Low Ply Drawings of Trees

We consider the recently introduced model of \emph{low ply graph drawing}, in which the ply-disks of the vertices do not have many common overlaps, which results in a good distribution of the vertices in the plane. The \emph{ply-disk} of a vertex in a straight-line drawing is the disk centered at it whose radius is half the length of its longest incident edge. The largest number of ply-disks having a common overlap is called the \emph{ply-number} of the drawing. We focus on trees. We first consider drawings of trees with constant ply-number, proving that they may require exponential area, even for stars, and that they may not even exist for bounded-degree trees. Then, we turn our attention to drawings with logarithmic ply-number and show that trees with maximum degree $6$ always admit such drawings in polynomial area.Comment: This is a complete access version of a paper that will appear in the proceedings of GD201

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 $[0,1]^n$. 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 $[-1,1]^n$.Comment: 33 pages, 2 figures, to appear in journa

Catching-up and falling behind knowledge spillover from American to German machine tool makers

In our days, German machine tool makers accuse their Chinese competitors of violating patent rights and illegally imitating German technology. A century ago, however, German machine tool makers used exactly the same methods to imitate American technology. To understand the dynamics of this catching-up process we use patent statistics to analyze firms? activities between 1877 and 1932. We show that German machine tool makers successfully deployed imitating and counterfeiting activities in the late 19th century and the 1920s to catchup to their American competitors. The German administration supported this strategy by stipulating a patent law that discriminated against foreign patent holders and probably also by delaying the granting of patents to foreign applicants. Parallel to the growing international competitiveness of German firms, however, the willingness to guarantee intellectual property rights of foreigners was also increasing because German firms had now to fear retaliatory measures in their own export markets when violating foreign property rights within Germany

Health-Related Quality of Life after Pediatric Traumatic Brain Injury: A Quantitative Comparison between Children’s and Parents’ Perspectives of the QOLIBRI-KID/ADO Questionnaire

Pediatric health-related quality of life (HRQoL) as a measure of subjective wellbeing and functioning has received increasing attention over the past decade. HRQoL in children and adolescents following pediatric traumatic brain injury (pTBI) has been poorly studied, and performing adequate measurements in this population is challenging. This study compares child/adolescent and parent reports of HRQoL following pTBI using the newly developed Quality of Life after Brain Injury in Children and Adolescents (QOLIBRI-KID/ADO) questionnaire. Three hundred dyads of 8–17-year-old children/adolescents and their parents were included in the study. The parent–child agreement, estimated using intraclass correlation coefficients and Cohen’s κ, displayed poor to moderate concordance. Approximately two-fifths of parents (39.3%) tended to report lower HRQoL for their children/adolescents on the total QOLIBRI-KID/ADO score. At the same time, about one-fifth (21.3%) reported higher HRQoL Total scores for their children/adolescents. The best agreement for parents rating adolescents (aged 13–17 years) was found in terms of the Total score and the Cognition and Self scale scores. To date, parent-reported HRQoL has been the preferred choice in pediatric research after TBI. However, with a parent–child disagreement of approximately 60%, our results highlight the importance of considering self-reports for children/adolescents capable of answering or completing the HRQoL measures

Biochar successfully replaces activated charcoal for in vitro culture of two white poplar clones reducing ethylene concentration

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Breaking the habit - the peculiar 2016 eruption of the unique recurrent nova M31N 2008-12a

Since its discovery in 2008, the Andromeda galaxy nova M31N 2008-12a has been observed in eruption every single year. This unprecedented frequency indicates an extreme object, with a massive white dwarf and a high accretion rate, which is the most promising candidate for the single-degenerate progenitor of a type-Ia supernova known to date. The previous three eruptions of M31N 2008-12a have displayed remarkably homogeneous multi-wavelength properties: (i) From a faint peak, the optical light curve declined rapidly by two magnitudes in less than two days; (ii) Early spectra showed initial high velocities that slowed down significantly within days and displayed clear He/N lines throughout; (iii) The supersoft X-ray source (SSS) phase of the nova began extremely early, six days after eruption, and only lasted for about two weeks. In contrast, the peculiar 2016 eruption was clearly different. Here we report (i) the considerable delay in the 2016 eruption date, (ii) the significantly shorter SSS phase, and (iii) the brighter optical peak magnitude (with a hitherto unobserved cusp shape). Early theoretical models suggest that these three different effects can be consistently understood as caused by a lower quiescence mass-accretion rate. The corresponding higher ignition mass caused a brighter peak in the free-free emission model. The less-massive accretion disk experienced greater disruption, consequently delaying re-establishment of effective accretion. Without the early refueling, the SSS phase was shortened. Observing the next few eruptions will determine whether the properties of the 2016 outburst make it a genuine outlier in the evolution of M31N 2008-12a