@article{BialonskiWendlerLehnertz2011,
  author    = {Bialonski, Stephan and Wendler, Martin and Lehnertz, Klaus},
  title     = {Unraveling spurious properties of interaction networks with tailored random networks},
  series = {Plos one},
  volume    = {6},
  journal   = {Plos one},
  number    = {8},
  publisher = {Plos},
  address   = {San Francisco},
  doi       = {10.1371/journal.pone.0022826},
  pages     = {e22826},
  year      = {2011},
  abstract  = {We investigate interaction networks that we derive from multivariate time series with methods frequently employed in diverse scientific fields such as biology, quantitative finance, physics, earth and climate sciences, and the neurosciences. Mimicking experimental situations, we generate time series with finite length and varying frequency content but from independent stochastic processes. Using the correlation coefficient and the maximum cross-correlation, we estimate interdependencies between these time series. With clustering coefficient and average shortest path length, we observe unweighted interaction networks, derived via thresholding the values of interdependence, to possess non-trivial topologies as compared to Erd{\"o}s-R{\´e}nyi networks, which would indicate small-world characteristics. These topologies reflect the mostly unavoidable finiteness of the data, which limits the reliability of typically used estimators of signal interdependence. We propose random networks that are tailored to the way interaction networks are derived from empirical data. Through an exemplary investigation of multichannel electroencephalographic recordings of epileptic seizures - known for their complex spatial and temporal dynamics - we show that such random networks help to distinguish network properties of interdependence structures related to seizure dynamics from those spuriously induced by the applied methods of analysis.},
  language  = {en}
}
@inproceedings{SavitskayaKistaubayevaAkimbekovetal.2013,
  author    = {Savitskaya, Irina S. and Kistaubayeva, Aida S. and Akimbekov, Nuraly S. and Digel, Ilya and Zhubanova, Azhar A.},
  title     = {Performance of Bio-Composite Carbonized Materials in Probiotic Applications},
  series = {World Academy of Science, Engineering and Technology International Journal of Biotechnology and Bioengineering},
  volume    = {7},
  booktitle = {World Academy of Science, Engineering and Technology International Journal of Biotechnology and Bioengineering},
  number    = {7},
  pages     = {685 -- 689},
  year      = {2013},
  language  = {en}
}
@inproceedings{FrotscherRaatschenStaat2012,
  author    = {Frotscher, Ralf and Raatschen, Hans-J{\"u}rgen and Staat, Manfred},
  title     = {Application of an edge-based smoothed finite element method on geometrically non-linear plates of non-linear material},
  series = {Proceedings European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012)},
  booktitle = {Proceedings European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012)},
  editor    = {Eberhardsteiner, J.},
  year      = {2012},
  language  = {en}
}
@article{BialonskiAnsmannKantz2015,
  author    = {Bialonski, Stephan and Ansmann, Gerrit and Kantz, Holger},
  title     = {Data-driven prediction and prevention of extreme events in a spatially extended excitable system},
  series = {Physical Review E},
  volume    = {92},
  journal   = {Physical Review E},
  number    = {4},
  issn      = {2470-0053},
  doi       = {10.1103/PhysRevE.92.042910},
  pages     = {042910},
  year      = {2015},
  language  = {en}
}
@article{AllefeldBialonski2007,
  author    = {Allefeld, Carsten and Bialonski, Stephan},
  title     = {Detecting synchronization clusters in multivariate time series via coarse-graining of Markov chains},
  series = {Physical Review E},
  volume    = {76},
  journal   = {Physical Review E},
  number    = {6},
  issn      = {2470-0053},
  doi       = {10.1103/PhysRevE.76.066207},
  pages     = {066207},
  year      = {2007},
  language  = {en}
}
@article{PhamStaat2013,
  author    = {Pham, Phu Tinh and Staat, Manfred},
  title     = {An Upper Bound Algorithm for Limit and Shakedown Analysis of Bounded Linearly Kinematic Hardening Structures},
  series = {Limit State of Materials and Structures : Direct Methods 2. Saxc{\´e}, G{\´e}ry de (Hrsg.)},
  journal   = {Limit State of Materials and Structures : Direct Methods 2. Saxc{\´e}, G{\´e}ry de (Hrsg.)},
