The branching pattern of major groups of land plants inferred from parsimony analysis of ribosomal RNA sequences

The parsimony and bootstrap branching pattern of major groups of land plants derived from relevant 5S rRNA sequence trees have been discussed in the light of paleobotanical and morphological evidences. Although 5S rRNA sequence information is not useful for dileneating angiosperm relationships, it does capture the earlier phase of land plant evolution. The consensus branching pattern indicates an ancient split of bryophytes and vascular plants from the charophycean algal stem. Among the bryophytes, Marchantia and Lophocolea appear to be phylogenetically close and together with Plagiomnium form a monophyletic group. Lycopodium and Psilotum arose early in vascular land plant evolution, independent of fem-sphenopsid branch. Gymnosperms are polyphyletic; conifers, Gnetales and cycads emerge in that order with ginkgo joining Cycas. Among the conifers, Metasequoia, Juniperus and Taxus emerge as a branch independent of Pinus which joins Gnetales. The phylogeny derived from the available ss-RNA sequences shows that angiosperms are monophyletic with monocots and dicots diverging from a common stem. The nucleotide replacements during angiosperm descent from the gymnosperm ancestor which presumably arose around 370 my ago indicates that monocots and dicots diverged around 180 my ago, which is compatible with the reported divergence estimate of around 200 my ago deduced from chloroplast DNA sequences

Stochastic Frank-Wolfe Methods for Nonconvex Optimization

We study Frank-Wolfe methods for nonconvex stochastic and finite-sum optimization problems. Frank-Wolfe methods (in the convex case) have gained tremendous recent interest in machine learning and optimization communities due to their projection-free property and their ability to exploit structured constraints. However, our understanding of these algorithms in the nonconvex setting is fairly limited. In this paper, we propose nonconvex stochastic Frank-Wolfe methods and analyze their convergence properties. For objective functions that decompose into a finite-sum, we leverage ideas from variance reduction techniques for convex optimization to obtain new variance reduced nonconvex Frank-Wolfe methods that have provably faster convergence than the classical Frank-Wolfe method. Finally, we show that the faster convergence rates of our variance reduced methods also translate into improved convergence rates for the stochastic setting

On the High-dimensional Power of Linear-time Kernel Two-Sample Testing under Mean-difference Alternatives

Nonparametric two sample testing deals with the question of consistently deciding if two distributions are different, given samples from both, without making any parametric assumptions about the form of the distributions. The current literature is split into two kinds of tests - those which are consistent without any assumptions about how the distributions may differ (\textit{general} alternatives), and those which are designed to specifically test easier alternatives, like a difference in means (\textit{mean-shift} alternatives). The main contribution of this paper is to explicitly characterize the power of a popular nonparametric two sample test, designed for general alternatives, under a mean-shift alternative in the high-dimensional setting. Specifically, we explicitly derive the power of the linear-time Maximum Mean Discrepancy statistic using the Gaussian kernel, where the dimension and sample size can both tend to infinity at any rate, and the two distributions differ in their means. As a corollary, we find that if the signal-to-noise ratio is held constant, then the test's power goes to one if the number of samples increases faster than the dimension increases. This is the first explicit power derivation for a general nonparametric test in the high-dimensional setting, and also the first analysis of how tests designed for general alternatives perform when faced with easier ones.Comment: 25 pages, 5 figure

Possible detection of singly-ionized oxygen in the Type Ia SN 2010kg

We present direct spectroscopic modeling of 11 high-S/N observed spectra of the Type Ia SN 2010kg, taken between -10 and +5 days with respect to B-maximum. The synthetic spectra, calculated with the SYN++ code, span the range between 4100 and 8500 \r{A}. Our results are in good agreement with previous findings for other Type Ia SNe. Most of the spectral features are formed at or close to the photosphere, but some ions, like Fe II and Mg II, also form features at ~2000 - 5000 km s$^{-1}$ above the photosphere. The well-known high-velocity features of the Ca II IR-triplet as well as Si II $\lambda$6355 are also detected. The single absorption feature at ~4400 \r{A}, which usually has been identified as due to Si III, is poorly fit with Si III in SN 2010kg. We find that the fit can be improved by assuming that this feature is due to either C III or O II, located in the outermost part of the ejecta, ~4000 - 5000 km s$^{-1}$ above the photosphere. Since the presence of C III is unlikely, because of the lack of the necessary excitation/ionization conditions in the outer ejecta, we identify this feature as due to O II. The simultaneous presence of O I and O II is in good agreement with the optical depth calculations and the temperature distribution in the ejecta of SN 2010kg. This could be the first identification of singly ionized oxygen in a Type Ia SN atmosphere.Comment: Submitted to MNRA