@article{ShinZoellerHolschneideretal.2011,
  author    = {Shin, Seoleun and Z{\"o}ller, Gert and Holschneider, Matthias and Reich, Sebastian},
  title     = {A multigrid solver for modeling complex interseismic stress fields},
  series = {Computers \& geosciences : an international journal devoted to the publication of papers on all aspects of geocomputation and to the distribution of computer programs and test data sets ; an official journal of the International Association for Mathematical Geology},
  volume    = {37},
  journal   = {Computers \& geosciences : an international journal devoted to the publication of papers on all aspects of geocomputation and to the distribution of computer programs and test data sets ; an official journal of the International Association for Mathematical Geology},
  number    = {8},
  publisher = {Elsevier},
  address   = {Oxford},
  issn      = {0098-3004},
  doi       = {10.1016/j.cageo.2010.11.011},
  pages     = {1075 -- 1082},
  year      = {2011},
  abstract  = {We develop a multigrid, multiple time stepping scheme to reduce computational efforts for calculating complex stress interactions in a strike-slip 2D planar fault for the simulation of seismicity. The key elements of the multilevel solver are separation of length scale, grid-coarsening, and hierarchy. In this study the complex stress interactions are split into two parts: the first with a small contribution is computed on a coarse level, and the rest for strong interactions is on a fine level. This partition leads to a significant reduction of the number of computations. The reduction of complexity is even enhanced by combining the multigrid with multiple time stepping. Computational efficiency is enhanced by a factor of 10 while retaining a reasonable accuracy, compared to the original full matrix-vortex multiplication. The accuracy of solution and computational efficiency depend on a given cut-off radius that splits multiplications into the two parts. The multigrid scheme is constructed in such a way that it conserves stress in the entire half-space.},
  language  = {en}
}
@article{ZollerHainzlHolschneideretal.2005,
  author    = {Zoller, Gert and Hainzl, Sebastian and Holschneider, Matthias and Ben-Zion, Yehuda},
  title     = {Aftershocks resulting from creeping sections in a heterogeneous fault},
  issn      = {0094-8276},
  year      = {2005},
  abstract  = {We show that realistic aftershock sequences with space-time characteristics compatible with observations are generated by a model consisting of brittle fault segments separated by creeping zones. The dynamics of the brittle regions is governed by static/kinetic friction, 3D elastic stress transfer and small creep deformation. The creeping parts are characterized by high ongoing creep velocities. These regions store stress during earthquake failures and then release it in the interseismic periods. The resulting postseismic deformation leads to aftershock sequences following the modified Omori law. The ratio of creep coefficients in the brittle and creeping sections determines the duration of the postseismic transients and the exponent p of the modified Omori law},
  language  = {en}
}
@article{SchindlerMoldenhawerStangeetal.2021,
  author    = {Schindler, Daniel and Moldenhawer, Ted and Stange, Maike and Lepro, Valentino and Beta, Carsten and Holschneider, Matthias and Huisinga, Wilhelm},
  title     = {Analysis of protrusion dynamics in amoeboid cell motility by means of regularized contour flows},
  series = {PLoS Computational Biology : a new community journal},
  volume    = {17},
  journal   = {PLoS Computational Biology : a new community journal},
  number    = {8},
  publisher = {PLoS},
  address   = {San Fransisco},
  issn      = {1553-734X},
  doi       = {10.1371/journal.pcbi.1009268},
  pages     = {33},
  year      = {2021},
  abstract  = {Amoeboid cell motility is essential for a wide range of biological processes including wound healing, embryonic morphogenesis, and cancer metastasis. It relies on complex dynamical patterns of cell shape changes that pose long-standing challenges to mathematical modeling and raise a need for automated and reproducible approaches to extract quantitative morphological features from image sequences. Here, we introduce a theoretical framework and a computational method for obtaining smooth representations of the spatiotemporal contour dynamics from stacks of segmented microscopy images. Based on a Gaussian process regression we propose a one-parameter family of regularized contour flows that allows us to continuously track reference points (virtual markers) between successive cell contours. We use this approach to define a coordinate system on the moving cell boundary and to represent different local geometric quantities in this frame of reference. In particular, we introduce the local marker dispersion as a measure to identify localized membrane expansions and provide a fully automated way to extract the properties of such expansions, including their area and growth time. The methods are available as an open-source software package called AmoePy, a Python-based toolbox for analyzing amoeboid cell motility (based on time-lapse microscopy data), including a graphical user interface and detailed documentation. Due to the mathematical rigor of our framework, we envision it to be of use for the development of novel cell motility models. We mainly use experimental data of the social amoeba Dictyostelium discoideum to illustrate and validate our approach. <br /> Author summary Amoeboid motion is a crawling-like cell migration that plays an important key role in multiple biological processes such as wound healing and cancer metastasis. This type of cell motility results from expanding and simultaneously contracting parts of the cell membrane. From fluorescence images, we obtain a sequence of points, representing the cell membrane, for each time step. By using regression analysis on these sequences, we derive smooth representations, so-called contours, of the membrane. Since the number of measurements is discrete and often limited, the question is raised of how to link consecutive contours with each other. In this work, we present a novel mathematical framework in which these links are described by regularized flows allowing a certain degree of concentration or stretching of neighboring reference points on the same contour. This stretching rate, the so-called local dispersion, is used to identify expansions and contractions of the cell membrane providing a fully automated way of extracting properties of these cell shape changes. We applied our methods to time-lapse microscopy data of the social amoeba Dictyostelium discoideum.},
