2,376 research outputs found

    A Fast 2-Approximation of Minimum Manhattan Networks

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    Given a set P of n points in the plane, a Manhattan network of P is a network that contains a rectilinear shortest path between every pair of points of P. A minimum Manhattan network of P is a Manhattan network of minimum total length. It is unknown whether it is NP-hard to construct a minimum Manhattan network. The best approximations published so far are a combinatorial 3-approximation algorithm in time O(n log n), and an LP-based 2-approximation algorithm. We present a new combinatorial 2-approximation for this problem in time O(n log n)

    Microbiological communities of North Atlantic, 3rd Dimension of the Logatchev-Hydrothermalfield - Cruise No. MSM03 of Research Vessel Maria S. Merian

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    Fahrtabschnitt MSM 03/1: Der nördliche Atlantik weist drei Eigenschaften auf, die ihn zu einem der interessantesten Meeresgebiete machen. Zum einen beginnt hier das Absinken von kalten und dichten Wassermassen nördlich von Grönland und Island und bildet dadurch einen wichtigen Faktor der globalen ozeanischen Wasserzirkulation, dem globalen StrömungsgĂŒrtel. Zum anderen transportiert die VerlĂ€ngerung des Golf Stromes, die Nordatlantische Drift, warmes OberflĂ€chenwasser bis nach Spitzbergen und beeinflußt so entscheidend das Klima in Europa. Schließlich fließen kalte OberflĂ€chenwĂ€sser an der KĂŒste Grönlands entlang sĂŒdwĂ€rts und transportieren nĂ€hrstoffreiches Wasser in den SĂŒden. WĂ€hrend der letzten 15 Jahre ist mit Hilfe von kultivierungsunabhĂ€ngigen Methoden die mikrobiellen Gemeinschaften in verschiedenen marinen Systemen sehr intensiv erforscht worden. Viele unbekannte und nicht kultivierte Organismen wie der weit verbreitete SAR11 Cluster wurden entdeckt und quantitativ verfolgt. KĂŒrzlich wurden Genomanalysen ganzer mikrobieller Gemeinschaften initiiert (Metagenomics). Jedoch bleibt solche Forschung oft auf kĂŒstennahe Standorte beschrĂ€nkt. Nur wenige Studien beschrieben bisher die mikrobielle DiversitĂ€t, Struktur und Funktion im offenen Ozean und ĂŒber ganze Meeresbecken hinweg. Das sogenannte AMT (Atlantic Meridional Transect) Programm ist eines dieser Studien, welche es sich zur Aufgabe gemacht hat, den gesamten Atlantischen Ozean von den britischen Inseln (50°N) bis zu den Falkland Inseln (50°S) zu untersuchen. Zweimal im Jahr werden in einem interdisziplinĂ€ren Ansatz der Einfluß der biotischen (Phytoplankton, Zooplankton, Mikrobiologie) und abiotischen Faktoren (physikalischen und chemischen Parameter) auf die gesamte mikrobielle Gemeinschaft untersucht. Erste Ergebnisse dieser Studien bestĂ€tigten zum Beispiel die Einnischung von verschiedenen Ökotypen des wichtigen PrimĂ€rproduzenten Prochlorococcus in distinkte Wasserkörper (Tiefe, Breitengrad) entlang des Atlantischen Ozeans. Eine erste Studie zur Erforschung des Picoplanktons nördlich des 50° Breitengrades stellte das PRIME Programm dar. Neuere Untersuchungen in dem Gebiet richteten sich auf die Bakterioplankton-Gemeinschaft von TiefenwĂ€ssern unterhalb von 1000 m. FĂŒr die OberflĂ€chengewĂ€sser dieser Region jedoch fehlt eine genauere Untersuchung der DiversitĂ€t, Struktur und Funktion der mikrobiellen Gemeinschaft mit modernen molekularbiologischen Methoden. Fahrtabschnitt MSM 03/2: Das Ziel der Forschungsfahrt ist die detaillierte Untersuchung des flachen Untergrundes im Logatchev Hydrothermalfeldam Mittelatlantischen RĂŒcken (MAR) bei 15°N mit bis zu 15 m tiefen Bohrungen. Die Fahrt findet im Rahmen des DFG-SPP 1144 statt und komplettiert die bisher gewonnenen OberflĂ€chenproben sowie die im Rahmen des ODP-Leg 209 gewonnenen Tiefen-proben. Das in 3000m Wassertiefe liegende und an Mantelgesteine gebundene Logatchev Hydrothermalfeld ist durch intensive Anreicherung an Kupfer, Gold, Kobalt und anderen Wertelementen am Meersboden und vermutlich auch im flachen Untergrund gekennzeichnet. Gleichzeitig sind die hydrothermalen Fluide an bestimmten Gasen wie CH4 und H2 sehr stark angereichert, was intensive Auswirkungen auf die an das Hydrothermalsystem gekoppelten Mikroorganismen hat. Die Mikroben sitzen auf den OberflĂ€chen der Untergrundgesteine und MineralprĂ€zipitate im Bereich der hydrothermalen Austrittsstellen, wobei letztere spezifische ökologische Nischen bilden. Neben der Untersuchung der Tiefenzonierungen der Mineralisationen und Alterationen sowie deren