Squarepants in a Tree: Sum of Subtree Clustering and Hyperbolic Pants Decomposition

We provide efficient constant factor approximation algorithms for the problems of finding a hierarchical clustering of a point set in any metric space, minimizing the sum of minimimum spanning tree lengths within each cluster, and in the hyperbolic or Euclidean planes, minimizing the sum of cluster perimeters. Our algorithms for the hyperbolic and Euclidean planes can also be used to provide a pants decomposition, that is, a set of disjoint simple closed curves partitioning the plane minus the input points into subsets with exactly three boundary components, with approximately minimum total length. In the Euclidean case, these curves are squares; in the hyperbolic case, they combine our Euclidean square pants decomposition with our tree clustering method for general metric spaces.Comment: 22 pages, 14 figures. This version replaces the proof of what is now Lemma 5.2, as the previous proof was erroneou

Characterisation of a putative glutamate 5‐kinase from <i>Leishmania donovani</i>

Previous metabolic studies have demonstrated that leishmania parasites are able to synthesise proline from glutamic acid and threonine from aspartic acid. The first committed step in both biosynthetic pathways involves an amino acid kinase, either a glutamate 5‐kinase (G5K; EC2.7.2.11) or an aspartokinase (EC2.7.2.4). Bioinformatic analysis of multiple leishmania genomes identifies a single amino acid‐kinase gene (LdBPK 262740.1) variously annotated as either a putative glutamate or aspartate kinase. To establish the catalytic function of this Leishmania donovani gene product, we have determined the physical and kinetic properties of the recombinant enzyme purified from Escherichia coli. The findings indicate that the enzyme is a bona fide G5K with no activity as an aspartokinase. Tetrameric G5K displays kinetic behaviour similar to its bacterial orthologues and is allosterically regulated by proline, the end product of the pathway. The structure‐activity relationships of proline analogues as inhibitors are broadly similar to the bacterial enzyme. However, unlike G5K from E. coli, leishmania G5K lacks a C‐terminal PUA (pseudouridine synthase and archaeosine transglycosylase) domain and does not undergo higher oligomerisation in the presence of proline. Gene replacement studies are suggestive, but not conclusive that G5K is essential

Widespread association between the ericoid mycorrhizal fungus Rhizoscyphus ericae and a leafy liverwort in the maritime and sub-Antarctic

A recent study identified a fungal isolate from the Antarctic leafy liverwort Cephaloziella varians as the ericoid mycorrhizal associate Rhizoscyphus ericae. However, nothing is known about the wider Antarctic distribution of R. ericae in C. varians, and inoculation experiments confirming the ability of the fungus to form coils in the liverwort are lacking. Using direct isolation and baiting with Vaccinium macrocarpon seedlings, fungi were isolated from C. varians sampled from eight sites across a 1875-km transect through sub- and maritime Antarctica. The ability of an isolate to form coils in aseptically grown C. varians was also tested. Fungi with 98–99% sequence identity to R. ericae internal transcribed spacer (ITS) region and partial large subunit ribosomal (r)DNA sequences were frequently isolated from C. varians at all sites sampled. The EF4/Fung5 primer set did not amplify small subunit rDNA from three of five R. ericae isolates, probably accounting for the reported absence of the fungus from C. varians in a previous study. Rhizoscyphus ericae was found to colonize aseptically-grown C. varians intracellularly, forming hyphal coils. This study shows that the association between R. ericae and C. varians is apparently widespread in Antarctica, and confirms that R. ericae is at least in part responsible for the formation of the coils observed in rhizoids of field-collected C. varians

Stable phantom-divide crossing in two scalar models with matter

We construct cosmological models with two scalar fields, which has the structure as in the ghost condensation model or k-essence model. The models can describe the stable phantom crossing, which should be contrasted with one scalar tensor models, where the infinite instability occurs at the crossing the phantom divide. We give a general formulation of the reconstruction in terms of the e-foldings N by including the matter although in the previous two scalar models, which are extensions of the scalar tensor model, it was difficult to give a formulation of the reconstruction when we include matters. In the formulation of the reconstruction, we start with a model with some arbitrary functions, and find the functions which generates the history in the expansion of the universe. We also give general arguments for the stabilities of the models and the reconstructed solution. The viability of a model is also investigated by comparing the observational data.Comment: 12 pages, 1 figur