  language  = {en}
}
@article{SchroeterHolschneiderSturm2012,
  author    = {Schr{\"o}ter, M-A and Holschneider, Matthias and Sturm, H.},
  title     = {Analytical and numerical analysis of imaging mechanism of dynamic scanning electron microscopy},
  series = {Nanotechnology},
  volume    = {23},
  journal   = {Nanotechnology},
  number    = {43},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {0957-4484},
  doi       = {10.1088/0957-4484/23/43/435501},
  pages     = {10},
  year      = {2012},
  abstract  = {The direct observation of small oscillating structures with the help of a scanning electron beam is a new approach to study the vibrational dynamics of cantilevers and microelectromechanical systems. In the scanning electron microscope, the conventional signal of secondary electrons (SE, dc part) is separated from the signal response of the SE detector, which is correlated to the respective excitation frequency for vibration by means of a lock-in amplifier. The dynamic response is separated either into images of amplitude and phase shift or into real and imaginary parts. Spatial resolution is limited to the diameter of the electron beam. The sensitivity limit to vibrational motion is estimated to be sub-nanometer for high integration times. Due to complex imaging mechanisms, a theoretical model was developed for the interpretation of the obtained measurements, relating cantilever shapes to interaction processes consisting of incident electron beam, electron-lever interaction, emitted electrons and detector response. Conclusions drawn from this new model are compared with numerical results based on the Euler-Bernoulli equation.},
  language  = {en}
}
@article{SchannerKorteHolschneider2022,
  author    = {Schanner, Maximilian and Korte, Monika and Holschneider, Matthias},
  title     = {ArchKalmag14k: A kalman-filter based global geomagnetic model for the holocene},
  series = {Journal of geophysical research : Solid earth},
  volume    = {127},
  journal   = {Journal of geophysical research : Solid earth},
  number    = {2},
  publisher = {American Geophysical Union},
  address   = {Washington},
  issn      = {2169-9313},
  doi       = {10.1029/2021JB023166},
  pages     = {17},
  year      = {2022},
  abstract  = {We propose a global geomagnetic field model for the last 14 thousand years, based on thermoremanent records. We call the model ArchKalmag14k. ArchKalmag14k is constructed by modifying recently proposed algorithms, based on space-time correlations. Due to the amount of data and complexity of the model, the full Bayesian posterior is numerically intractable. To tackle this, we sequentialize the inversion by implementing a Kalman-filter with a fixed time step. Every step consists of a prediction, based on a degree dependent temporal covariance, and a correction via Gaussian process regression. Dating errors are treated via a noisy input formulation. Cross correlations are reintroduced by a smoothing algorithm and model parameters are inferred from the data. Due to the specific statistical nature of the proposed algorithms, the model comes with space and time-dependent uncertainty estimates. The new model ArchKalmag14k shows less variation in the large-scale degrees than comparable models. Local predictions represent the underlying data and agree with comparable models, if the location is sampled well. Uncertainties are bigger for earlier times and in regions of sparse data coverage. We also use ArchKalmag14k to analyze the appearance and evolution of the South Atlantic anomaly together with reverse flux patches at the core-mantle boundary, considering the model uncertainties. While we find good agreement with earlier models for recent times, our model suggests a different evolution of intensity minima prior to 1650 CE. In general, our results suggest that prior to 6000 BCE the data is not sufficient to support global models.},
  language  = {en}
}
@article{HolschneiderNarteauShebalinetal.2012,
  author    = {Holschneider, Matthias and Narteau, C. and Shebalin, P. and Peng, Z. and Schorlemmer, Danijel},
  title     = {Bayesian analysis of the modified Omori law},
  series = {Journal of geophysical research : Solid earth},
  volume    = {117},
  journal   = {Journal of geophysical research : Solid earth},
  number    = {6089},
  publisher = {American Geophysical Union},
  address   = {Washington},
  issn      = {2169-9313},
  doi       = {10.1029/2011JB009054},
  pages     = {12},
  year      = {2012},
  abstract  = {In order to examine variations in aftershock decay rate, we propose a Bayesian framework to estimate the {K, c, p}-values of the modified Omori law (MOL), lambda(t) = K(c + t)(-p). The Bayesian setting allows not only to produce a point estimator of these three parameters but also to assess their uncertainties and posterior dependencies with respect to the observed aftershock sequences. Using a new parametrization of the MOL, we identify the trade-off between the c and p-value estimates and discuss its dependence on the number of aftershocks. Then, we analyze the influence of the catalog completeness interval [t(start), t(stop)] on the various estimates. To test this Bayesian approach on natural aftershock sequences, we use two independent and non-overlapping aftershock catalogs of the same earthquakes in Japan. Taking into account the posterior uncertainties, we show that both the handpicked (short times) and the instrumental (long times) catalogs predict the same ranges of parameter values. We therefore conclude that the same MOL may be valid over short and long times.},