Altersstellungen, ist die vermutete direkte Interaktion zwischen den Mikroorganismen (subsurface biosphere) und den hydrothermalen Mineralbildungen ein weiterer wichtiger wissenschaftlicher Aspekt. Auf der MSM03/2-Reise wird erstmals das ferngesteuerte BohrgerĂ€t Rockdrill2 des British Geological Survey eingesetzt. Neben deutschen Wissenschaftlern der Fachrichtungen LagerstĂ€ttenkunde, Petrologie, Geochemie und Mikrobiologie werden britische Techniker und Ingenieure sowie Wissenschaftler aus Russland und China an der Fahrt teilnehmen.Leg MSM 03/1 The North Atlantic Ocean has three features which makes it one of the most interesting parts of the world’s oceans. First, the extensive downwelling of cold and dense water masses north of Greenland and Iceland mark an important point in the global ocean water circulation, known as the “global conveyer belt”. Second, the extension of the Gulf Stream, the North Atlantic drift, is transporting warm surface water masses to high latitudes up to Spitzbergen thereby significantly influencing the climate of Europe. Third, cold surface water masses flow southwards along the coast of Greenland transporting nutrient rich waters to the south. The components of the microbial community inhabiting different marine systems have been intensively investigated by cultivation independent methods over the past 15 years. Many unknown and yet-uncultured organisms like the ubiquous SAR11 cluster have been detected and quantitatively monitored. Recently genomic analysis of whole microbial communities (=metagenomics) have been initiated. However such research is often restricted to few sites or limited to near-shore sites. Only few open ocean and basin – scale studies of the microbial community diversity, structure and function have been conducted so far. One of these studies is the British Atlantic Meridional Transect (AMT) program, which monitors the entire Atlantic Ocean from the app. 50°S (Falkland Islands) to app. 50°N (United Kingdom) twice a year. By an integrated approach of many disciplines including physical and chemical oceanography, microbiology, phytoplankton and zooplankton research the variability of microorganisms and the biotic and abiotic factors are studied. First results confirmed, for example, the nichepartitioning of different ecotypes of the imprimary producer Prochlorococcus in distinct water layers (depth, latitude) across the Atlantic Ocean. A first study of the picoplankton community north of 50°N of the Atlantic Ocean was done in 1996 during the PRIME cruise. Recent studies in the same area have focused on the bacterioplankton community of deep water masses below 1000 m water depths. An in-depth analysis of the diversity, structure and function of the microbial community in the photic layer down to genus and group level wit modern molecular tools was not yet conducted for this area. Leg MSM 03/2 The main objective of this cruise is the investigation of the shallow subsurface in the Logatchev hydrothermal field on the Mid Atlantic Ridge at 15°N by drilling up to 15 m deep cores. The cruise will take place within the DFG-SPP 1144 and will complete the surface sampling realized so far as well as deep sampling carried out by ODP Leg 209. The ultramafic-hosted Logatchev hydrothermal field situated in 3000m water depth is characterized by large enrichments of Cu, Au, Co, and other valuable elements at the seafloor and supposedly in the shallow subsurface. Hydrothermal fluids are largely enriched in certain gases like CH4 and H2 which is clearly linked to the microbiology associated with this hydrothermal system. The surfaces of rocks and minerals in the subsurface of the hydrothermal vent systems represent specific ecological niches for microorganisms which will be found associated to these interfaces. Apart from the investigation of the depth zonations of the mineralization and alteration as well as their age relationships is the establishmentof the variability of the subsurface biosphere and their supposed direct influence on the formation and transformation of hydrothermal mineral precipitations another major scientific aspect of the project. As drilling device the newly built, remotely operated Rockdrill2 of the British Geological Survey in Edinburgh (UK) will be used. Scientists from Germany representing the fields of economic geology, petrology, geochemistry and microbiology, technicians and engineers from UK as well as scientists from Russia and China will take part in the cruise

