The Planar Tree Packing Theorem

Packing graphs is a combinatorial problem where several given graphs are being mapped into a common host graph such that every edge is used at most once. In the planar tree packing problem we are given two trees T1 and T2 on n vertices and have to find a planar graph on n vertices that is the edge-disjoint union of T1 and T2. A clear exception that must be made is the star which cannot be packed together with any other tree. But according to a conjecture of Garc\'ia et al. from 1997 this is the only exception, and all other pairs of trees admit a planar packing. Previous results addressed various special cases, such as a tree and a spider tree, a tree and a caterpillar, two trees of diameter four, two isomorphic trees, and trees of maximum degree three. Here we settle the conjecture in the affirmative and prove its general form, thus making it the planar tree packing theorem. The proof is constructive and provides a polynomial time algorithm to obtain a packing for two given nonstar trees.Comment: Full version of our SoCG 2016 pape

Ausweitung der gesetzlichen Rentenversicherung auf Selbständige: Merkliche Effekte auch in der mittleren Frist

Ein häufig genannter Vorschlag zur Reform der gesetzlichen Rentenversicherung (GRV) ist die Ausweitung des Versichertenkreises. Dabei geht es zum einen um die bessere Alterssicherung von bislang nicht Versicherten und zum zweiten um die Stabilisierung der finanziellen Grundlagen der GRV. Dieser Bericht untersucht die finanziellen Auswirkungen einer Versicherungspflicht für Mini- und Midi-Jobs und für Selbständige. Es wird gezeigt, dass der Einbezug von Mini- und Midi-Jobbern kaum eine Auswirkung auf die Finanzlage der GRV hat, aber die Einbeziehung von nicht obligatorisch abgesicherten Selbständigen in die Versicherungspflicht die Finanzen der GRV auf mittlere Sicht merklich entlasten könnte. Eine besondere Bedeutung kommt der zeitlichen Umsetzung der Reform zu. Die entlastenden Effekte bei einer Einbeziehung der Selbständigen ergeben sich dadurch, dass zunächst mehr Beiträge ins System fließen, aber noch keine Renten ausgezahlt werden müssen. Wenn man sofort alle Selbständigen in die GRV übernehmen würde, wäre die maximale Entlastung beim Beitragssatz bereits nach wenigen Jahren erreicht. Würde man die Versicherungspflicht nur auf neue Selbständige ausdehnen, wäre der maximale Effekt erst nach dem Jahr 2040 erreicht.A frequently mentioned proposal for reforming the statutory pension insurance system (GRV) involves expanding the group of insured economically active persons. Such a reform aims at two primary benefits: offering pensions to those who are currently uninsured and stabilizing the GRV's financial foundations. This report examines the financial impact of a compulsory insurance for mini- and midi-jobbers as well as the self-employed. It is shown that the inclusion of mini- and midi-jobbers would have little impact on the GRV's financial position, but that the inclusion of self-employed workers could markedly improve it in the medium term. Behavioral adaptations are not taken into account. The chronology of the reform's implementation is of particular importance: the favorable effects of including self-employed individuals arise from the fact that initially, more contributions will be flowing into the system, but no pensions will have been paid out yet. If all existing self-employed individuals were to be included into the GRV at this very moment, the maximum positive effects would be achieved in just a few years; if only newly self-employed individuals were to be included, the maximum effect would not materialize until after 2040

Dimension- and space-based intertrial effects in visual pop-out search: modulation by task demands for focal-attentional processing

Two experiments compared reaction times (RTs) in visual search for singleton feature targets defined, variably across trials, in either the color or the orientation dimension. Experiment 1 required observers to simply discern target presence versus absence (simple-detection task); Experiment 2 required them to respond to a detection-irrelevant form attribute of the target (compound-search task). Experiment 1 revealed a marked dimensional intertrial effect of 34ms for an target defined in a changed versus a repeated dimension, and an intertrial target distance effect, with an 4-ms increase in RTs (per unit of distance) as the separation of the current relative to the preceding target increased. Conversely, in Experiment 2, the dimension change effect was markedly reduced (11ms), while the intertrial target distance effect was markedly increased (11ms per unit of distance). The results suggest that dimension change/repetition effects are modulated by the amount of attentional focusing required by the task, with space-based attention altering the integration of dimension-specific feature contrast signals at the level of the overall-saliency ma

Foreword

Early Middle Cambrian bituminous coquinoid limestones from a tectonically isolated outcrop in southwestern Kyrgyzstan yield a remarkably diverse fauna, with stem-group cnidarians, trilobites, rhynchonelliformean brachiopods, and other shelly fossils. The fossil site is in the northern foothills of the Turkestan Range and thus forms part of the westernmost extension of the South Tien Shan. The fauna includes two fairly well known trilobite species, Glabrella ventrosa Lermontova, 1940 and Dorypyge richthofeniformis Lermontova, 1940, that provide confident support for an Amgan age of the rocks. New described taxa include the stem-group cnidarian Cambroctoconus kyrgyzstanicus Peel sp. nov., the trilobite Olenoides sagittatus Geyer sp. nov., and the helcionelloid Manasoconus bifrons Peel gen. et sp. nov. Additional fossils within the samples include the trilobites Olenoides sp. A, Kootenia sp., and Pseudoeteraspis? sp.; the rhynchonelliform brachiopods Narynella cf. ferganensis (Andreeva, 1962), Narynella? sp., Austrohedra? sp. nov., and two species of uncertain generic affinity; the tommotiid Tesella sp.; the hyolithelminth Hyolithellus sp.; and the palaeoscolecid Hadimopanella oezgueli Gedik, 1977. Of particular interest is Cambroctoconus kyrgyzstanicus with an octagonal corallum and a sparsely septate calyx

Optimisation of the enzyme-linked lectin assay for enhanced glycoprotein and glycoconjugate analysis

Lectin’s are proteins capable of recognising and binding to specific oligosaccharide tructures found on glycoproteins and other biomoloecules. As such they have found tility for glycoanalytical applications. One common difficulty encountered in the pplication of these proteins, particularly in multi-well plate assay formats known as Enzyme Linked Lectin Assays (ELLA’s), is in finding appropriate blocking solutions to prevent non-specific binding with plate surfaces. Many commonly used blocking agents contain carbohydrates and generate significant background signals in ELLA’s, limiting the utility of the assay. In this study we examined the suitability of a range of blocking reagents, including rotein based, synthetic and commercially available carbohydrate free blocking eagents, for ELLA applications. Each blocking reagent was assessed against a panel f 19 commercially available biotinylated lectins exhibiting diverse structures and arbohydrate specificities. We identified the synthetic polymer Polyvinyl Alcohol PVA) as the best global blocking agent for performing ELLA’s. We ultimately present n ELLA methodology facilitating broad spectrum lectin analysis of glycoconjugates nd extending the utility of the ELLA

Library Design in Combinatorial Chemistry by Monte Carlo Methods

Strategies for searching the space of variables in combinatorial chemistry experiments are presented, and a random energy model of combinatorial chemistry experiments is introduced. The search strategies, derived by analogy with the computer modeling technique of Monte Carlo, effectively search the variable space even in combinatorial chemistry experiments of modest size. Efficient implementations of the library design and redesign strategies are feasible with current experimental capabilities.Comment: 5 pages, 3 figure