On the variational distance of two trees

A widely studied model for generating sequences is to ``evolve'' them on a tree according to a symmetric Markov process. We prove that model trees tend to be maximally ``far apart'' in terms of variational distance.Comment: Published at http://dx.doi.org/10.1214/105051606000000196 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Phylogenetic mixtures on a single tree can mimic a tree of another topology

Phylogenetic mixtures model the inhomogeneous molecular evolution commonly observed in data. The performance of phylogenetic reconstruction methods where the underlying data is generated by a mixture model has stimulated considerable recent debate. Much of the controversy stems from simulations of mixture model data on a given tree topology for which reconstruction algorithms output a tree of a different topology; these findings were held up to show the shortcomings of particular tree reconstruction methods. In so doing, the underlying assumption was that mixture model data on one topology can be distinguished from data evolved on an unmixed tree of another topology given enough data and the ``correct'' method. Here we show that this assumption can be false. For biologists our results imply that, for example, the combined data from two genes whose phylogenetic trees differ only in terms of branch lengths can perfectly fit a tree of a different topology

Dynamics of a birth-death process based on combinatorial innovation

A feature of human creativity is the ability to take a subset of existing items (e.g. objects, ideas, or techniques) and combine them in various ways to give rise to new items, which, in turn, fuel further growth. Occasionally, some of these items may also disappear (extinction). We model this process by a simple stochastic birth--death model, with non-linear combinatorial terms in the growth coefficients to capture the propensity of subsets of items to give rise to new items. In its simplest form, this model involves just two parameters $(P, \alpha)$. This process exhibits a characteristic 'hockey-stick' behaviour: a long period of relatively little growth followed by a relatively sudden 'explosive' increase. We provide exact expressions for the mean and variance of this time to explosion and compare the results with simulations. We then generalise our results to allow for more general parameter assignments, and consider possible applications to data involving human productivity and creativity.Comment: 21 pages, 4 figure

A wireless ultrasonic NDT sensor system

Ultrasonic condition monitoring technologies have been traditionally utilized in industrial and construction environments where structural integrity is of concern. Such techniques include active systems with either single or multiple transmit-receiver combinations used to obtain defect positioning and magnitude. Active sensors are implemented in two ways; in a thickness operation mode, or as an area-mapping tool operating over longer distances. In addition, passive ultrasonic receivers can be employed to detect and record acoustic emission activity. Existing equipment requires cabling for such systems leading to expensive, complicated installations. This work describes the development and operation of a system that combines these existing ultrasonic technologies with modern wireless techniques within a miniaturized, battery-operated design. A completely wireless sensor has been designed that can independently record and analyze ultrasonic signals. Integrated into the sensor are custom ultrasonic transducers, associated analogue drive and receive electronics, and a Texas Instruments Digital Signal Processor (DSP) used to both control the system and implement the signal processing routines. BlueTooth wireless communication is used for connection to a central observation station, from where network operation can be controlled. Extending battery life is of prime importance and the device employs several strategies to do this. Low voltage transducer excitation suffers from poor signal-to-noise ratios, which can be enhanced by signal processing routines implemented on the DSP. Routines investigated include averaging, digital filtering and pulse compression