    Note on maximal split-stable subgraphs

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    A multigraph G=(V,RâˆȘB) with red and blue edges is an R/B-split graph if V is the union of a red and a blue stable set. Gavril has shown that R/B-split graphs yield a common generalization of split graphs and König–EgervĂĄry graphs. Moreover, R/B-split graphs can be recognized in linear time. In this note, we address the corresponding optimization problem: identify a set of vertices of maximal cardinality that decomposes into a red and a blue stable set. This problem is NP-hard in general. We investigate the complexity of special and related cases (e.g., (anti-)chains in partial orders and stable matroid bases) and exhibit some NP-hard cases as well as polynomial ones

    A small remark on Bernstein’s theorem

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    We investigate splitting-type variational problems with some linear growth conditions. For balanced solutions of the associated Euler– Lagrange equation, we receive a result analogous to Bernstein’s theorem on non-parametric minimal surfaces. Without assumptions of this type, Bernstein’s theorem cannot be carried over to the splitting case, which follows from an elementary counterexample. We also include some modifications of our main theorem

    25 Jahre Dolina Gesellschaft fĂŒr Landeskunde e. V.

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    Seit 25 Jahren ist die DOLINA Gesellschaft fĂŒr Landeskunde e. V. eine kulturelle Institution auf der SĂŒdlichen Frankenalb. Von Anfang an hat sie sich nicht nur der Erforschung der Natur- und Kulturlandschaft des Juras unter besonderer Beachtung des frĂŒhen Eisenbergbaus verschrieben, sondern auch der Jugend- und Erwachsenenbildung. Ihre zahlreichen Veranstaltungen machten sie in der Öffentlichkeit bekannt und beliebt. Aus Anlass des JubilĂ€ums informiert der Band ĂŒber die Geschichte des Vereins und bietet eine umfangreiche Dokumentation der vielfĂ€ltigen AktivitĂ€ten

    On the Approximability of Range Assignment Problems

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    We consider combinatorial optimization problems motivated by the following scenario. We are given a set of radio stations which can all send and receive data via wireless communication. Each radio station can be assigned an individual range up to which it transmits data. Given a certain connectivity requirement, the optimization task is to find a configuration of ranges (or range assignment) of minimal total power consumption providing the required network property. A problem of this kind is called range assignment problem. Three important problems of this type are examined in this thesis. First, we choose a quite abstract approach, allowing arbitrary distance functions without geometrical interpretation. We give the first thorough structural analysis of these problems in different setups. Our results identify easy cases as well as hard ones in terms of complexity as well as various levels of approximability for the individual problems. They also reveal interesting differences between the three problems themselves. We then turn to geometrical instances, on which there already exists a line of research regarding complexity and approximability in the literature. We contribute to this research by designing new reductions which are more simple and versatile than the ones used before, and produce new and better results. Using our reductions we can solve open problems posed in prior work. In the last chapter, we turn to approximation algorithms. We give a tight analysis of a well-known approximation algorithm for two of the problems as a function of the input size. A thorough analysis of two natural greedy paradigms is given, with tight results in the general and many special cases. We conclude with the design and analysis of a new approximation algorithm for one problem, and identify the first approximation scheme for some special geometric instances
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