@phdthesis{Schwarz2020,
  author    = {Schwarz, Michael},
  title     = {Nodal domains and boundary representation for Dirichlet forms},
  school      = {Universit{\"a}t Potsdam},
  pages     = {164},
  year      = {2020},
  language  = {en}
}
@article{SeeligRabeMalemShinitskietal.2020,
  author    = {Seelig, Stefan A. and Rabe, Maximilian Michael and Malem-Shinitski, Noa and Risse, Sarah and Reich, Sebastian and Engbert, Ralf},
  title     = {Bayesian parameter estimation for the SWIFT model of eye-movement control during reading},
  series = {Journal of mathematical psychology},
  volume    = {95},
  journal   = {Journal of mathematical psychology},
  publisher = {Elsevier},
  address   = {San Diego},
  issn      = {0022-2496},
  doi       = {10.1016/j.jmp.2019.102313},
  pages     = {32},
  year      = {2020},
  abstract  = {Process-oriented theories of cognition must be evaluated against time-ordered observations. Here we present a representative example for data assimilation of the SWIFT model, a dynamical model of the control of fixation positions and fixation durations during natural reading of single sentences. First, we develop and test an approximate likelihood function of the model, which is a combination of a spatial, pseudo-marginal likelihood and a temporal likelihood obtained by probability density approximation Second, we implement a Bayesian approach to parameter inference using an adaptive Markov chain Monte Carlo procedure. Our results indicate that model parameters can be estimated reliably for individual subjects. We conclude that approximative Bayesian inference represents a considerable step forward for computational models of eye-movement control, where modeling of individual data on the basis of process-based dynamic models has not been possible so far.},
  language  = {en}
}
@article{WiljesTong2020,
  author    = {Wiljes, Jana de and Tong, Xin T.},
  title     = {Analysis of a localised nonlinear ensemble Kalman Bucy filter with complete and accurate observations},
  series = {Nonlinearity},
  volume    = {33},
  journal   = {Nonlinearity},
  number    = {9},
  publisher = {IOP Publ.},
  address   = {Bristol},
  issn      = {0951-7715},
  doi       = {10.1088/1361-6544/ab8d14},
  pages     = {4752 -- 4782},
  year      = {2020},
  abstract  = {Concurrent observation technologies have made high-precision real-time data available in large quantities. Data assimilation (DA) is concerned with how to combine this data with physical models to produce accurate predictions. For spatial-temporal models, the ensemble Kalman filter with proper localisation techniques is considered to be a state-of-the-art DA methodology. This article proposes and investigates a localised ensemble Kalman Bucy filter for nonlinear models with short-range interactions. We derive dimension-independent and component-wise error bounds and show the long time path-wise error only has logarithmic dependence on the time range. The theoretical results are verified through some simple numerical tests.},
  language  = {en}
}
@article{PurintonBookhagen2020,
  author    = {Purinton, Benjamin and Bookhagen, Bodo},
  title     = {Multiband (X, C, L) radar amplitude analysis for a mixed sand- and gravel-bed river in the eastern Central Andes},
  series = {Remote sensing of environment : an interdisciplinary journal},
  volume    = {246},
  journal   = {Remote sensing of environment : an interdisciplinary journal},
  publisher = {Elsevier},
  address   = {New York},
  issn      = {0034-4257},
  doi       = {10.1016/j.rse.2020.111799},
  pages     = {16},
  year      = {2020},
  abstract  = {Synthetic Aperture Radar (SAR) amplitude measurements from spaceborne sensors are sensitive to surface roughness conditions near their radar wavelength. These backscatter signals are often exploited to assess the roughness of plowed agricultural fields and water surfaces, and less so to complex, heterogeneous geological surfaces. The bedload of mixed sand- and gravel-bed rivers can be considered a mixture of smooth (compacted sand) and rough (gravel) surfaces. Here, we assess backscatter gradients over a large high-mountain alluvial river in the eastern Central Andes with aerially exposed sand and gravel bedload using X-band TerraSAR-X/TanDEM-X, C-band Sentinel-1, and L-band ALOS-2 PALSAR-2 radar scenes. In a first step, we present theory and hypotheses regarding radar response to an alluvial channel bed. We test our hypotheses by comparing backscatter responses over vegetation-free endmember surfaces from inside and outside of the active channel-bed area. We then develop methods to extract smoothed backscatter gradients downstream along the channel using kernel density estimates. In a final step, the local variability of sand-dominated patches is analyzed using Fourier frequency analysis, by fitting stretched-exponential and power-law regression models to the 2-D power spectrum of backscatter amplitude. We find a large range in backscatter depending on the heterogeneity of contiguous smooth- and rough-patches of bedload material. The SAR amplitude signal responds primarily to the fraction of smooth-sand bedload, but is further modified by gravel elements. The sensitivity to gravel is more apparent in longer wavelength L-band radar, whereas C- and X-band is sensitive only to sand variability. Because the spatial extent of smooth sand patches in our study area is typically< 50 m, only higher resolution sensors (e.g., TerraSAR-X/TanDEM-X) are useful for power spectrum analysis. Our results show the potential for mapping sand-gravel transitions and local geomorphic complexity in alluvial rivers with aerially exposed bedload using SAR amplitude.},
