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

Testing Observational Techniques with 3D MHD Jets in Clusters

Observations of X-ray cavities formed by powerful jets from AGN in galaxy cluster cores are commonly used to estimate the mechanical luminosity of these sources. We test the reliability of observationally measuring this power with synthetic X-ray observations of 3-D MHD simulations of jets in a galaxy cluster environment. We address the role that factors such as jet intermittency and orientation of the jets on the sky have on the reliability of observational measurements of cavity enthalpy and age. An estimate of the errors in these quantities can be made by directly comparing ``observationally'' derived values with values from the simulations. In our tests, cavity enthalpy, age and mechanical luminosity derived from observations are within a factor of two of the simulation values.Comment: 4 pages, 3 figures; to appear in proceedings of The Monster's Fiery Breath: Feedback in Galaxies, Groups, and Clusters (AIP conference series

Real-World Repetition Estimation by Div, Grad and Curl

We consider the problem of estimating repetition in video, such as performing push-ups, cutting a melon or playing violin. Existing work shows good results under the assumption of static and stationary periodicity. As realistic video is rarely perfectly static and stationary, the often preferred Fourier-based measurements is inapt. Instead, we adopt the wavelet transform to better handle non-static and non-stationary video dynamics. From the flow field and its differentials, we derive three fundamental motion types and three motion continuities of intrinsic periodicity in 3D. On top of this, the 2D perception of 3D periodicity considers two extreme viewpoints. What follows are 18 fundamental cases of recurrent perception in 2D. In practice, to deal with the variety of repetitive appearance, our theory implies measuring time-varying flow and its differentials (gradient, divergence and curl) over segmented foreground motion. For experiments, we introduce the new QUVA Repetition dataset, reflecting reality by including non-static and non-stationary videos. On the task of counting repetitions in video, we obtain favorable results compared to a deep learning alternative

Garnet–monazite rare earth element relationships in sub-solidus metapelites: a case study from Bhutan

A key aim of modern metamorphic geochronology is to constrain precise and accurate rates and timescales of tectonic processes. One promising approach in amphibolite and granulite-facies rocks links the geochronological information recorded in zoned accessory phases such as monazite to the pressure–temperature information recorded in zoned major rock-forming minerals such as garnet. Both phases incorporate rare earth elements (REE) as they crystallize and their equilibrium partitioning behaviour potentially provides a useful way of linking time to temperature. We report REE data from sub-solidus amphibolite-facies metapelites from Bhutan, where overlapping ages, inclusion relationships and Gd/Lu ratios suggest that garnet and monazite co-crystallized. The garnet–monazite REE relationships in these samples show a steeper pattern across the heavy (H)REE than previously reported. The difference between our dataset and the previously reported data may be due to a temperature-dependence on the partition coefficients, disequilibrium in either dataset, differences in monazite chemistry or the presence or absence of a third phase that competed for the available REE during growth. We urge caution against using empirically-derived partition coefficients from natural samples as evidence for, or against, equilibrium of REE-bearing phases until monazite–garnet partitioning behaviour is better constrained

Intention to adopt Cloud-based e-Learning in Nigerian Educational Institutions

Institutions of higher education must utilize innovative information and communication technologies for teaching in Nigeria. Thus, cloud-based e-Learning is essential to curtail educational challenges such as limited infrastructure, funds, and student-to-lecturer ratio. Recently, there has been widespread enthusiasm regarding Cloud computing for e-Learning; adopting and strategically utilizing these technologies remains a significant challenge for higher education institutions. Furthermore, there is a limited understanding of how cloud-based e-learning can transform Nigerian educational establishments. Cloud-based e-Learning systems' technological components have been the subject of numerous study studies, but little is known about how they operate from an organizational perspective. Accordingly, using the Technology-Organization-Environment theory, the goal of this study is to investigate the variables that influence the adoption of cloud-based e-learning. The findings of the research show that relative benefit and competing pressure have a big impact on whether cloud-based e-learning is adopted. However, compatibility, security, and top management commitment do not appear to be significant determinants. These findings will help Nigerian education institutions, the ministry of education, and practitioners to understand the critical factors for adopting this technology for improved education