@article{DashkovskiySlynko2022,
  author    = {Dashkovskiy, Sergey and Slynko, Vitalii},
  title     = {Stability conditions for impulsive dynamical systems},
  series = {Mathematics of Control, Signals, and Systems},
  volume    = {34},
  journal   = {Mathematics of Control, Signals, and Systems},
  number    = {1},
  issn      = {1435-568X},
  doi       = {10.1007/s00498-021-00305-y},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-268390},
  pages     = {95-128},
  year      = {2022},
  abstract  = {In this work, we consider impulsive dynamical systems evolving on an infinite-dimensional space and subjected to external perturbations. We look for stability conditions that guarantee the input-to-state stability for such systems. Our new dwell-time conditions allow the situation, where both continuous and discrete dynamics can be unstable simultaneously. Lyapunov like methods are developed for this purpose. Illustrative finite and infinite dimensional examples are provided to demonstrate the application of the main results. These examples cannot be treated by any other published approach and demonstrate the effectiveness of our results.},
  language  = {en}
}
@phdthesis{Schoenlein2012,
  author    = {Sch{\"o}nlein, Michael},
  title     = {Stability and Robustness of Fluid Networks: A Lyapunov Perspective},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-72235},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2012},
  abstract  = {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.},
  subject      = {Warteschlangennetz},
  language  = {en}
}
@article{ZukherNovikovaTikhonovetal.2014,
  author    = {Zukher, Inna and Novikova, Maria and Tikhonov, Anton and Nesterchuk, Mikhail V. and Osterman, Ilya A. and Djordjevic, Marko and Sergiev, Petr V. and Sharma, Cynthia M. and Severinov, Konstantin},
  title     = {Ribosome-controlled transcription termination is essential for the production of antibiotic microcin C},
  series = {Nucleic Acids Research},
  volume    = {42},
  journal   = {Nucleic Acids Research},
  number    = {19},
  issn      = {0305-1048},
  doi       = {10.1093/nar/gku880},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-114839},
  pages     = {11891-11902},
  year      = {2014},
  abstract  = {Microcin C (McC) is a peptide-nucleotide antibiotic produced by Escherichia coli cells harboring a plasmid-borne operon mccABCDE. The heptapeptide MccA is converted into McC by adenylation catalyzed by the MccB enzyme. Since MccA is a substrate for MccB, a mechanism that regulates the MccA/MccB ratio likely exists. Here, we show that transcription from a promoter located upstream of mccA directs the synthesis of two transcripts: a short highly abundant transcript containing the mccA ORF and a longer minor transcript containing mccA and downstream ORFs. The short transcript is generated when RNA polymerase terminates transcription at an intrinsic terminator located in the intergenic region between the mccA and mccB genes. The function of this terminator is strongly attenuated by upstream mcc sequences. Attenuation is relieved and transcription termination is induced when ribosome binds to the mccA ORF. Ribosome binding also makes the mccA RNA exceptionally stable. Together, these two effects-ribosome induced transcription termination and stabilization of the message-account for very high abundance of the mccA transcript that is essential for McC production. The general scheme appears to be evolutionary conserved as ribosome-induced transcription termination also occurs in a homologous operon from Helicobacter pylori.},
  language  = {en}
}
@article{StaigerCadotKooteretal.2012,
  author    = {Staiger, Christine and Cadot, Sidney and Kooter, Raul and Dittrich, Marcus and M{\"u}ller, Tobias and Klau, Gunnar W. and Wessels, Lodewyk F. A.},
  title     = {A Critical Evaluation of Network and Pathway-Based Classifiers for Outcome Prediction in Breast Cancer},
  series = {PLoS One},
  volume    = {7},
  journal   = {PLoS One},
  number    = {4},
  doi       = {10.1371/journal.pone.0034796},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-131323},
  pages     = {e34796},
  year      = {2012},
  abstract  = {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.},
  language  = {en}
}