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  • 1
    Electronic Resource
    Electronic Resource
    The Vanishing Defibrillator Syndrome: Incidence, Mechanism, and Clinical Relevance (1997)
    Oxford, UK : Blackwell Publishing Ltd
    Pacing and clinical electrophysiology 20 (1997), S. 0 
    Details
    ISSN: 1540-8159
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Medicine
    Notes: Intraperitoneal migration of an abdominally implanted cardioverter defibrillator is a complication not yet fully described. In a consecutive series of 195 patients, migration occurred between I and 20 months in 5 (8%) of the 63 patients in whom a subrectus abdomini placement of the generator was chosen. It was unrelated to the patients'clinical characteristics or the defibrillator model. Dysuria and inability to interrogate the device were present in every subject, and the diagnosis was confirmed by the characteristic abdominal x-ray appearance and the findings at the time of surgery. Adhesions involving the omentum, and in one case, the small bowels, were present in three patients and seem to be related to the length of intraabdominal permanence of the generator. Because this complication may be due to specific anatomical characteristics of the aponeurosis of the abdominal muscles, it is likely that its incidence will be unchanged by the use of smaller devices. A close follow-up of the generators implanted deep to the rectus fascia is therefore advisable.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1540-8159.1997.tb05500.x
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    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    Norm-graphs and bipartite turán numbers (1996)
    Springer
    Combinatorica 16 (1996), S. 399-406 
    Details
    ISSN: 1439-6912
    Keywords: 05 C 35 ; 14 A 25
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For everyt〉1 and positiven we construct explicit examples of graphsG with |V (G)|=n, |E(G)|≥c t ·n 2−1/t which do not contain a complete bipartite graghK t,t !+1 This establishes the exact order of magnitude of the Turán numbers ex (n, K t,s ) for any fixedt and alls≥t!+1, improving over the previous probabilistic lower bounds for such pairs (t, s). The construction relies on elementary facts from commutative algebra.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01261323
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    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    On Erdős's Eulerian Trail Game (1999)
    Springer
    Graphs and combinatorics 15 (1999), S. 233-237 
    Details
    ISSN: 1435-5914
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract.  Paul Erdős proposed the following graph game. Starting with the empty graph on n vertices, two players, Trailmaker and Breaker, draw edges alternatingly. Each edge drawn has to start at the endpoint of the previously drawn edge, so the sequence of edges defines a trail. The game ends when it is impossible to continue the trail, and Trailmaker wins if the trail is eulerian. For all values of n, we determine which player has a winning strategy.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s003730050043
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    Paper (German National Licenses)
    Fulltext
  • 4
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    New Ramsey Multiplicity Bounds and Search Heuristics (2022)
    Details
    Publication Date: 2022-11-29
    Description: We study two related problems concerning the number of monochromatic cliques in two-colorings of the complete graph that go back to questions of Erdős. Most notably, we improve the 25-year-old upper bounds of Thomason on the Ramsey multiplicity of K4 and K5 and we settle the minimum number of independent sets of size 4 in graphs with clique number at most 4. Motivated by the elusiveness of the symmetric Ramsey multiplicity problem, we also introduce an off-diagonal variant and obtain tight results when counting monochromatic K4 or K5 in only one of the colors and triangles in the other. The extremal constructions for each problem turn out to be blow-ups of a finite graph and were found through search heuristics. They are complemented by lower bounds and stability results established using Flag Algebras, resulting in a fully computer-assisted approach. More broadly, these problems lead us to the study of the region of possible pairs of clique and independent set densities that can be realized as the limit of some sequence of graphs.
    Language: English
    Type: conferenceobject , doc-type:conferenceObject
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    OPUS
  • 5
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    Fully Computer-assisted Proofs in Extremal Combinatorics (2023)
    Details
    Publication Date: 2023-08-02
    Description: We present a fully computer-assisted proof system for solving a particular family of problems in Extremal Combinatorics. Existing techniques using Flag Algebras have proven powerful in the past, but have so far lacked a computational counterpart to derive matching constructive bounds. We demonstrate that common search heuristics are capable of finding constructions far beyond the reach of human intuition. Additionally, the most obvious downside of such heuristics, namely a missing guarantee of global optimality, can often be fully eliminated in this case through lower bounds and stability results coming from the Flag Algebra approach. To illustrate the potential of this approach, we study two related and well-known problems in Extremal Graph Theory that go back to questions of Erdős from the 60s. Most notably, we present the first major improvement in the upper bound of the Ramsey multiplicity of the complete graph on 4 vertices in 25 years, precisely determine the first off-diagonal Ramsey multiplicity number, and settle the minimum number of independent sets of size four in graphs with clique number strictly less than five.
    Language: English
    Type: conferenceobject , doc-type:conferenceObject
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    OPUS
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