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

Brain Weight and Life-Span in Primate Species

In haplorhine primates (tarsiers, monkeys, apes, and humans), there is a significant correlation between brain weight and maximum life-span when the effect of body size is removed. There is also a significant correlation in haplorhine primates between brain weight and female age at first reproduction. For strepsirhine primates (lorises and lemurs), there are no significant correlations between brain weight and either life-span or female reproductive age when the effect of body size is removed. This lack of correlation in strepsirhine primates may be related to the fact that these primates are nocturnal and/or natives of the island of Madagascar, both of which conditions may reduce competition for resources and predation pressure. These findings suggest that in haplorhine primates the genetic systems controlling brain growth are linked to the systems governing the life cycle so that species with longer cycles have larger brains. When the effect of body weight is removed, leaf-eating haplorhines have significantly smaller brains and shorter lives than haplorhines with other diets. Harem-living haplorhines also have significantly smaller brains and shorter life-spans than troop-living haplorhines when the effect of body weight is removed. We also sought to test the rate-of-living hypothesis by determining whether primates with basal metabolic rates that are higher than would be expected for their body size have shorter maximum life-spans than would be expected for their body size. Metabolic rate is not correlated with life-span or female age at first reproduction when the effect of body size is removed

Identifying evolutionary trees and substitution parameters for the general Markov model with invariable sites

The general Markov plus invariable sites (GM+I) model of biological sequence evolution is a two-class model in which an unknown proportion of sites are not allowed to change, while the remainder undergo substitutions according to a Markov process on a tree. For statistical use it is important to know if the model is identifiable; can both the tree topology and the numerical parameters be determined from a joint distribution describing sequences only at the leaves of the tree? We establish that for generic parameters both the tree and all numerical parameter values can be recovered, up to clearly understood issues of `label swapping.' The method of analysis is algebraic, using phylogenetic invariants to study the variety defined by the model. Simple rational formulas, expressed in terms of determinantal ratios, are found for recovering numerical parameters describing the invariable sites

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

Tropical Geometry of Statistical Models

This paper presents a unified mathematical framework for inference in graphical models, building on the observation that graphical models are algebraic varieties. From this geometric viewpoint, observations generated from a model are coordinates of a point in the variety, and the sum-product algorithm is an efficient tool for evaluating specific coordinates. The question addressed here is how the solutions to various inference problems depend on the model parameters. The proposed answer is expressed in terms of tropical algebraic geometry. A key role is played by the Newton polytope of a statistical model. Our results are applied to the hidden Markov model and to the general Markov model on a binary tree.Comment: 14 pages, 3 figures. Major revision. Applications now in companion paper, "Parametric Inference for Biological Sequence Analysis

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