A eubacterial origin for the human tRNA nucleotidyltransferase?

tRNA CCA-termini are generated and maintained by tRNA nucleotidyltransferases. Together with poly(A) polymerases and other enzymes they belong to the nucleotidyltransferase superfamily. However, sequence alignments within this family do not allow to distinguish between CCA-adding enzymes and poly(A) polymerases. Furthermore, due to the lack of sequence information about animal CCA-adding enzymes, identification of corresponding animal genes was not possible so far. Therefore, we looked for the human homolog using the baker's yeast tRNA nucleotidyltransferase as a query sequence in a BLAST search. This revealed that the human gene transcript CGI-47, (\#AF151805) deposited in GenBank is likely to encode such an enzyme. To identify the nature of this protein, the cDNA of the transcript was cloned and the recombinant protein biochemically characterized, indicating that CGI-47 encodes a bona fide CCA-adding enzyme and not a poly(A) polymerase. This confirmed animal CCA-adding enzyme allowed us to identify putative homologs from other animals. Calculation of a neighbor-joining tree, using an alignment of several CCA-adding enzymes, revealed that the animal enzymes resemble more eubacterial ones than eukaryotic plant and fungal tRNA nucleotidyltransferases, suggesting that the animal nuclear cca genes might have been derived from the endosymbiotic progenitor of mitochondria and are therefore of eubacterial origin

Thiophaeococcus mangrovi gen. nov., sp. nov., a photosynthetic marine gammaproteobacterium isolated from Bhitarkanika mangrove forest, India

A coccoid, phototrophic purple sulfur bacterium was isolated in pure culture from a mud sample collected from brackish water in the Bhitarkanika mangrove forest of Orissa, India, in a medium containing 2 % NaCl (w/v). This bacterium, strain JA304T, was Gram-negative and had a requirement for NaCl. Intracellular photosynthetic membranes were of the vesicular type. The colour of the phototrophically grown culture was saddle-brown. Bacteriochlorophyll a and the carotenoid lycopene were present as photosynthetic pigments. Strain JA304T was able to grow photolithoautotrophically and could photoassimilate a number of organic substrates. Yeast extract was required for growth of strain JA304T. The DNA G+C content was 68.1–68.9 mol%. 16S rRNA gene sequence comparisons indicate that the isolate represents a member of the Chromatiaceae within the class Gammaproteobacteria. According to sequence comparison data, strain JA304T is positioned distinctly outside the group formed by the four genera Thiocystis, Chromatium, Allochromatium and Thermochromatium, with only 86.7–91.0 % sequence similarity. Distinct morphological, physiological and genotypic differences from these previously described taxa support the classification of this isolate as a representative of a novel species in a new genus, for which the name Thiophaeococcus mangrovi gen. nov., sp. nov. is proposed. The type strain of Thiophaeococcus mangrovi is JA304T (=JCM 14889T =DSM 19863T). PABA, para-aminobenzoic acid The GenBank/EMBL/DDBJ accession number for the 16S rRNA gene sequence of strain JA304T is AM748925. A phase-contrast micrograph and whole-cell absorption spectrum and an acetone spectrum of extracted pigments of strain JA304T are available as supplementary material with the online version of this paper

Low- and Medium-Dispersion Spectropolarimetry of Nova V475 Sct (Nova Scuti 2003): Discovery of an Asymmetric High-Velocity Wind in a Moderately Fast Nova

