Principal components analysis in the space of phylogenetic trees

Phylogenetic analysis of DNA or other data commonly gives rise to a collection or sample of inferred evolutionary trees. Principal Components Analysis (PCA) cannot be applied directly to collections of trees since the space of evolutionary trees on a fixed set of taxa is not a vector space. This paper describes a novel geometrical approach to PCA in tree-space that constructs the first principal path in an analogous way to standard linear Euclidean PCA. Given a data set of phylogenetic trees, a geodesic principal path is sought that maximizes the variance of the data under a form of projection onto the path. Due to the high dimensionality of tree-space and the nonlinear nature of this problem, the computational complexity is potentially very high, so approximate optimization algorithms are used to search for the optimal path. Principal paths identified in this way reveal and quantify the main sources of variation in the original collection of trees in terms of both topology and branch lengths. The approach is illustrated by application to simulated sets of trees and to a set of gene trees from metazoan (animal) species.Comment: Published in at http://dx.doi.org/10.1214/11-AOS915 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

An L^2-Index Theorem for Dirac Operators on S^1 * R^3

An expression is found for the $L^2$-index of a Dirac operator coupled to a connection on a $U_n$ vector bundle over $S^1\times{\mathbb R}^3$. Boundary conditions for the connection are given which ensure the coupled Dirac operator is Fredholm. Callias' index theorem is used to calculate the index when the connection is independent of the coordinate on $S^1$. An excision theorem due to Gromov, Lawson, and Anghel reduces the index theorem to this special case. The index formula can be expressed using the adiabatic limit of the $\eta$-invariant of a Dirac operator canonically associated to the boundary. An application of the theorem is to count the zero modes of the Dirac operator in the background of a caloron (periodic instanton).Comment: 14 pages, Latex, to appear in the Journal of Functional Analysi

Foundations of the Wald Space for Phylogenetic Trees

Evolutionary relationships between species are represented by phylogenetic trees, but these relationships are subject to uncertainty due to the random nature of evolution. A geometry for the space of phylogenetic trees is necessary in order to properly quantify this uncertainty during the statistical analysis of collections of possible evolutionary trees inferred from biological data. Recently, the wald space has been introduced: a length space for trees which is a certain subset of the manifold of symmetric positive definite matrices. In this work, the wald space is introduced formally and its topology and structure is studied in detail. In particular, we show that wald space has the topology of a disjoint union of open cubes, it is contractible, and by careful characterization of cube boundaries, we demonstrate that wald space is a Whitney stratified space of type (A). Imposing the metric induced by the affine invariant metric on symmetric positive definite matrices, we prove that wald space is a geodesic Riemann stratified space. A new numerical method is proposed and investigated for construction of geodesics, computation of Fr\'echet means and calculation of curvature in wald space. This work is intended to serve as a mathematical foundation for further geometric and statistical research on this space.Comment: 42 pages, 15 figure

Types of Stickiness in BHV Phylogenetic Tree Spaces and Their Degree

It has been observed that the sample mean of certain probability distributions in Billera-Holmes-Vogtmann (BHV) phylogenetic spaces is confined to a lower-dimensional subspace for large enough sample size. This non-standard behavior has been called stickiness and poses difficulties in statistical applications when comparing samples of sticky distributions. We extend previous results on stickiness to show the equivalence of this sampling behavior to topological conditions in the special case of BHV spaces. Furthermore, we propose to alleviate statistical comparision of sticky distributions by including the directional derivatives of the Fr\'echet function: the degree of stickiness.Comment: 8 Pages, 1 Figure, conference submission to GSI 202

Virology Experts in the Boundary Zone Between Science, Policy and the Public: A Biographical Analysis

This article aims to open up the biographical black box of three experts working in the boundary zone between science, policy and public debate. A biographical-narrative approach is used to analyse the roles played by the virologists Albert Osterhaus, Roel Coutinho and Jaap Goudsmit in policy and public debate. These figures were among the few leading virologists visibly active in the Netherlands during the revival of infectious diseases in the 1980s. Osterhaus and Coutinho in particular are still the key figures today, as demonstrated during the outbreak of novel influenza A (H1N1). This article studies the various political and communicative challenges and dilemmas encountered by these three virologists, and discusses the way in which, strategically or not, they handled those challenges and dilemmas during the various stages of the field’s recent history. Important in this respect is their pursuit of a public role that is both effective and credible. We will conclude with a reflection on the H1N1 pandemic, and the historical and biographical ties between emerging governance arrangements and the experts involved in the development of such arrangements

CSF1R inhibitor JNJ-40346527 attenuates microglial proliferation and neurodegeneration in P301S mice

Neuroinflammation and microglial activation are significant processes in Alzheimer’s disease pathology. Recent genome-wide association studies have highlighted multiple immune-related genes in association with Alzheimer’s disease, and experimental data have demonstrated microglial proliferation as a significant component of the neuropathology. In this study, we tested the efficacy of the selective CSF1R inhibitor JNJ-40346527 (JNJ-527) in the P301S mouse tauopathy model. We first demonstrated the anti-proliferative effects of JNJ-527 on microglia in the ME7 prion model, and its impact on the inflammatory profile, and provided potential CNS biomarkers for clinical investigation with the compound, including pharmacokinetic/pharmacodynamics and efficacy assessment by TSPO autoradiography and CSF proteomics. Then, we showed for the first time that blockade of microglial proliferation and modification of microglial phenotype leads to an attenuation of tau-induced neurodegeneration and results in functional improvement in P301S mice. Overall, this work strongly supports the potential for inhibition of CSF1R as a target for the treatment of Alzheimer’s disease and other tau-mediated neurodegenerative diseases