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

Coatings for FEL optics preparation and characterization of B4C and Pt

Large X ray mirrors are required for beam transport at both present day and future free electron lasers FELs and synchrotron sources worldwide. The demand for large mirrors with lengths up to 1 m single layers consisting of light or heavy elements has increased during the last few decades. Accordingly, surface finishing technology is now able to produce large substrate lengths with micro roughness on the sub nanometer scale. At the Helmholtz Zentrum Geesthacht HZG , a 4.5 m long sputtering facility enables us to deposit a desired single layer material some tens of nanometers thick. For the European XFEL project, the shape error should be less than 2 nm over the whole 1 m X ray mirror length to ensure the safe and efficient delivery of X ray beams to the scientific instruments. The challenge is to achieve thin film deposition on silicon substrates, benders and gratings without any change in mirror shape. Thin films of boron carbide and platinum with a thickness in the range 30 100 nm were manufactured using the HZG sputtering facility. This setup is able to cover areas of up to 1500 mm x120 mm in one step using rectangular sputtering sources. The coatings produced were characterized using various thin film methods. It was possible to improve the coating process to achieve a very high uniformity of the layer thickness. The movement of the substrate in front of the sputtering source has been optimized. Avariation in B4C layer thickness below 1 nm peak to valley was achieved at a mean thickness of 51.8 nm over a deposition length of 1.5 m. In the case of Pt, reflectometry and micro roughness measurements were performed. The uniformity in layer thickness was about 1 nm peak to valley . The micro roughness of the Pt layers showed no significant change in the coated state for layer thicknesses of 32 nm and 102 nm compared with the uncoated substrate state. The experimental results achieved will be discussed with regard to current restrictions and future development

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

Cells' Flow and Immune Cell Priming under alternating g-forces in Parabolic Flight

Gravitational stress in general and microgravity (mu g) in particular are regarded as major stress factors responsible for immune system dysfunction in space. To assess the effects of alternating mu g and hypergravity (hyper-g) on immune cells, the attachment of peripheral blood mononuclear cells (PBMCs) to adhesion molecules under flow conditions and the antigen-induced immune activation in whole blood were investigated in parabolic flight (PF). In contrast to hyper-g (1.8 g) and control conditions (1 g), flow and rolling speed of PBMCs were moderately accelerated during mu g-periods which were accompanied by a clear reduction in rolling rate. Whole blood analyses revealed a "primed" state of monocytes after PF with potentiated antigen-induced pro-inflammatory cytokine responses. At the same time, concentrations of anti-inflammatory cytokines were increased and monocytes displayed a surface molecule pattern that indicated immunosuppression. The results suggest an immunologic counterbalance to avoid disproportionate immune responses. Understanding the interrelation of immune system impairing and enhancing effects under different gravitational conditions may support the design of countermeasures to mitigate immune deficiencies in space

A Generalization of the Directed Graph Layering Problem

The Directed Layering Problem (DLP) solves a step of the widely used layer-based layout approach to automatically draw directed acyclic graphs. To cater for cyclic graphs, classically a preprocessing step is used that solves the Feedback Arc Set Problem (FASP)to make the graph acyclic before a layering is determined. Here, we present the Generalized Layering Problem (GLP) which solves the combination of DLP and FASP simultaneously, allowing general graphs as input. We show GLP to be NP- complete, present integer programming models to solve it, and perform thorough evaluations on different sets of graphs and with different implementations for the steps of the layer- based approach. We observe that GLP reduces the number of dummy nodes significantly, can produce more compact drawings and improves on graphs where DLP yields poor aspect ratios

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

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