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  • 1
    ISSN: 1434-4726
    Keywords: Acoustically evoked potential ; Age differences ; Multivariate variance and discriminant analysis ; Langsames akustisch evoziertes Potential ; Altersunterschiede ; Multivariate Varianz- und Diskriminanzanalyse
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Description / Table of Contents: Zusammenfassung Da ein Beitrag spezifischer Hirnstrukturen zur Entstehung des langsamen akustisch evozierten Potentials (AEP) als gesichert gilt, ist es wahrscheinlich, daß das AEP mehr Information über den Funktionszustand des akustischen Sinneskanals enthält, als die bisher übliche Ausmessung von nur 3 Werten (N1P2-Amplitude, 2 Latenzen) liefert. Die Prüfung dieser Hypothese ist mit einem multivariaten mathematischen Verfahren möglich, das den gesamten AEP-Zeitverlauf in die Analyse einbezieht. Wir arbeiten gegenwärtig mit der multivariaten Varianz- und Diskriminanzanalyse. Als statistisches Verfahren geht diese Analyse von Stichproben aus, in unserem Fall von Patientengruppen mit bestimmten otologischen Erkrankungen. Um Fehler bei der Zusammensetzung dieser Stichproben zu vermeiden, waren Voruntersuchungen zur Altersabhängigkeit des AEP bei normalhörenden Erwachsenen erforderlich, über deren Ergebnisse hier berichtet wird. Mittels der multivariaten Varianzanalyse wurden die AEP von 3 Altersgruppen (Gruppe 1: 15–34 Jahre, Gruppe 2: 35–44 Jahre, Gruppe 3: 45–60 Jahre) untersucht. Sowohl bei 1000 Hz als auch bei 4000 Hz konnten dabei signifikante Unterschiede zwischen den Gruppenmittelwerten der 3 Altersklassen gefunden werden, die mit der üblichen N1P2-Amplitudenauswertung (t-Test) nicht nachweisbar sind. Weiterhin ist mit Hilfe der Diskriminanzanalyse eine relativ sichere Unterscheidung der individuellen Potentiale der Altersgruppen 1 und 3 möglich.
    Notes: Summary Many authors consider the nature of the slow acoustically evoked potentials to be partly a specific one. Therefore the AEP-time behavior probably contains more information about the functional state of the acoustical channel than it is got by the usual measurement of only 3 values (N1P2-amplitude, 2 latencies). A test of this hypothesis is possible with a multivariate mathematical procedure, which involves the whole AEP-time behavior. We are using the multivariate variance- and discriminant analysis. For the application of this statistical method random samples of patients with certain otologic diseases are needed. To avoid mistakes in grouping these samples some preliminary investigations had been necesssary: This paper reports the results of multivariate investigations concerning age differences of the AEP in normal hearing adults. By means of the multivariate variance analysis the AEP of 3 age groups were examined (group 1: 15–34 years, group 2: 35–44 years, group 3: 45–60 years). At 1000 Hz as well as at 4000 Hz significant differences between the group averages were found, which were not detectable by the usual N1P2-amplitude measurement. Furthermore with the discriminant analysis it is possible to perform a relatively reliable differentiation between the individual AEP of the age groups 1 and 3.
    Type of Medium: Electronic Resource
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  • 2
    Publication Date: 2021-01-22
    Description: The problem of allocating operating rooms (OR) to surgical cases is a challenging task, involving both combinatorial aspects and uncertainty handling. We formulate this problem as a parallel machines scheduling problem, in which job durations follow a lognormal distribution, and a fixed assignment of jobs to machines must be computed. We propose a cutting-plane approach to solve the robust counterpart of this optimization problem. To this end, we develop an algorithm based on fixed-point iterations that identifies worst-case scenarios and generates cut inequalities. The main result of this article uses Hilbert's projective geometry to prove the convergence of this procedure under mild conditions. We also propose two exact solution methods for a similar problem, but with a polyhedral uncertainty set, for which only approximation approaches were known. Our model can be extended to balance the load over several planning periods in a rolling horizon. We present extensive numerical experiments for instances based on real data from a major hospital in Berlin. In particular, we find that: (i) our approach performs well compared to a previous model that ignored the distribution of case durations; (ii) compared to an alternative stochastic programming approach, robust optimization yields solutions that are more robust against uncertainty, at a small price in terms of average cost; (iii) the \emph{longest expected processing time first} (LEPT) heuristic performs well and efficiently protects against extreme scenarios, but only if a good prediction model for the durations is available. Finally, we draw a number of managerial implications from these observations.
    Language: English
    Type: article , doc-type:article
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  • 3
    Publication Date: 2020-08-05
    Description: The problem of allocating operating rooms (OR) to surgical cases is a challenging task, involving both combinatorial aspects and uncertainty handling. We formulate this problem as a parallel machines scheduling problem, in which job durations follow a lognormal distribution, and a fixed assignment of jobs to machines must be computed. We propose a cutting-plane approach to solve the robust counterpart of this optimization problem. To this end, we develop an algorithm based on fixed-point iterations that identifies worst-case scenarios and generates cut inequalities. The main result of this article uses Hilbert's projective geometry to prove the convergence of this procedure under mild conditions. We also propose two exact solution methods for a similar problem, but with a polyhedral uncertainty set, for which only approximation approaches were known. Our model can be extended to balance the load over several planning periods in a rolling horizon. We present extensive numerical experiments for instances based on real data from a major hospital in Berlin. In particular, we find that: (i) our approach performs well compared to a previous model that ignored the distribution of case durations; (ii) compared to an alternative stochastic programming approach, robust optimization yields solutions that are more robust against uncertainty, at a small price in terms of average cost; (iii) the \emph{longest expected processing time first} (LEPT) heuristic performs well and efficiently protects against extreme scenarios, but only if a good prediction model for the durations is available. Finally, we draw a number of managerial implications from these observations.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
    Format: application/pdf
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