@article{KraemerMarwan2019,
  author    = {Kr{\"a}mer, Hauke Kai and Marwan, Norbert},
  title     = {Border effect corrections for diagonal line based recurrence quantification analysis measures},
  series = {Modern physics letters : A, Particles and fields, gravitation, cosmology, nuclear physics},
  volume    = {383},
  journal   = {Modern physics letters : A, Particles and fields, gravitation, cosmology, nuclear physics},
  number    = {34},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0375-9601},
  doi       = {10.1016/j.physleta.2019.125977},
  pages     = {16},
  year      = {2019},
  abstract  = {Recurrence Quantification Analysis (RQA) defines a number of quantifiers, which base upon diagonal line structures in the recurrence plot (RP). Due to the finite size of an RP, these lines can be cut by the borders of the RP and, thus, bias the length distribution of diagonal lines and, consequently, the line based RQA measures. In this letter we investigate the impact of the mentioned border effects and of the thickening of diagonal lines in an RP (caused by tangential motion) on the estimation of the diagonal line length distribution, quantified by its entropy. Although a relation to the Lyapunov spectrum is theoretically expected, the mentioned entropy yields contradictory results in many studies. Here we summarize correction schemes for both, the border effects and the tangential motion and systematically compare them to methods from the literature. We show that these corrections lead to the expected behavior of the diagonal line length entropy, in particular meaning zero values in case of a regular motion and positive values for chaotic motion. Moreover, we test these methods under noisy conditions, in order to supply practical tools for applied statistical research.},
  language  = {en}
}
@article{FahleHohenbrinkDietrichetal.2015,
  author    = {Fahle, Marcus and Hohenbrink, Tobias Ludwig and Dietrich, Ottfried and Lischeid, Gunnar},
  title     = {Temporal variability of the optimal monitoring setup assessed using information theory},
  series = {Water resources research},
  volume    = {51},
  journal   = {Water resources research},
  number    = {9},
  publisher = {American Geophysical Union},
  address   = {Washington},
  issn      = {0043-1397},
  doi       = {10.1002/2015WR017137},
  pages     = {7723 -- 7743},
  year      = {2015},
  abstract  = {Hydrology is rich in methods that use information theory to evaluate monitoring networks. Yet in most existing studies, only the available data set as a whole is used, which neglects the intraannual variability of the hydrological system. In this paper, we demonstrate how this variability can be considered by extending monitoring evaluation to subsets of the available data. Therefore, we separately evaluated time windows of fixed length, which were shifted through the data set, and successively extended time windows. We used basic information theory measures and a greedy ranking algorithm based on the criterion of maximum information/minimum redundancy. The network investigated monitored surface and groundwater levels at quarter-hourly intervals and was located at an artificially drained lowland site in the Spreewald region in north-east Germany. The results revealed that some of the monitoring stations were of value permanently while others were needed only temporally. The prevailing meteorological conditions, particularly the amount of precipitation, affected the degree of similarity between the water levels measured. The hydrological system tended to act more individually during periods of no or little rainfall. The optimal monitoring setup, its stability, and the monitoring effort necessary were influenced by the meteorological forcing. Altogether, the methodology presented can help achieve a monitoring network design that has a more even performance or covers the conditions of interest (e.g., floods or droughts) best.},
  language  = {en}
}