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Understanding the evolution of Boraginales: insights from morphology, phylogeny, biogeography and taxonomy
Vasile, MariaAnna (20240814)Boraginales are a mediumsized angiosperm order within Lamiids, with very diverse fruit morphology, which has been traditionally used for nomenclatural subdivisions. This thesis attempts to elucidate some aspects of the ... 
Totalsynthesis of Pentamycin
Babczyk, Alexander (20240814)The polyene macrolide pentamycin, first isolated from Streptomyces penticus in 1958, displays impressive biological activities against various pathogens, including Trichomonas vaginalis or Candida albicans, and can be used ... 
Godsdienstpedagogische cartografie
Roebben, Bert (20240514)In een wereld in transitie, zoals we die sinds enkele jaren meemaken, veranderen ook de religieuze vormingsprocessen. Soms is die verandering zo diepgaand dat er sprake is van een radicale onderbreking, zoals in tijden van ... 
Numerical stochastic homogenization by quasilocal effective diffusion tensors
Gallistl, Dietmar; Peterseim, Daniel (201702)This paper proposes a numerical upscaling procedure for elliptic boundary value problems with diffusion tensors that vary randomly on small scales. The resulting effective deterministic model is given through a quasilocal ... 
On the decay rate of the singular values of bivariate functions
Griebel, Michael; Li, Guanglian (201711)In this work, we establish a new truncation error estimate of the singular value decomposition (SVD) for a class of Sobolev smooth bivariate functions <em>κ</em> ∈ <em>L<sup>2</sup></em>(Ω, <em>H<sup>s</sup></em>(<em>D</em>)), ... 
εdimension in infinite dimensional hyperbolic cross approximation and application to parametric elliptic PDEs
Dũng, Dinh; Griebel, Michael; Huy, Vu Nhat; Rieger, Christian (2017)In this article, we present a costbenefit analysis of the approximation in tensor products of Hilbert spaces of Sobolevanalytic type. The Sobolev part is defined on a finite dimensional domain, whereas the analytical ... 
Lowrank approximation to heterogeneous elliptic problems
Li, Guanglian (201703)In this work, we investigate the lowrank approximation of elliptic problems in heterogeneous media by means of Kolmogrov <em>n</em>width and asymptotic expansion. This class of problems arises in practical applications ... 
Second order optimality conditions for optimal control of quasilinear parabolic equations
Bonifacius, Lucas; Neitzel, Ira (201703)We discuss an optimal control problem governed by a quasilinear parabolic PDE including mixed boundary conditions and Neumann boundary control, as well as distributed control. Second order necessary and sufficient optimality ... 
On the expected uniform error of geometric Brownian motion approximated by the LévyCiesielski construction
Brown, Bruce; Griebel, Michael; Kuo, Frances Y.; Sloan, Ian H. (201706)It is known that the Brownian bridge or LévyCiesielski construction of Brownian paths almost surely converges uniformly to the true Brownian path. In the present article the focus is on the error. In particular, we show ... 
Singular value decomposition versus sparse grids: Refined complexity estimates
Griebel, Michael; Harbrecht, Helmut (2017)We compare the cost complexities of two approximation schemes for functions which live on the product domain <em>Ω<sub>1</sub></em> × <em>Ω<sub>2</sub></em> of sufficiently smooth domains <em>Ω<sub>1</sub></em> ⊂ ... 
On the convergence rate of sparse grid least squares regression
Bohn, Bastian (201708)While sparse grid least squares regression algorithms have been frequently used to tackle Big Data problems with a huge number of input data in the last 15 years, a thorough theoretical analysis of stability properties, ... 
A collection of nonsmooth Riemannian optimization problems
Absil, PierreAntoine; Hosseini, Seyedehsomayeh (201709)Nonsmooth Riemannian optimization is a still scarcely explored subfield of optimization theory that concerns the general problem of minimizing (or maximizing), over a domain endowed with a manifold structure, a realvalued ... 
A representer theorem for deep kernel learning
Bohn, Bastian; Griebel, Michael; Rieger, Christian (201705)In this paper we provide a finitesample and an infinitesample representer theorem for the concatenation of (linear combinations of) kernel functions of reproducing kernel Hilbert spaces. These results serve as mathematical ... 
Tangent and normal cones for lowrank matrices
Hosseini, Seyedehsomayeh; Luke, D. Russel; Uschmajew, André (201710)In [D. R. Luke, <em>J. Math. Imaging Vision</em>, 47(3):231238, 2013] the structure of the Mordukhovich normal cone to varieties of low rank matrices at rankdeficient points has been determined. A simplified proof of ... 
Upscaled HDG methods for Brinkman equations with highcontrast heterogeneous coefficient
Guanglian Li; Ke Shi (201710)In this paper, we present new upscaled HDG methods for Brinkman equations in the context of highcontrast heterogeneous media. The a priori error estimates are derived in terms of both fine and coarse scale parameters that ... 
Stochastic subspace correction in Hilbert space
Griebel, Michael; Oswald, Peter (201711)We consider an incremental approximation method for solving variational problems in infinitedimensional separable Hilbert spaces, where in each step a randomly and independently selected subproblem from an infinite ... 
On the degree of illposedness of multidimensional magnetic particle imaging
Kluth, Tobias; Jin, Bangti; Li, Guanglian (201712)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 ... 
Kernelbased stochastic collocation for the random twophase NavierStokes equations
Michael Griebel; Christian Rieger; Peter Zaspel (201810)In this work, we apply stochastic collocation methods with radial kernel basis functions for an uncertainty quantification of the random incompressible twophase Navier–Stokes equations. Our approach is nonintrusive and ... 
Optimally rotated coordinate systems for adaptive leastsquares regression on sparse grids
Bastian Bohn; Michael Griebel; Jens Oettershagen (201802)For lowdimensional 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, gridbased ... 
Antiviral and antimicrobial inflammasome formation in intestinal epithelial cells
Gohr, Florian Nikolaus (20240813)Inflammasomes coordinate inflammation by inducing rapid cytokine secretion and protect against invading pathogens by initiating death of infected cells. We developed and characterised a novel fluorescent reporter that ...