418 research outputs found
Internal Transcribed Spacer 2 (nu ITS2 rRNA) Sequence-Structure Phylogenetics: Towards an Automated Reconstruction of the Green Algal Tree of Life
L). Some have advocated the use of the nuclear-encoded, internal transcribed spacer two (ITS2) as an alternative to the traditional chloroplast markers. However, the ITS2 is broadly perceived to be insufficiently conserved or to be confounded by introgression or biparental inheritance patterns, precluding its broad use in phylogenetic reconstruction or as a DNA barcode. A growing body of evidence has shown that simultaneous analysis of nucleotide data with secondary structure information can overcome at least some of the limitations of ITS2. The goal of this investigation was to assess the feasibility of an automated, sequence-structure approach for analysis of IT2 data from a large sampling of phylum Chlorophyta.Sequences and secondary structures from 591 chlorophycean, 741 trebouxiophycean and 938 ulvophycean algae, all obtained from the ITS2 Database, were aligned using a sequence structure-specific scoring matrix. Phylogenetic relationships were reconstructed by Profile Neighbor-Joining coupled with a sequence structure-specific, general time reversible substitution model. Results from analyses of the ITS2 data were robust at multiple nodes and showed considerable congruence with results from published phylogenetic analyses.Our observations on the power of automated, sequence-structure analyses of ITS2 to reconstruct phylum-level phylogenies of the green algae validate this approach to assessing diversity for large sets of chlorophytan taxa. Moreover, our results indicate that objections to the use of ITS2 for DNA barcoding should be weighed against the utility of an automated, data analysis approach with demonstrated power to reconstruct evolutionary patterns for highly divergent lineages
Error bounds for monomial convexification in polynomial optimization
Convex hulls of monomials have been widely studied in the literature, and
monomial convexifications are implemented in global optimization software for
relaxing polynomials. However, there has been no study of the error in the
global optimum from such approaches. We give bounds on the worst-case error for
convexifying a monomial over subsets of . This implies additive error
bounds for relaxing a polynomial optimization problem by convexifying each
monomial separately. Our main error bounds depend primarily on the degree of
the monomial, making them easy to compute. Since monomial convexification
studies depend on the bounds on the associated variables, in the second part,
we conduct an error analysis for a multilinear monomial over two different
types of box constraints. As part of this analysis, we also derive the convex
hull of a multilinear monomial over .Comment: 33 pages, 2 figures, to appear in journa
Discovery of an intermediate-luminosity red transient in M51 and its likely dust-obscured, infrared-variable progenitor
We present the discovery of an optical transient (OT) in Messier 51,
designated M51 OT2019-1 (also ZTF19aadyppr, AT 2019abn, ATLAS19bzl), by the
Zwicky Transient Facility (ZTF). The OT rose over 15 days to an observed
luminosity of (), in the
luminosity gap between novae and typical supernovae (SNe). Spectra during the
outburst show a red continuum, Balmer emission with a velocity width of
km s, Ca II and [Ca II] emission, and absorption features
characteristic of an F-type supergiant. The spectra and multiband light curves
are similar to the so-called "SN impostors" and intermediate-luminosity red
transients (ILRTs). We directly identify the likely progenitor in archival
Spitzer Space Telescope imaging with a m luminosity of
and a color redder than 0.74 mag, similar
to those of the prototype ILRTs SN 2008S and NGC 300 OT2008-1. Intensive
monitoring of M51 with Spitzer further reveals evidence for variability of the
progenitor candidate at [4.5] in the years before the OT. The progenitor is not
detected in pre-outburst Hubble Space Telescope optical and near-IR images. The
optical colors during outburst combined with spectroscopic temperature
constraints imply a higher reddening of mag and higher
intrinsic luminosity of
() near peak than seen in previous ILRT
candidates. Moreover, the extinction estimate is higher on the rise than on the
plateau, suggestive of an extended phase of circumstellar dust destruction.
These results, enabled by the early discovery of M51 OT2019-1 and extensive
pre-outburst archival coverage, offer new clues about the debated origins of
ILRTs and may challenge the hypothesis that they arise from the
electron-capture induced collapse of extreme asymptotic giant branch stars.Comment: 21 pages, 5 figures, published in ApJ
Evolutionary distances in the twilight zone -- a rational kernel approach
Phylogenetic tree reconstruction is traditionally based on multiple sequence
alignments (MSAs) and heavily depends on the validity of this information
bottleneck. With increasing sequence divergence, the quality of MSAs decays
quickly. Alignment-free methods, on the other hand, are based on abstract
string comparisons and avoid potential alignment problems. However, in general
they are not biologically motivated and ignore our knowledge about the
evolution of sequences. Thus, it is still a major open question how to define
an evolutionary distance metric between divergent sequences that makes use of
indel information and known substitution models without the need for a multiple
alignment. Here we propose a new evolutionary distance metric to close this
gap. It uses finite-state transducers to create a biologically motivated
similarity score which models substitutions and indels, and does not depend on
a multiple sequence alignment. The sequence similarity score is defined in
analogy to pairwise alignments and additionally has the positive semi-definite
property. We describe its derivation and show in simulation studies and
real-world examples that it is more accurate in reconstructing phylogenies than
competing methods. The result is a new and accurate way of determining
evolutionary distances in and beyond the twilight zone of sequence alignments
that is suitable for large datasets.Comment: to appear in PLoS ON
Nonlinear Integer Programming
Research efforts of the past fifty years have led to a development of linear
integer programming as a mature discipline of mathematical optimization. Such a
level of maturity has not been reached when one considers nonlinear systems
subject to integrality requirements for the variables. This chapter is
dedicated to this topic.
The primary goal is a study of a simple version of general nonlinear integer
problems, where all constraints are still linear. Our focus is on the
computational complexity of the problem, which varies significantly with the
type of nonlinear objective function in combination with the underlying
combinatorial structure. Numerous boundary cases of complexity emerge, which
sometimes surprisingly lead even to polynomial time algorithms.
We also cover recent successful approaches for more general classes of
problems. Though no positive theoretical efficiency results are available, nor
are they likely to ever be available, these seem to be the currently most
successful and interesting approaches for solving practical problems.
It is our belief that the study of algorithms motivated by theoretical
considerations and those motivated by our desire to solve practical instances
should and do inform one another. So it is with this viewpoint that we present
the subject, and it is in this direction that we hope to spark further
research.Comment: 57 pages. To appear in: M. J\"unger, T. Liebling, D. Naddef, G.
Nemhauser, W. Pulleyblank, G. Reinelt, G. Rinaldi, and L. Wolsey (eds.), 50
Years of Integer Programming 1958--2008: The Early Years and State-of-the-Art
Surveys, Springer-Verlag, 2009, ISBN 354068274
Engineering Branch-and-Cut Algorithms for the Equicut Problem
A minimum equicut of an edge-weighted graph is a partition of the nodes of the graph into two sets of equal size such hat the sum of the weights of edges joining nodes in different partitions is minimum. We compare basic linear and semidefnite relaxations for the equicut problem, and and that linear bounds are competitive with the corresponding semidefnite ones but can be computed much faster. Motivated by an application of equicut in theoretical physics, we revisit an approach by Brunetta et al. and present an enhanced branch-and-cut algorithm. Our computational results suggest that the proposed branch-andcut algorithm has a better performance than the algorithm of Brunetta et al.. Further, it is able to solve to optimality in reasonable time several instances with more than 200 nodes from the physics application
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