@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{RoppLesurBaerenzungetal.2020, author = {Ropp, Guillaume and Lesur, Vincent and B{\"a}renzung, Julien and Holschneider, Matthias}, title = {Sequential modelling of the Earth's core magnetic field}, series = {Earth, Planets and Space}, volume = {72}, journal = {Earth, Planets and Space}, number = {1}, publisher = {Springer}, address = {New York}, issn = {1880-5981}, doi = {10.1186/s40623-020-01230-1}, pages = {15}, year = {2020}, abstract = {We describe a new, original approach to the modelling of the Earth's magnetic field. The overall objective of this study is to reliably render fast variations of the core field and its secular variation. This method combines a sequential modelling approach, a Kalman filter, and a correlation-based modelling step. Sources that most significantly contribute to the field measured at the surface of the Earth are modelled. Their separation is based on strong prior information on their spatial and temporal behaviours. We obtain a time series of model distributions which display behaviours similar to those of recent models based on more classic approaches, particularly at large temporal and spatial scales. Interesting new features and periodicities are visible in our models at smaller time and spatial scales. An important aspect of our method is to yield reliable error bars for all model parameters. These errors, however, are only as reliable as the description of the different sources and the prior information used are realistic. Finally, we used a slightly different version of our method to produce candidate models for the thirteenth edition of the International Geomagnetic Reference Field.}, language = {en} } @article{SchannerMauerbergerKorteetal.2021, author = {Schanner, Maximilian Arthus and Mauerberger, Stefan and Korte, Monika and Holschneider, Matthias}, title = {Correlation based time evolution of the archeomagnetic field}, series = {Journal of geophysical research : JGR ; an international quarterly. B, Solid earth}, volume = {126}, journal = {Journal of geophysical research : JGR ; an international quarterly. B, Solid earth}, number = {7}, publisher = {American Geophysical Union}, address = {Washington}, issn = {2169-9313}, doi = {10.1029/2020JB021548}, pages = {22}, year = {2021}, abstract = {In a previous study, a new snapshot modeling concept for the archeomagnetic field was introduced (Mauerberger et al., 2020, ). By assuming a Gaussian process for the geomagnetic potential, a correlation-based algorithm was presented, which incorporates a closed-form spatial correlation function. This work extends the suggested modeling strategy to the temporal domain. A space-time correlation kernel is constructed from the tensor product of the closed-form spatial correlation kernel with a squared exponential kernel in time. Dating uncertainties are incorporated into the modeling concept using a noisy input Gaussian process. All but one modeling hyperparameters are marginalized, to reduce their influence on the outcome and to translate their variability to the posterior variance. The resulting distribution incorporates uncertainties related to dating, measurement and modeling process. Results from application to archeomagnetic data show less variation in the dipole than comparable models, but are in general agreement with previous findings.}, language = {en} } @article{BaerenzungHolschneiderWichtetal.2020, author = {Baerenzung, Julien and Holschneider, Matthias and Wicht, Johannes and Lesur, Vincent and Sanchez, Sabrina}, title = {The Kalmag model as a candidate for IGRF-13}, series = {Earth, planets and space}, volume = {72}, journal = {Earth, planets and space}, number = {1}, publisher = {Springer}, address = {New York}, issn = {1880-5981}, doi = {10.1186/s40623-020-01295-y}, pages = {13}, year = {2020}, abstract = {We present a new model of the geomagnetic field spanning the last 20 years and called Kalmag. Deriving from the assimilation of CHAMP and Swarm vector field measurements, it separates the different contributions to the observable field through parameterized prior covariance matrices. To make the inverse problem numerically feasible, it has been sequentialized in time through the combination of a Kalman filter and a smoothing algorithm. The model provides reliable estimates of past, present and future mean fields and associated uncertainties. The version presented here is an update of our IGRF candidates; the amount of assimilated data has been doubled and the considered time window has been extended from [2000.5, 2019.74] to [2000.5, 2020.33].}, language = {en} } @article{MoldenhawerMorenoSchindleretal.2022, author = {Moldenhawer, Ted and Moreno, Eduardo and Schindler, Daniel and Flemming, Sven and Holschneider, Matthias and Huisinga, Wilhelm and Alonso, Sergio and Beta, Carsten}, title = {Spontaneous transitions between amoeboid and keratocyte-like modes of migration}, series = {Frontiers in Cell and Developmental Biology}, volume = {10}, journal = {Frontiers in Cell and Developmental Biology}, publisher = {Frontiers Media}, address = {Lausanne}, issn = {2296-634X}, doi = {10.3389/fcell.2022.898351}, pages = {13}, year = {2022}, abstract = {The motility of adherent eukaryotic cells is driven by the dynamics of the actin cytoskeleton. Despite the common force-generating actin machinery, different cell types often show diverse modes of locomotion that differ in their shape dynamics, speed, and persistence of motion. Recently, experiments in Dictyostelium discoideum have revealed that different motility modes can be induced in this model organism, depending on genetic modifications, developmental conditions, and synthetic changes of intracellular signaling. Here, we report experimental evidence that in a mutated D. discoideum cell line with increased Ras activity, switches between two distinct migratory modes, the amoeboid and fan-shaped type of locomotion, can even spontaneously occur within the same cell. We observed and characterized repeated and reversible switchings between the two modes of locomotion, suggesting that they are distinct behavioral traits that coexist within the same cell. We adapted an established phenomenological motility model that combines a reaction-diffusion system for the intracellular dynamics with a dynamic phase field to account for our experimental findings.