Rectilinear Steiner Trees in Narrow Strips

A rectilinear Steiner tree for a set $P$ of points in $\mathbb{R}^2$ is a tree that connects the points in $P$ using horizontal and vertical line segments. The goal of Minimal Rectilinear Steiner Tree is to find a rectilinear Steiner tree with minimal total length. We investigate how the complexity of Minimal Rectilinear Steiner Tree for point sets $P$ inside the strip $(-\infty,+\infty)\times [0,\delta]$ depends on the strip width $\delta$. We obtain two main results. 1) We present an algorithm with running time $n^{O(\sqrt{\delta})}$ for sparse point sets, that is, point sets where each $1\times\delta$ rectangle inside the strip contains $O(1)$ points. 2) For random point sets, where the points are chosen randomly inside a rectangle of height $\delta$ and expected width $n$, we present an algorithm that is fixed-parameter tractable with respect to $\delta$ and linear in $n$. It has an expected running time of $2^{O(\delta \sqrt{\delta})} n$.Comment: 21 pages, 13 figure

TSP in a Simple Polygon

We study the Traveling Salesman Problem inside a simple polygon. In this problem, which we call tsp in a simple polygon, we wish to compute a shortest tour that visits a given set S of n sites inside a simple polygon P with m edges while staying inside the polygon. This natural problem has, to the best of our knowledge, not been studied so far from a theoretical perspective. It can be solved exactly in poly(n,m) + 2^O(?nlog n) time, using an algorithm by Marx, Pilipczuk, and Pilipczuk (FOCS 2018) for subset tsp as a subroutine. We present a much simpler algorithm that solves tsp in a simple polygon directly and that has the same running time

Die Differenz der Beobachtung. Einleitende Bemerkungen zur Luhmann-Rezeption

Schmidt J. Die Differenz der Beobachtung. Einleitende Bemerkungen zur Luhmann-Rezeption. In: de Berg H, Schmidt J, eds. Rezeption und Reflexion. Zur Resonanz der Systemtheorie Niklas Luhmanns außerhalb der Soziologie. Suhrkamp-Taschenbuch Wissenschaft. Vol 1501. 1. Auflage. Frankfurt a.M.: Suhrkamp; 2000: 7-30

Revealing methyl-esterification patterns of pectins by enzymatic fingerprinting:Beyond the degree of blockiness

Citrus pectins were studied by enzymatic fingerprinting using a simultaneous enzyme treatment with endo-polygalacturonase (endo-PG) from Kluyveromyces fragilis and pectin lyase (PL) from Aspergillus niger to reveal the methyl-ester distribution patterns over the pectin backbone. Using HILIC-MS combined with HPAEC enabled the separation and identification of the diagnostic oligomers released. Structural information on the pectins was provided by using novel descriptive parameters such as degree of blockiness of methyl-esterified oligomers by PG (DBPGme) and degree of blockiness of methyl-esterified oligomers by PL (DBPLme). This approach enabled us to clearly differentiate citrus pectins with various methyl-esterification patterns. The simultaneous use of PG and PL showed additional information, which is not revealed in digests using PG or PL alone. This approach can be valuable to differentiate pectins having the same DM and to get specific structural information on pectins and therefore to be able to better predict their physical and biochemical functionalities

Health related quality of life in patients with type I diabetes mellitus:generic & disease-specific measurement

Background & objectives: An ideal instrument for the assessment of health related quality of life (HRQOL) in patients with diabetes mellitus type I (T1DM) should incorporate the benefits of both generic and disease-specific instruments. The objective of this study was to investigate the responsiveness and the ability to provide information about diabetes-specific associations with HRQOL, of two generic instruments, in comparison with two diabetes-specific instruments, in patients with T1DM. Methods: In a Dutch cohort of 234 patients with T1DM we longitudinally assessed HRQOL using both generic and diabetes-specific instruments. We investigated the responsiveness, the associations with diabetes-specific variables and the Identification of specific patients by the Instruments used. Results: The generic RAND-36 was able to detect statistically significant and clinically relevant changes in HRQOL over time. Moreover, the RAND-36 was associated with (changes In) diabetes. specific variables. The generic and diabetes-specific Instruments partly Identified different patients with lowest HRQOL. Interpretation & conclusion: The RAND-36 was highly responsive to changes in HRQOL in patients with T1DM and revealed diabetes-specific associations with HRQOL. A low correlation between the generic and diabetes-specific instruments and partly different identification of patients with lower HRQOL support the complementary use of these instruments In patients with T1DM

The impact of the level and distribution of methyl-esters of pectins on TLR2-1 dependent anti-inflammatory responses

Pectins have anti-inflammatory effects via Toll-like receptor (TLR) inhibition in a degree of methyl-esterification-(DM)-dependent manner. However, pectins also vary in distribution of methyl-esters over the galactumnic-acid (GalA) backbone (Degree of Blockiness - DB) and impact of this on anti-inflammatory capacity is unknown. Pectins mainly inhibit TLR2-1 but magnitude depends on both DM and DB. Low DM pectins (DM18/19) with both low (DB86) and high DB (DB94) strongly inhibit TLR2-1. However, pectins with intermediate DM (DM43/ DM49) and high DB (DB60), but not with low DB (DB33), inhibit TLR2-1 as strongly as low DM. High DM pectins (DM84/88) with DB71 and DB91 do not inhibit TLR2-1 strongly. Pectin-binding to TLR2 was confirmed by capture-ELISA. In human macrophages, low DM and intermediate DM pectins with high DB inhibited TLR2-1 induced IL-6 secretion. Both high number and blockwise distribution of non-esterified GalA in pectins are responsible for the anti-inflammatory effects via inhibition of TLR2-1