  publisher = {Springer},
  address   = {Dordrecht},
  isbn      = {978-94-007-5424-9},
  pages     = {71 -- 87},
  year      = {2013},
  language  = {en}
}
@book{Laack2000,
  author    = {Laack, Walter van},
  title     = {Key to Eternity / Walter van Laack. [Transl. by Anneliese Wolstenholme]},
  publisher = {van Laack},
  address   = {Aachen},
  isbn      = {978-3-8311-0344-7},
  pages     = {256 S.},
  year      = {2000},
  language  = {en}
}
@article{StaatVu2012,
  author    = {Staat, Manfred and Vu, Duc Khoi},
  title     = {Limit analysis of flaws in pressurized pipes and cylindrical vessels Part II: Circumferential defects},
  series = {Engineering Fracture Mechanics ; 97(2013), H. 1},
  volume    = {97},
  journal   = {Engineering Fracture Mechanics ; 97(2013), H. 1},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0013-7944},
  doi       = {10.1016/j.engfracmech.2012.05.017},
  pages     = {314 -- 333},
  year      = {2012},
  abstract  = {Upper and lower bound theorems of limit analyses have been presented in part I of the paper. Part II starts with the finite element discretization of these theorems and demonstrates how both can be combined in a primal-dual optimization problem. This recently proposed numerical method is used to guide the development of a new class of closed-form limit loads for circumferential defects, which show that only large defects contribute to plastic collapse with a rapid loss of strength with increasing crack sizes. The formulae are compared with primal-dual FEM limit analyses and with burst tests. Even closer predictions are obtained with iterative limit load solutions for the von Mises yield function and for the Tresca yield function. Pressure loading of the faces of interior cracks in thick pipes reduces the collapse load of circumferential defects more than for axial flaws. Axial defects have been treated in part I of the paper.},
  language  = {en}
}
@article{StulpeRuch1998,
  author    = {Stulpe, Werner and Ruch, Ernst},
  title     = {Proof of the Mixing Theorem for Statistical Systems in Classical Physics. Ruch, Ernst; Stulpe, Werner},
  series = {Acta Applicandae Mathematicae. 53 (1998), H. 3},
  journal   = {Acta Applicandae Mathematicae. 53 (1998), H. 3},
  isbn      = {1572-9036},
  pages     = {329 -- 352},
  year      = {1998},
  language  = {en}
}
@article{PourshahidiEngelmannOffenhaeusseretal.2022,
  author    = {Pourshahidi, Ali Mohammad and Engelmann, Ulrich M. and Offenh{\"a}usser, Andreas and Krause, Hans-Joachim},
  title     = {Resolving ambiguities in core size determination of magnetic nanoparticles from magnetic frequency mixing data},
  series = {Journal of Magnetism and Magnetic Materials},
  volume    = {563},
  journal   = {Journal of Magnetism and Magnetic Materials},
  number    = {In progress, Art. No. 169969},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0304-8853},
  doi       = {10.1016/j.jmmm.2022.169969},
  year      = {2022},
  abstract  = {Frequency mixing magnetic detection (FMMD) has been widely utilized as a measurement technique in magnetic immunoassays. It can also be used for the characterization and distinction (also known as "colourization") of different types of magnetic nanoparticles (MNPs) based on their core sizes. In a previous work, it was shown that the large particles contribute most of the FMMD signal. This leads to ambiguities in core size determination from fitting since the contribution of the small-sized particles is almost undetectable among the strong responses from the large ones. In this work, we report on how this ambiguity can be overcome by modelling the signal intensity using the Langevin model in thermodynamic equilibrium including a lognormal core size distribution fL(dc,d0,σ) fitted to experimentally measured FMMD data of immobilized MNPs. For each given median diameter d0, an ambiguous amount of best-fitting pairs of parameters distribution width σ and number of particles Np with R2 > 0.99 are extracted. By determining the samples' total iron mass, mFe, with inductively coupled plasma optical emission spectrometry (ICP-OES), we are then able to identify the one specific best-fitting pair (σ, Np) one uniquely. With this additional externally measured parameter, we resolved the ambiguity in core size distribution and determined the parameters (d0, σ, Np) directly from FMMD measurements, allowing precise MNPs sample characterization.},
  language  = {en}
}