TY - THES A1 - Schönlein, Michael T1 - Stability and Robustness of Fluid Networks: A Lyapunov Perspective T1 - Stabilität und Robustheit von Fluidnetzwerken: Eine Lyapunov Perspektive N2 - In the verification of positive Harris recurrence of multiclass queueing networks the stability analysis for the class of fluid networks is of vital interest. This thesis addresses stability of fluid networks from a Lyapunov point of view. In particular, the focus is on converse Lyapunov theorems. To gain an unified approach the considerations are based on generic properties that fluid networks under widely used disciplines have in common. It is shown that the class of closed generic fluid network models (closed GFNs) is too wide to provide a reasonable Lyapunov theory. To overcome this fact the class of strict generic fluid network models (strict GFNs) is introduced. In this class it is required that closed GFNs satisfy additionally a concatenation and a lower semicontinuity condition. We show that for strict GFNs a converse Lyapunov theorem is true which provides a continuous Lyapunov function. Moreover, it is shown that for strict GFNs satisfying a trajectory estimate a smooth converse Lyapunov theorem holds. To see that widely used queueing disciplines fulfill the additional conditions, fluid networks are considered from a differential inclusions perspective. Within this approach it turns out that fluid networks under general work-conserving, priority and proportional processor-sharing disciplines define strict GFNs. Furthermore, we provide an alternative proof for the fact that the Markov process underlying a multiclass queueing network is positive Harris recurrent if the associate fluid network defining a strict GFN is stable. The proof explicitely uses the Lyapunov function admitted by the stable strict GFN. Also, the differential inclusions approach shows that first-in-first-out disciplines play a special role. N2 - Für den Nachweis der positiven Harris-Rekurrenz bei Multiklassenwarteschlangennetzwerken ist die Stabilitätsanalyse der Klasse von Fluidnetzwerken von wesentlicher Bedeutung. Gegenstand dieser Arbeit ist die Stabilität von Fluidnetzwerken aus der Sicht von Lyapunov. Ein besonderes Augenmerk wird dabei auf konverse Lyapunov Theoreme gelegt. Hierzu wird ein axiomatischer Zugang gewählt, der auf generischen Eigenschaften gängiger Fluidnetzwerke basiert. Die Arbeit zeigt, dass die Klasse der abgeschlossenen generischen Fluidnetzwerk (abgeschlossene GFN) Modelle zu weit gefasst ist, um eine umfassende Lyapunovtheorie zu ermöglichen. Um dies zu beheben, wird die Klasse der strikten GFN Modelle eingeführt. In dieser Klasse wird verlangt, dass abgeschlossene GFN Modelle zusätzlich eine Verkettungs- sowie eine Unterhalbstetigkeitsbedingung erfüllen. Aus der Arbeit geht hervor, dass für strikte GFN Modelle Stabilität äquivalent zu der Existenz einer stetigen Lyapunov-Funktion ist. Darüberhinaus wird eine Regularitätseigenschaft an die Trajektorien des stikten GFN Modells gegeben, welche die Konstruktion glatter Lyapunov-Funktionen ermöglicht. Für den Nachweis, dass Fluidnetzwerke unter gängigen Disziplinen die zusätzlichen Eigenschaften erfüllen, werden diese als Differentialinklusionen aufgefasst. Dabei zeigt sich, dass allgemein arbeitserhaltende Fluidnetzwerke und Fluidnetzwerke mit Prioritäten strikte GFN Modelle liefern. Zudem zeigt die Arbeit einen alternativen Beweis dafür, dass der einem Multiklassenwarteschlangennetzwerk zugrunde liegende Markovprozess positiv Harris-rekurrent ist, falls das zugehörige Fluidnetzwerk ein striktes GFN Modell definiert und stabil ist. Dabei wird explizit die Lyapunov-Funktion des Fluidnetzwerkes ausgenutzt. Außerdem zeigt die Betrachtung von Fluidnetzwerken mittels Differentialinklusionen, dass first-in-first-out Fluidnetzwerken eine Sonderrolle zukommt. KW - Warteschlangennetz KW - Ljapunov-Funktion KW - Ljapunov-Stabilitätstheorie KW - Fluidnetzwerk KW - Lyapunov Funktion KW - Stabilität KW - queueing networks KW - fluid networks KW - stability KW - Lyapunov functions Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-72235 ER - TY - JOUR A1 - Staiger, Christine A1 - Cadot, Sidney A1 - Kooter, Raul A1 - Dittrich, Marcus A1 - Müller, Tobias A1 - Klau, Gunnar W. A1 - Wessels, Lodewyk F. A. T1 - A Critical Evaluation of Network and Pathway-Based Classifiers for Outcome Prediction in Breast Cancer JF - PLoS One N2 - Recently, several classifiers that combine primary tumor data, like gene expression data, and secondary data sources, such as protein-protein interaction networks, have been proposed for predicting outcome in breast cancer. In these approaches, new composite features are typically constructed by aggregating the expression levels of several genes. The secondary data sources are employed to guide this aggregation. Although many studies claim that these approaches improve classification performance over single genes classifiers, the gain in performance is difficult to assess. This stems mainly from the fact that different breast cancer data sets and validation procedures are employed to assess the performance. Here we address these issues by employing a large cohort of six breast cancer data sets as benchmark set and by performing an unbiased evaluation of the classification accuracies of the different approaches. Contrary to previous claims, we find that composite feature classifiers do not outperform simple single genes classifiers. We investigate the effect of (1) the number of selected features; (2) the specific gene set from which features are selected; (3) the size of the training set and (4) the heterogeneity of the data set on the performance of composite feature and single genes classifiers. Strikingly, we find that randomization of secondary data sources, which destroys all biological information in these sources, does not result in a deterioration in performance of composite feature classifiers. Finally, we show that when a proper correction for gene set size is performed, the stability of single genes sets is similar to the stability of composite feature sets. Based on these results there is currently no reason to prefer prognostic classifiers based on composite features over single genes classifiers for predicting outcome in breast cancer. KW - modules KW - protein-interaction networks KW - expression signature KW - classification KW - set KW - metastasis KW - stability KW - survival KW - database KW - markers Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-131323 VL - 7 IS - 4 ER -