  language  = {en}
}
@article{MalemShinitskiOpperReichetal.2020,
  author    = {Malem-Shinitski, Noa and Opper, Manfred and Reich, Sebastian and Schwetlick, Lisa and Seelig, Stefan A. and Engbert, Ralf},
  title     = {A mathematical model of local and global attention in natural scene viewing},
  series = {PLoS Computational Biology : a new community journal},
  volume    = {16},
  journal   = {PLoS Computational Biology : a new community journal},
  number    = {12},
  publisher = {PLoS},
  address   = {San Fransisco},
  issn      = {1553-734X},
  doi       = {10.1371/journal.pcbi.1007880},
  pages     = {21},
  year      = {2020},
  abstract  = {Author summary <br /> Switching between local and global attention is a general strategy in human information processing. We investigate whether this strategy is a viable approach to model sequences of fixations generated by a human observer in a free viewing task with natural scenes. Variants of the basic model are used to predict the experimental data based on Bayesian inference. Results indicate a high predictive power for both aggregated data and individual differences across observers. The combination of a novel model with state-of-the-art Bayesian methods lends support to our two-state model using local and global internal attention states for controlling eye movements. <br /> Understanding the decision process underlying gaze control is an important question in cognitive neuroscience with applications in diverse fields ranging from psychology to computer vision. The decision for choosing an upcoming saccade target can be framed as a selection process between two states: Should the observer further inspect the information near the current gaze position (local attention) or continue with exploration of other patches of the given scene (global attention)? Here we propose and investigate a mathematical model motivated by switching between these two attentional states during scene viewing. The model is derived from a minimal set of assumptions that generates realistic eye movement behavior. We implemented a Bayesian approach for model parameter inference based on the model's likelihood function. In order to simplify the inference, we applied data augmentation methods that allowed the use of conjugate priors and the construction of an efficient Gibbs sampler. This approach turned out to be numerically efficient and permitted fitting interindividual differences in saccade statistics. Thus, the main contribution of our modeling approach is two-fold; first, we propose a new model for saccade generation in scene viewing. Second, we demonstrate the use of novel methods from Bayesian inference in the field of scan path modeling.},
  language  = {en}
}
@article{PornsawadSungcharoenBoeckmann2020,
  author    = {Pornsawad, Pornsarp and Sungcharoen, Parada and B{\"o}ckmann, Christine},
  title     = {Convergence rate of the modified Landweber method for solving inverse potential problems},
  series = {Mathematics : open access journal},
  volume    = {8},
  journal   = {Mathematics : open access journal},
  number    = {4},
  publisher = {MDPI},
  address   = {Basel},
  issn      = {2227-7390},
  doi       = {10.3390/math8040608},
  pages     = {22},
  year      = {2020},
  abstract  = {In this paper, we present the convergence rate analysis of the modified Landweber method under logarithmic source condition for nonlinear ill-posed problems. The regularization parameter is chosen according to the discrepancy principle. The reconstructions of the shape of an unknown domain for an inverse potential problem by using the modified Landweber method are exhibited.},
  language  = {en}
}
@article{deWiljesPathirajaReich2020,
  author    = {de Wiljes, Jana and Pathiraja, Sahani Darschika and Reich, Sebastian},
  title     = {Ensemble transform algorithms for nonlinear smoothing problems},
  series = {SIAM journal on scientific computing},
  volume    = {42},
  journal   = {SIAM journal on scientific computing},
  number    = {1},
  publisher = {Society for Industrial and Applied Mathematics},
  address   = {Philadelphia},
  issn      = {1064-8275},
  doi       = {10.1137/19M1239544},
  pages     = {A87 -- A114},
  year      = {2020},
