The Faculty of Mathematics and Natural Sciences: Mathematisch-Naturwissenschaftliche Fakultät: Recent submissions
Now showing items 601-620 of 5047
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Stochastic subspace correction in Hilbert space
(2017-11)We consider an incremental approximation method for solving variational problems in infinite-dimensional separable Hilbert spaces, where in each step a randomly and independently selected subproblem from an infinite ... -
On the degree of ill-posedness of multi-dimensional magnetic particle imaging
(2017-12)Magnetic particle imaging is an imaging modality of relatively recent origin, and it exploits the nonlinear magnetization response for reconstructing the concentration of nanoparticles. Since first invented in 2005, it has ... -
Kernel-based stochastic collocation for the random two-phase Navier-Stokes equations
(2018-10)In this work, we apply stochastic collocation methods with radial kernel basis functions for an uncertainty quantification of the random incompressible two-phase Navier–Stokes equations. Our approach is nonintrusive and ... -
Optimally rotated coordinate systems for adaptive least-squares regression on sparse grids
(2018-02)For low-dimensional data sets with a large amount of data points, standard kernel methods are usually not feasible for regression anymore. Besides simple linear models or involved heuristic deep learning models, grid-based ... -
Analyse der amorphen und amyloiden Aggregatsequestrierung in Mitochondrien
(2024-08-12)Proteine müssen, um ihre Funktionen auszuführen, richtig gefaltet sein. Fehlgefaltete Proteine können Aggregate bilden, welche toxisch für die Zellen sind. Daher ist zum Schutz der Proteinhomöostase die Verhinderung der ... -
Machine Learning for Path Deformation and Bayesian Data Analysis in Selected Lattice Field Theories
(2024-08-12)Our collective understanding of the laws of nature has a long history of an intricate interplay between theoretical considerations and experimental falsification. As computational power increases, simulations, at the ... -
Interconnect Optimization in Chip Design
(2024-08-12)In this thesis, we take a closer look at the buffering problem. We review the literature on the buffering problem and examine how different algorithms try to solve it. We present an overview over the different aspects that ... -
Comparative studies of lipid metabolism in drought-tolerant and drought-sensitive plants and deep understanding of the resurrection grass Oropetium thomaeum
(2024-08-12)1. Increasing water scarcity is known as a crucial challenge to sustainable development of the planet. Water scarcity will impact 40% of the world’s population at risk of drought by 2030. Most higher plants are unable to ... -
Simulation of micron-scale drop impact
(2018-10)The numerical simulation of droplet impact is of interest for a vast variety of industrial processes, where practical experiments are costly and time-consuming. In these simulations, the dynamic contact angle is a key ... -
Haar system as Schauder basis in Besov spaces: the limiting cases for 0 < p ≤ 1
(2018-09)We show that the <em>d</em>-dimensional Haar system <em>H<sup>d</sup></em> on the unit cube <em>I<sup>d</sup></em> is a Schauder basis in the classical Besov space B<em><sup>s</sup><sub>p,q,1</sub></em>(<em>I<sup>d</sup></em>), ... -
Stochastic subspace correction methods and fault tolerance
(2018-07)We present convergence results in expectation for stochastic subspace correction schemes and their accelerated versions to solve symmetric positive-definite variational problems, and discuss their potential for achieving ... -
Incremental kernel based approximations for Bayesian inverse problems
(2018-05)We provide an interpretation for the covariance of the predictive process of Bayesian Gaussian process regression as reproducing kernel of a subset of the Cameron Martin space of the prior. We demonstrate that this ... -
Iterated Landweber method for radial basis functions interpolation with finite accuracy
(2018-05)We consider the reconstruction of a function stemming from a reproducing kernel Hilbert space using data which is perturbed by a deterministic error of maximal size ε<sub>∞</sub>. The accuracy ε<sub>∞</sub> ... -
Sampling inequalities for anisotropic tensor product grids
(2018-04)We derive sampling inequalities for discrete point sets which are of anisotropic tensor product form. Such sampling inequalities can be used to prove convergence for arbitrary stable reconstruction processes. As usual in ... -
Kernel-based reconstructions for parametric PDEs
(2018-03)In uncertainty quantification, an unknown quantity has to be reconstructed which depends typically on the solution of a partial differential equation. This partial differential equation itself may depend on parameters, ... -
Estimates for generalized sparse grid hierarchical basis preconditioners
(2018-03)We reconsider some estimates from the 1994 paper [6] concerning the hierarchical basis preconditioner for sparse grid discretizations. The improvement is in three directions: We consider arbitrary space dimensions <em>d</em> ... -
Generalized sparse grid interpolation based on the fast discrete Fourier transform
(2019-03)In [9], an algorithm for trigonometric interpolation involving only so-called <em>standard information</em> of multivariate functions on generalized sparse grids has been suggested and a study on its application for the ... -
Analysis of tensor approximation schemes for continuous functions
(2019-03)In this article, we analyze tensor approximation schemes for continuous functions. We assume that the function to be approximated lies in an isotropic Sobolev space and discuss the cost when approximating this function in ... -
On the numerical approximation of the Karhunen-Loève expansion for lognormal random fields
(2019-07)The Karhunen-Loève (KL) expansion is a popular method for approximating random fields by transforming an infinite-dimensional stochastic domain into a finite-dimensional parameter space. Its numerical approximation is of ... -
Maximum approximated likelihood estimation
(2019-08)Empirical economic research frequently applies maximum likelihood estimation in cases where the likelihood function is analytically intractable. Most of the theoretical literature focuses on maximum simulated likelihood ...