  language  = {en}
}
@article{MakaravaBenmehdiHolschneider2011,
  author    = {Makarava, Natallia and Benmehdi, Sabah and Holschneider, Matthias},
  title     = {Bayesian estimation of self-similarity exponent},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {84},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {2},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {1539-3755},
  doi       = {10.1103/PhysRevE.84.021109},
  pages     = {9},
  year      = {2011},
  abstract  = {In this study we propose a Bayesian approach to the estimation of the Hurst exponent in terms of linear mixed models. Even for unevenly sampled signals and signals with gaps, our method is applicable. We test our method by using artificial fractional Brownian motion of different length and compare it with the detrended fluctuation analysis technique. The estimation of the Hurst exponent of a Rosenblatt process is shown as an example of an H-self-similar process with non-Gaussian dimensional distribution. Additionally, we perform an analysis with real data, the Dow-Jones Industrial Average closing values, and analyze its temporal variation of the Hurst exponent.},
  language  = {en}
}
@article{MakaravaBettenbuehlEngbertetal.2012,
  author    = {Makarava, Natallia and Bettenb{\"u}hl, Mario and Engbert, Ralf and Holschneider, Matthias},
  title     = {Bayesian estimation of the scaling parameter of fixational eye movements},
  series = {epl : a letters journal exploring the frontiers of physics},
  volume    = {100},
  journal   = {epl : a letters journal exploring the frontiers of physics},
  number    = {4},
  publisher = {EDP Sciences},
  address   = {Mulhouse},
  issn      = {0295-5075},
  doi       = {10.1209/0295-5075/100/40003},
  pages     = {6},
  year      = {2012},
  abstract  = {In this study we re-evaluate the estimation of the self-similarity exponent of fixational eye movements using Bayesian theory. Our analysis is based on a subsampling decomposition, which permits an analysis of the signal up to some scale factor. We demonstrate that our approach can be applied to simulated data from mathematical models of fixational eye movements to distinguish the models' properties reliably.},
  language  = {en}
}
@article{BenmehdiMakaravaBenhamidoucheetal.2011,
  author    = {Benmehdi, Sabah and Makarava, Natallia and Benhamidouche, N. and Holschneider, Matthias},
  title     = {Bayesian estimation of the self-similarity exponent of the Nile River fluctuation},
  series = {Nonlinear processes in geophysics},
  volume    = {18},
  journal   = {Nonlinear processes in geophysics},
  number    = {3},
  publisher = {Copernicus},
  address   = {G{\"o}ttingen},
  issn      = {1023-5809},
  doi       = {10.5194/npg-18-441-2011},
  pages     = {441 -- 446},
  year      = {2011},
  abstract  = {The aim of this paper is to estimate the Hurst parameter of Fractional Gaussian Noise (FGN) using Bayesian inference. We propose an estimation technique that takes into account the full correlation structure of this process. Instead of using the integrated time series and then applying an estimator for its Hurst exponent, we propose to use the noise signal directly. As an application we analyze the time series of the Nile River, where we find a posterior distribution which is compatible with previous findings. In addition, our technique provides natural error bars for the Hurst exponent.},
  language  = {en}
}
@article{BernerTrauthHolschneider2022,
  author    = {Berner, Nadine and Trauth, Martin H. and Holschneider, Matthias},
  title     = {Bayesian inference about Plio-Pleistocene climate transitions in Africa},
  series = {Quaternary science reviews : the international multidisciplinary research and review journal},
  volume    = {277},
  journal   = {Quaternary science reviews : the international multidisciplinary research and review journal},
  publisher = {Elsevier},
  address   = {Oxford},
  issn      = {0277-3791},
  doi       = {10.1016/j.quascirev.2021.107287},
  pages     = {12},
  year      = {2022},
  abstract  = {During the last 5 Ma the Earth's ocean-atmosphere system passed through several major transitions, many of which are discussed as possible triggers for human evolution. A classic in this context is the possible influence of the closure of the Panama Strait, the intensification of Northern Hemisphere Glaciation, a stepwise increase in aridity in Africa, and the first appearance of the genus Homo about 2.5 - 2.7 Ma ago. Apart from the fact that the correlation between these events does not necessarily imply causality, many attempts to establish a relationship between climate and evolution fail due to the challenge of precisely localizing an a priori unknown number of changes potentially underlying complex climate records. The kernel-based Bayesian inference approach applied here allows inferring the location, generic shape, and temporal scale of multiple transitions in established records of Plio-Pleistocene African climate. By defining a transparent probabilistic analysis strategy, we are able to identify conjoint changes occurring across the investigated terrigenous dust records from Ocean Drilling Programme (ODP) sites in the Atlantic Ocean (ODP 659), Arabian (ODP 721/722) and Mediterranean Sea (ODP 967). The study indicates a two-step transition in the African climate proxy records at (2.35-2.10) Ma and (1.70 - 1.50) Ma, that may be associated with the reorganization of the Hadley-Walker Circulation. .},
  language  = {en}
}