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

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

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

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

Multiple ITS Copies Reveal Extensive Hybridization within Rheum (Polygonaceae), a Genus That Has Undergone Rapid Radiation

During adaptive radiation events, characters can arise multiple times due to parallel evolution, but transfer of traits through hybridization provides an alternative explanation for the same character appearing in apparently non-sister lineages. The signature of hybridization can be detected in incongruence between phylogenies derived from different markers, or from the presence of two divergent versions of a nuclear marker such as ITS within one individual.In this study, we cloned and sequenced ITS regions for 30 species of the genus Rheum, and compared them with a cpDNA phylogeny. Seven species contained two divergent copies of ITS that resolved in different clades from one another in each case, indicating hybridization events too recent for concerted evolution to have homogenised the ITS sequences. Hybridization was also indicated in at least two further species via incongruence in their position between ITS and cpDNA phylogenies. None of the ITS sequences present in these nine species matched those detected in any other species, which provides tentative evidence against recent introgression as an explanation. Rheum globulosum, previously indicated by cpDNA to represent an independent origin of decumbent habit, is indicated by ITS to be part of clade of decumbent species, which acquired cpDNA of another clade via hybridization. However decumbent and glasshouse morphology are confirmed to have arisen three and two times, respectively.These findings suggested that hybridization among QTP species of Rheum has been extensive, and that a role of hybridization in diversification of Rheum requires investigation

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

Changes in Prefrontal-Limbic Function in Major Depression after 15 Months of Long-Term Psychotherapy

Neuroimaging studies of depression have demonstrated treatment-specific changes involving the limbic system and regulatory regions in the prefrontal cortex. While these studies have examined the effect of short-term, interpersonal or cognitive-behavioural psychotherapy, the effect of long-term, psychodynamic intervention has never been assessed. Here, we investigated recurrently depressed (DSM-IV) unmedicated outpatients (N = 16) and control participants matched for sex, age, and education (N = 17) before and after 15 months of psychodynamic psychotherapy. Participants were scanned at two time points, during which presentations of attachment-related scenes with neutral descriptions alternated with descriptions containing personal core sentences previously extracted from an attachment interview. Outcome measure was the interaction of the signal difference between personal and neutral presentations with group and time, and its association with symptom improvement during therapy. Signal associated with processing personalized attachment material varied in patients from baseline to endpoint, but not in healthy controls. Patients showed a higher activation in the left anterior hippocampus/amygdala, subgenual cingulate, and medial prefrontal cortex before treatment and a reduction in these areas after 15 months. This reduction was associated with improvement in depressiveness specifically, and in the medial prefrontal cortex with symptom improvement more generally. This is the first study documenting neurobiological changes in circuits implicated in emotional reactivity and control after long-term psychodynamic psychotherapy

Individualized and Clinically Derived Stimuli Activate Limbic Structures in Depression: An fMRI Study

In the search for neurobiological correlates of depression, a major finding is hyperactivity in limbic-paralimbic regions. However, results so far have been inconsistent, and the stimuli used are often unspecific to depression. This study explored hemodynamic responses of the brain in patients with depression while processing individualized and clinically derived stimuli.Eighteen unmedicated patients with recurrent major depressive disorder and 17 never-depressed control subjects took part in standardized clinical interviews from which individualized formulations of core interpersonal dysfunction were derived. In the patient group such formulations reflected core themes relating to the onset and maintenance of depression. In controls, formulations reflected a major source of distress. This material was thereafter presented to subjects during functional magnetic resonance imaging (fMRI) assessment.Increased hemodynamic responses in the anterior cingulate cortex, medial frontal gyrus, fusiform gyrus and occipital lobe were observed in both patients and controls when viewing individualized stimuli. Relative to control subjects, patients with depression showed increased hemodynamic responses in limbic-paralimbic and subcortical regions (e.g. amygdala and basal ganglia) but no signal decrease in prefrontal regions.This study provides the first evidence that individualized stimuli derived from standardized clinical interviewing can lead to hemodynamic responses in regions associated with self-referential and emotional processing in both groups and limbic-paralimbic and subcortical structures in individuals with depression. Although the regions with increased responses in patients have been previously reported, this study enhances the ecological value of fMRI findings by applying stimuli that are of personal relevance to each individual's depression