  abstract  = {Several numerical tools designed to overcome the challenges of smoothing in a non-linear and non-Gaussian setting are investigated for a class of particle smoothers. The considered family of smoothers is induced by the class of linear ensemble transform filters which contains classical filters such as the stochastic ensemble Kalman filter, the ensemble square root filter, and the recently introduced nonlinear ensemble transform filter. Further the ensemble transform particle smoother is introduced and particularly highlighted as it is consistent in the particle limit and does not require assumptions with respect to the family of the posterior distribution. The linear update pattern of the considered class of linear ensemble transform smoothers allows one to implement important supplementary techniques such as adaptive spread corrections, hybrid formulations, and localization in order to facilitate their application to complex estimation problems. These additional features are derived and numerically investigated for a sequence of increasingly challenging test problems.},
  language  = {en}
}
@misc{KolbeEvans2020,
  author    = {Kolbe, Benedikt Maximilian and Evans, Myfanwy E.},
  title     = {Isotopic tiling theory for hyperbolic surfaces},
  series = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {1},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-54428},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-544285},
  pages     = {30},
  year      = {2020},
  abstract  = {In this paper, we develop the mathematical tools needed to explore isotopy classes of tilings on hyperbolic surfaces of finite genus, possibly nonorientable, with boundary, and punctured. More specifically, we generalize results on Delaney-Dress combinatorial tiling theory using an extension of mapping class groups to orbifolds, in turn using this to study tilings of covering spaces of orbifolds. Moreover, we study finite subgroups of these mapping class groups. Our results can be used to extend the Delaney-Dress combinatorial encoding of a tiling to yield a finite symbol encoding the complexity of an isotopy class of tilings. The results of this paper provide the basis for a complete and unambiguous enumeration of isotopically distinct tilings of hyperbolic surfaces.},
  language  = {en}
}
@book{ZassZagrebnovSukiasyanetal.2020,
  author    = {Zass, Alexander and Zagrebnov, Valentin and Sukiasyan, Hayk and Melkonyan, Tatev and Rafler, Mathias and Poghosyan, Suren and Zessin, Hans and Piatnitski, Andrey and Zhizhina, Elena and Pechersky, Eugeny and Pirogov, Sergei and Yambartsev, Anatoly and Mazzonetto, Sara and Lykov, Alexander and Malyshev, Vadim and Khachatryan, Linda and Nahapetian, Boris and Jursenas, Rytis and Jansen, Sabine and Tsagkarogiannis, Dimitrios and Kuna, Tobias and Kolesnikov, Leonid and Hryniv, Ostap and Wallace, Clare and Houdebert, Pierre and Figari, Rodolfo and Teta, Alessandro and Boldrighini, Carlo and Frigio, Sandro and Maponi, Pierluigi and Pellegrinotti, Alessandro and Sinai, Yakov G.},
  title     = {Proceedings of the XI international conference stochastic and analytic methods in mathematical physics},
  number    = {6},
  editor    = {Roelly, Sylvie and Rafler, Mathias and Poghosyan, Suren},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  isbn      = {978-3-86956-485-2},
  issn      = {2199-4951},
  doi       = {10.25932/publishup-45919},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-459192},
  publisher      = {Universit{\"a}t Potsdam},
  pages     = {xiv, 194},
  year      = {2020},
  abstract  = {The XI international conference Stochastic and Analytic Methods in Mathematical Physics was held in Yerevan 2 - 7 September 2019 and was dedicated to the memory of the great mathematician Robert Adol'fovich Minlos, who passed away in January 2018. The present volume collects a large majority of the contributions presented at the conference on the following domains of contemporary interest: classical and quantum statistical physics, mathematical methods in quantum mechanics, stochastic analysis, applications of point processes in statistical mechanics. The authors are specialists from Armenia, Czech Republic, Denmark, France, Germany, Italy, Japan, Lithuania, Russia, UK and Uzbekistan. A particular aim of this volume is to offer young scientists basic material in order to inspire their future research in the wide fields presented here.},
  language  = {en}
}
@misc{MazzonettoSalimova2020,
  author    = {Mazzonetto, Sara and Salimova, Diyora},
  title     = {Existence, uniqueness, and numerical approximations for stochastic burgers equations},
  series = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {4},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-51579},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-515796},
  pages     = {26},
  year      = {2020},
  abstract  = {In this article, we propose an all-in-one statement which includes existence, uniqueness, regularity, and numerical approximations of mild solutions for a class of stochastic partial differential equations (SPDEs) with non-globally monotone nonlinearities. The proof of this result exploits the properties of an existing fully explicit space-time discrete approximation scheme, in particular the fact that it satisfies suitable a priori estimates. We also obtain almost sure and strong convergence of the approximation scheme to the mild solutions of the considered SPDEs. We conclude by applying the main result of the article to the stochastic Burgers equations with additive space-time white noise.},
  language  = {en}
}