}, language = {en} } @article{MauerbergerSchannerKorteetal.2020, author = {Mauerberger, Stefan and Schanner, Maximilian Arthus and Korte, Monika and Holschneider, Matthias}, title = {Correlation based snapshot models of the archeomagnetic field}, series = {Geophysical journal international}, volume = {223}, journal = {Geophysical journal international}, number = {1}, publisher = {Oxford Univ. Press}, address = {Oxford}, issn = {0956-540X}, doi = {10.1093/gji/ggaa336}, pages = {648 -- 665}, year = {2020}, abstract = {For the time stationary global geomagnetic field, a new modelling concept is presented. A Bayesian non-parametric approach provides realistic location dependent uncertainty estimates. Modelling related variabilities are dealt with systematically by making little subjective apriori assumptions. Rather than parametrizing the model by Gauss coefficients, a functional analytic approach is applied. The geomagnetic potential is assumed a Gaussian process to describe a distribution over functions. Apriori correlations are given by an explicit kernel function with non-informative dipole contribution. A refined modelling strategy is proposed that accommodates non-linearities of archeomagnetic observables: First, a rough field estimate is obtained considering only sites that provide full field vector records. Subsequently, this estimate supports the linearization that incorporates the remaining incomplete records. The comparison of results for the archeomagnetic field over the past 1000 yr is in general agreement with previous models while improved model uncertainty estimates are provided.}, 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.
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{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} } @article{SharmaHainzlZoelleretal.2020, author = {Sharma, Shubham and Hainzl, Sebastian and Z{\"o}ller, Gert and Holschneider, Matthias}, title = {Is Coulomb stress the best choice for aftershock forecasting?}, series = {Journal of geophysical research : Solid earth}, volume = {125}, journal = {Journal of geophysical research : Solid earth}, number = {9}, publisher = {American Geophysical Union}, address = {Washington}, issn = {2169-9313}, doi = {10.1029/2020JB019553}, pages = {12}, year = {2020}, abstract = {The Coulomb failure stress (CFS) criterion is the most commonly used method for predicting spatial distributions of aftershocks following large earthquakes. However, large uncertainties are always associated with the calculation of Coulomb stress change. The uncertainties mainly arise due to nonunique slip inversions and unknown receiver faults; especially for the latter, results are highly dependent on the choice of the assumed receiver mechanism. Based on binary tests (aftershocks yes/no), recent studies suggest that alternative stress quantities, a distance-slip probabilistic model as well as deep neural network (DNN) approaches, all are superior to CFS with predefined receiver mechanism. To challenge this conclusion, which might have large implications, we use 289 slip inversions from SRCMOD database to calculate more realistic CFS values for a layered half-space and variable receiver mechanisms. We also analyze the effect of the magnitude cutoff, grid size variation, and aftershock duration to verify the use of receiver operating characteristic (ROC) analysis for the ranking of stress metrics. The observations suggest that introducing a layered half-space does not improve the stress maps and ROC curves. However, results significantly improve for larger aftershocks and shorter time periods but without changing the ranking. We also go beyond binary testing and apply alternative statistics to test the ability to estimate aftershock numbers, which confirm that simple stress metrics perform better than the classic Coulomb failure stress calculations and are also better than the distance-slip probabilistic model.}, language = {en} } @article{CotroneiDiSalvoHolschneideretal.2017, author = {Cotronei, Mariantonia and Di Salvo, Rosa and Holschneider, Matthias and Puccio, Luigia}, title = {Interpolation in reproducing kernel Hilbert spaces based on random subdivision schemes}, series = {Journal of computational and applied mathematics}, volume = {311}, journal = {Journal of computational and applied mathematics}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0377-0427}, doi = {10.1016/j.cam.2016.08.002}, pages = {342 -- 353}, year = {2017}, abstract = {In this paper we present a Bayesian framework for interpolating data in a reproducing kernel Hilbert space associated with a random subdivision scheme, where not only approximations of the values of a function at some missing points can be obtained, but also uncertainty estimates for such predicted values. This random scheme generalizes the usual subdivision by taking into account, at each level, some uncertainty given in terms of suitably scaled noise sequences of i.i.d. Gaussian random variables with zero mean and given variance, and generating, in the limit, a Gaussian process whose correlation structure is characterized and used for computing realizations of the conditional posterior distribution. The hierarchical nature of the procedure may be exploited to reduce the computational cost compared to standard techniques in the case where many prediction points need to be considered.}, language = {en} }