Polyhedral computational geometry for averaging metric phylogenetic trees

This paper investigates the computational geometry relevant to calculations of the Frechet mean and variance for probability distributions on the phylogenetic tree space of Billera, Holmes and Vogtmann, using the theory of probability measures on spaces of nonpositive curvature developed by Sturm. We show that the combinatorics of geodesics with a specified fixed endpoint in tree space are determined by the location of the varying endpoint in a certain polyhedral subdivision of tree space. The variance function associated to a finite subset of tree space has a fixed $C^\infty$ algebraic formula within each cell of the corresponding subdivision, and is continuously differentiable in the interior of each orthant of tree space. We use this subdivision to establish two iterative methods for producing sequences that converge to the Frechet mean: one based on Sturm's Law of Large Numbers, and another based on descent algorithms for finding optima of smooth functions on convex polyhedra. We present properties and biological applications of Frechet means and extend our main results to more general globally nonpositively curved spaces composed of Euclidean orthants.Comment: 43 pages, 6 figures; v2: fixed typos, shortened Sections 1 and 5, added counter example for polyhedrality of vistal subdivision in general CAT(0) cubical complexes; v1: 43 pages, 5 figure

Early voice recordings of Japanese storytelling

This paper will use one of the 1903 recordings to articulate some of the unique characteristics of Japan's professional storytelling tradition as it existed during the Meiji period. First, I will sketch the background leading up to the ninjobanashi boom of the 1880s and 1890s. Then, after describing the quirks of fate whereby the rare recordings were made, I will present a transcription and analysis of one ninjobanashi from the series, illustrating some of the oral components typical of the genre. In the process I hope to give readers unfamiliar with the Japanese oral tradition a taste of the art form as it existed during its Golden Age approximately a century ago.Not

Sample preparation for nanoanalytical electron microscopy using the FIB lift-out method and low energy ion milling

Thinning specimens to electron transparency for electron microscopy analysis can be done by conventional (2 - 4 kV) argon ion milling or focused ion beam (FIB) lift-out techniques. Both these methods tend to leave ''mottling'' visible on thin specimen areas, and this is believed to be surface damage caused by ion implantation and amorphisation. A low energy (250 - 500 V) Argon ion polish has been shown to greatly improve specimen quality for crystalline silicon samples. Here we investigate the preparation of technologically important materials for nanoanalysis using conventional and lift-out methods followed by a low energy polish in a GentleMill™ low energy ion mill. We use a low energy, low angle (6 - 8°) ion beam to remove the surface damage from previous processing steps. We assess this method for the preparation of technologically important materials, such as steel, silicon and GaAs. For these materials the ability to create specimens from specific sites, and to be able to image and analyse these specimens with the full resolution and sensitivity of the STEM, allows a significant increase of the power and flexibility of nanoanalytical electron microscopy

Biological inventory of the Southern Nevada Water Project, second stage

The present report is a biological inventory of the Southern Nevada Water Project, Second Stage. The boundaries of the project encompass sections of North Las Vegas, Las Vegas, East Las Vegas and areas along Las Vegas Wash extending to its drainage point in Las Vegas Bay in Lake Mead. Therefore, it encompasses a wide array of ecological situations and landscapes ranging from essentially natural to various stages of urban development. This biological inventory presents basic ecological classifications, descriptions of vegetation, lists of vascular plants and vertebrates known to occur in the area. Each major group, i.e., plants, fish, amphibians, reptiles, birds and mammals are characterized ecologically by biotic community. Basic life history data are given for all species of vertebrates found on the project area. Species of special status such as threatened, endangered, protected or of game status are further discussed

Constructing Elliptic Curves over Q(T)\mathbb{Q}(T) with Moderate Rank

We give several new constructions for moderate rank elliptic curves over $\mathbb{Q}(T)$. In particular we construct infinitely many rational elliptic surfaces (not in Weierstrass form) of rank 6 over $\mathbb{Q}$ using polynomials of degree two in $T$. While our method generates linearly independent points, we are able to show the rank is exactly 6 \emph{without} having to verify the points are independent. The method generalizes; however, the higher rank surfaces are not rational, and we need to check that the constructed points are linearly independent.Comment: 11 page