@article{Buerger2017,
  author    = {B{\"u}rger, Gerhard},
  title     = {On trend detection},
  series = {Hydrological processes},
  volume    = {31},
  journal   = {Hydrological processes},
  publisher = {Wiley},
  address   = {Hoboken},
  issn      = {0885-6087},
  doi       = {10.1002/hyp.11280},
  pages     = {4039 -- 4042},
  year      = {2017},
  abstract  = {A main obstacle to trend detection in time series occurs when they are autocorrelated. By reducing the effective sample size of a series, autocorrelation leads to decreased trend significance. Numerous recipes attempt to mitigate the effect of autocorrelation, either by adjusting for the reduced effective sample size or by removing the autocorrelated components of a series. This short note deals with the latter, also called prewhitening (PW). It is known that removal of autocorrelation also removes part of the trend, which may affect the signal-to-noise ratio. Two popular methods have dealt with this problem, the trend-free prewhitening (TFPW) and the iterative prewhitening. Although it is generally accepted that both methods reduce the adverse effects of PW on the trend magnitude, corresponding effects on statistical significance have not been clearly stated for TFPW. Using a Monte Carlo approach, it is demonstrated that both methods entail quite different Type-I error rates. The iterative prewhitening produces rates that are generally close to the nominal significance level. The TFPW, however, shows very high Type-I error rates with increasing autocorrelation. The corresponding rate of false trend detections is unacceptable for applications, so that published trends based on TFPW need to be reassessed.},
  language  = {en}
}
@article{DieterichLindemannMoskoppetal.2022,
  author    = {Dieterich, Peter and Lindemann, Otto and Moskopp, Mats Leif and Tauzin, Sebastien and Huttenlocher, Anna and Klages, Rainer and Chechkin, Aleksei V. and Schwab, Albrecht},
  title     = {Anomalous diffusion and asymmetric tempering memory in neutrophil chemotaxis},
  series = {PLoS Computational Biology : a new community journal},
  volume    = {18},
  journal   = {PLoS Computational Biology : a new community journal},
  number    = {5},
  publisher = {PLoS},
  address   = {San Fransisco},
  issn      = {1553-734X},
  doi       = {10.1371/journal.pcbi.1010089},
  pages     = {26},
  year      = {2022},
  abstract  = {Neutrophil granulocytes are essential for the first host defense. After leaving the blood circulation they migrate efficiently towards sites of inflammation. They are guided by chemoattractants released from cells within the inflammatory foci. On a cellular level, directional migration is a consequence of cellular front-rear asymmetry which is induced by the concentration gradient of the chemoattractants. The generation and maintenance of this asymmetry, however, is not yet fully understood. Here we analyzed the paths of chemotacting neutrophils with different stochastic models to gain further insight into the underlying mechanisms. Wildtype chemotacting neutrophils show an anomalous superdiffusive behavior. CXCR2 blockade and TRPC6-knockout cause the tempering of temporal correlations and a reduction of chemotaxis. Importantly, such tempering is found both in vitro and in vivo. These findings indicate that the maintenance of anomalous dynamics is crucial for chemotactic behavior and the search efficiency of neutrophils. The motility of neutrophils and their ability to sense and to react to chemoattractants in their environment are of central importance for the innate immunity. Neutrophils are guided towards sites of inflammation following the activation of G-protein coupled chemoattractant receptors such as CXCR2 whose signaling strongly depends on the activity of Ca2+ permeable TRPC6 channels. It is the aim of this study to analyze data sets obtained in vitro (murine neutrophils) and in vivo (zebrafish neutrophils) with a stochastic mathematical model to gain deeper insight into the underlying mechanisms. The model is based on the analysis of trajectories of individual neutrophils. Bayesian data analysis, including the covariances of positions for fractional Brownian motion as well as for exponentially and power-law tempered model variants, allows the estimation of parameters and model selection. Our model-based analysis reveals that wildtype neutrophils show pure superdiffusive fractional Brownian motion. This so-called anomalous dynamics is characterized by temporal long-range correlations for the movement into the direction of the chemotactic CXCL1 gradient. Pure superdiffusion is absent vertically to this gradient. This points to an asymmetric 'memory' of the migratory machinery, which is found both in vitro and in vivo. CXCR2 blockade and TRPC6-knockout cause tempering of temporal correlations in the chemotactic gradient. This can be interpreted as a progressive loss of memory, which leads to a marked reduction of chemotaxis and search efficiency of neutrophils. In summary, our findings indicate that spatially differential regulation of anomalous dynamics appears to play a central role in guiding efficient chemotactic behavior.},
  language  = {en}
}
@article{NoonanFlemingTuckeretal.2020,
  author    = {Noonan, Michael J. and Fleming, Christen H. and Tucker, Marlee A. and Kays, Roland and Harrison, Autumn-Lynn and Crofoot, Margaret C. and Abrahms, Briana and Alberts, Susan C. and Ali, Abdullahi H. and Blaum, Niels},
  title     = {Effects of body size on estimation of mammalian area requirements},
  series = {Conservation Biology},
  volume    = {34},
  journal   = {Conservation Biology},
  number    = {4},
  publisher = {Wiley-Blackwell},
  address   = {Oxford},
  pages     = {12},
  year      = {2020},
