves, and the study of the algebraic variety formed by the joint distributions to which it gives rise. Tree identifiability is first established for this general model through the use of certain phylogenetic invariants.Comment: 20 pages, 1 figur