We present low-resolution ($R\sim 90$) and medium-resolution ($R\sim 2500$) spectropolarimetry of Nova V475 Sct with the HBS instrument, mounted on the 0.91-m telescope at the Okayama Astrophysical Observatory, and with FOCAS, mounted on the 8.2-m Subaru telescope. We estimated the interstellar polarization toward the nova from the steady continuum polarization components and H$\alpha$ line emission components. After subtracting the interstellar polarization component from the observations, we found that the H$\alpha$ emission seen on 2003 October 7 was clearly polarized. In the polarized flux spectrum, the H$\alpha$ emission had a distinct red wing extending to $\sim +4900$ km s$^{-1}$ and a shoulder around $+3500$ km s$^{-1}$, showing a constant position angle of linear polarization \theta_{\rm *}\simeq 155\arcdeg\pm 15\arcdeg. This suggests that the nova had an asymmetric outflow with a velocity of $v_{\rm wind}\simeq 3500$ km s$^{-1}$ or more, which is six times higher than the expansion velocity of the ionized shell at the same epoch. Such a high-velocity component has not previously been reported for a nova in the `moderately fast' speed class. Our observations suggest the occurrence of violent mass-loss activity in the nova binary system even during the common-envelope phase. The position angle of the polarization in the H$\alpha$ wing is in good agreement with that of the continuum polarization found on 2003 September 26 ($p_{\rm *}\simeq 0.4$--0.6 %), which disappeared within the following 2 d. The uniformity of the PA between the continuum polarization and the wing polarization on October 7 suggests that the axis of the circumstellar asymmetry remained nearly constant during the period of our observations.Comment: 27 pages, 7 figures, accepted for publication in A

Sequence alignment, mutual information, and dissimilarity measures for constructing phylogenies

Existing sequence alignment algorithms use heuristic scoring schemes which cannot be used as objective distance metrics. Therefore one relies on measures like the p- or log-det distances, or makes explicit, and often simplistic, assumptions about sequence evolution. Information theory provides an alternative, in the form of mutual information (MI) which is, in principle, an objective and model independent similarity measure. MI can be estimated by concatenating and zipping sequences, yielding thereby the "normalized compression distance". So far this has produced promising results, but with uncontrolled errors. We describe a simple approach to get robust estimates of MI from global pairwise alignments. Using standard alignment algorithms, this gives for animal mitochondrial DNA estimates that are strikingly close to estimates obtained from the alignment free methods mentioned above. Our main result uses algorithmic (Kolmogorov) information theory, but we show that similar results can also be obtained from Shannon theory. Due to the fact that it is not additive, normalized compression distance is not an optimal metric for phylogenetics, but we propose a simple modification that overcomes the issue of additivity. We test several versions of our MI based distance measures on a large number of randomly chosen quartets and demonstrate that they all perform better than traditional measures like the Kimura or log-det (resp. paralinear) distances. Even a simplified version based on single letter Shannon entropies, which can be easily incorporated in existing software packages, gave superior results throughout the entire animal kingdom. But we see the main virtue of our approach in a more general way. For example, it can also help to judge the relative merits of different alignment algorithms, by estimating the significance of specific alignments.Comment: 19 pages + 16 pages of supplementary materia

Minimum triplet covers of binary phylogenetic X-trees

Trees with labelled leaves and with all other vertices of degree three play an important role in systematic biology and other areas of classification. A classical combinatorial result ensures that such trees can be uniquely reconstructed from the distances between the leaves (when the edges are given any strictly positive lengths). Moreover, a linear number of these pairwise distance values suffices to determine both the tree and its edge lengths. A natural set of pairs of leaves is provided by any `triplet cover' of the tree (based on the fact that each non-leaf vertex is the median vertex of three leaves). In this paper we describe a number of new results concerning triplet covers of minimum size. In particular, we characterize such covers in terms of an associated graph being a 2-tree. Also, we show that minimum triplet covers are `shellable' and thereby provide a set of pairs for which the inter-leaf distance values will uniquely determine the underlying tree and its associated branch lengths

The unification of inflation and late-time acceleration in the frame of kk-essence

By using the formulation of the reconstruction, we explicitly construct models of $k$-essence, which unify the inflation in the early universe and the late accelerating expansion of the present universe by a single scalar field. Due to the higher derivative terms, the solution describing the unification can be stable in the space of solutions, which makes the restriction for the initial condition relaxed. The higher derivative terms also eliminate tachyon. Therefore we can construct a model describing the time development, which cannot be realized by a usual inflaton or quintessence models of the canonical scalar field due to the instability or the existence of tachyon. We also propose a mechanism of the reheating by the quantum effects coming from the variation of the energy density of the scalar field.Comment: LaTeX, 13 pages, 10 figure