  abstract  = {Accurately quantifying species' area requirements is a prerequisite for effective area-based conservation. This typically involves collecting tracking data on species of interest and then conducting home-range analyses. Problematically, autocorrelation in tracking data can result in space needs being severely underestimated. Based on the previous work, we hypothesized the magnitude of underestimation varies with body mass, a relationship that could have serious conservation implications. To evaluate this hypothesis for terrestrial mammals, we estimated home-range areas with global positioning system (GPS) locations from 757 individuals across 61 globally distributed mammalian species with body masses ranging from 0.4 to 4000 kg. We then applied block cross-validation to quantify bias in empirical home-range estimates. Area requirements of mammals <10 kg were underestimated by a mean approximately15\%, and species weighing approximately100 kg were underestimated by approximately50\% on average. Thus, we found area estimation was subject to autocorrelation-induced bias that was worse for large species. Combined with the fact that extinction risk increases as body mass increases, the allometric scaling of bias we observed suggests the most threatened species are also likely to be those with the least accurate home-range estimates. As a correction, we tested whether data thinning or autocorrelation-informed home-range estimation minimized the scaling effect of autocorrelation on area estimates. Data thinning required an approximately93\% data loss to achieve statistical independence with 95\% confidence and was, therefore, not a viable solution. In contrast, autocorrelation-informed home-range estimation resulted in consistently accurate estimates irrespective of mass. When relating body mass to home range size, we detected that correcting for autocorrelation resulted in a scaling exponent significantly >1, meaning the scaling of the relationship changed substantially at the upper end of the mass spectrum.},
  language  = {en}
}
@misc{NoonanFlemingTuckeretal.2020,
  author    = {Noonan, Michael J. and Fleming, Christen H. and Tucker, Marlee A. and Kays, Roland and Harrison, Autumn-Lynn and Crofoot, Margaret C. and Abrahms, Briana and Alberts, Susan C. and Ali, Abdullahi H. and Blaum, Niels},
  title     = {Effects of body size on estimation of mammalian area requirements},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {4},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-52682},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-526824},
  pages     = {14},
  year      = {2020},
  abstract  = {Accurately quantifying species' area requirements is a prerequisite for effective area-based conservation. This typically involves collecting tracking data on species of interest and then conducting home-range analyses. Problematically, autocorrelation in tracking data can result in space needs being severely underestimated. Based on the previous work, we hypothesized the magnitude of underestimation varies with body mass, a relationship that could have serious conservation implications. To evaluate this hypothesis for terrestrial mammals, we estimated home-range areas with global positioning system (GPS) locations from 757 individuals across 61 globally distributed mammalian species with body masses ranging from 0.4 to 4000 kg. We then applied block cross-validation to quantify bias in empirical home-range estimates. Area requirements of mammals <10 kg were underestimated by a mean approximately15\%, and species weighing approximately100 kg were underestimated by approximately50\% on average. Thus, we found area estimation was subject to autocorrelation-induced bias that was worse for large species. Combined with the fact that extinction risk increases as body mass increases, the allometric scaling of bias we observed suggests the most threatened species are also likely to be those with the least accurate home-range estimates. As a correction, we tested whether data thinning or autocorrelation-informed home-range estimation minimized the scaling effect of autocorrelation on area estimates. Data thinning required an approximately93\% data loss to achieve statistical independence with 95\% confidence and was, therefore, not a viable solution. In contrast, autocorrelation-informed home-range estimation resulted in consistently accurate estimates irrespective of mass. When relating body mass to home range size, we detected that correcting for autocorrelation resulted in a scaling exponent significantly >1, meaning the scaling of the relationship changed substantially at the upper end of the mass spectrum.},
  language  = {en}
}
@phdthesis{Zaks2001,
  author    = {Zaks, Michael A.},
  title     = {Fractal Fourier spectra in dynamical systems},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-0000500},
  school      = {Universit{\"a}t Potsdam},
  year      = {2001},
  abstract  = {Eine klassische Art, die Dynamik nichtlinearer Systeme zu beschreiben, besteht in der Analyse ihrer Fourierspektren. F{\"u}r periodische und quasiperiodische Prozesse besteht das Fourierspektrum nur aus diskreten Deltafunktionen. Das Spektrum einer chaotischen Bewegung ist hingegen durch das Vorhandensein einer stetigen Komponente gekennzeichnet. In der Arbeit geht es um einen eigenartigen, weder regul{\"a}ren noch vollst{\"a}ndig chaotischen Zustand mit sogenanntem singul{\"a}rstetigen Leistungsspektrum. Unsere Analyse ergab verschiedene F{\"a}lle aus weit auseinanderliegenden Gebieten, in denen singul{\"a}r stetige (fraktale) Spektren auftreten. Die Beispiele betreffen sowohl physikalische Prozesse, die auf iterierte diskrete Abbildungen oder gar symbolische Sequenzen reduzierbar sind, wie auch Prozesse, deren Beschreibung auf den gew{\"o}hnlichen oder partiellen Differentialgleichungen basiert.},
  subject      = {Nichtlineares dynamisches System / Harmonische Analyse / Fraktal},
  language  = {en}
}