08 Fakultät Mathematik und Physik
Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/9
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Item Open Access An approximation of solutions to heat equations defined by generalized measure theoretic Laplacians(2020) Ehnes, Tim; Hambly, BenWe consider the heat equation defined by a generalized measure theoretic Laplacian on [0, 1]. This equation describes heat diffusion in a bar such that the mass distribution of the bar is given by a non-atomic Borel probabiliy measure μ, where we do not assume the existence of a strictly positive mass density. We show that weak measure convergence implies convergence of the corresponding generalized Laplacians in the strong resolvent sense. We prove that strong semigroup convergence with respect to the uniform norm follows, which implies uniform convergence of solutions to the corresponding heat equations. This provides, for example, an interpretation for the mathematical model of heat diffusion on a bar with gaps in that the solution to the corresponding heat equation behaves approximately like the heat flow on a bar with sufficiently small mass on these gaps.Item Open Access Ordinal patterns in clusters of subsequent extremes of regularly varying time series(2020) Oesting, Marco; Schnurr, AlexanderIn this paper, we investigate temporal clusters of extremes defined as subsequent exceedances of high thresholds in a stationary time series. Two meaningful features of these clusters are the probability distribution of the cluster size and the ordinal patterns giving the relative positions of the data points within a cluster. Since these patterns take only the ordinal structure of consecutive data points into account, the method is robust under monotone transformations and measurement errors. We verify the existence of the corresponding limit distributions in the framework of regularly varying time series, develop non-parametric estimators and show their asymptotic normality under appropriate mixing conditions. The performance of the estimators is demonstrated in a simulated example and a real data application to discharge data of the river Rhine.Item Open Access Lossless transformations and excess risk bounds in statistical inference(2023) Györfi, László; Linder, Tamás; Walk, HarroWe study the excess minimum risk in statistical inference, defined as the difference between the minimum expected loss when estimating a random variable from an observed feature vector and the minimum expected loss when estimating the same random variable from a transformation (statistic) of the feature vector. After characterizing lossless transformations, i.e., transformations for which the excess risk is zero for all loss functions, we construct a partitioning test statistic for the hypothesis that a given transformation is lossless, and we show that for i.i.d. data the test is strongly consistent. More generally, we develop information-theoretic upper bounds on the excess risk that uniformly hold over fairly general classes of loss functions. Based on these bounds, we introduce the notion of a δ -lossless transformation and give sufficient conditions for a given transformation to be universally δ -lossless. Applications to classification, nonparametric regression, portfolio strategies, information bottlenecks, and deep learning are also surveyed.Item Open Access Implications of modeling seasonal differences in the extremal dependence of rainfall maxima(2022) Jurado, Oscar E.; Oesting, Marco; Rust, Henning W.For modeling extreme rainfall, the widely used Brown-Resnick max-stable model extends the concept of the variogram to suit block maxima, allowing the explicit modeling of the extremal dependence shown by the spatial data. This extremal dependence stems from the geometrical characteristics of the observed rainfall, which is associated with different meteorological processes and is usually considered to be constant when designing the model for a study. However, depending on the region, this dependence can change throughout the year, as the prevailing meteorological conditions that drive the rainfall generation process change with the season. Therefore, this study analyzes the impact of the seasonal change in extremal dependence for the modeling of annual block maxima in the Berlin-Brandenburg region. For this study, two seasons were considered as proxies for different dominant meteorological conditions: summer for convective rainfall and winter for frontal/stratiform rainfall. Using maxima from both seasons, we compared the skill of a linear model with spatial covariates (that assumed spatial independence) with the skill of a Brown-Resnick max-stable model. This comparison showed a considerable difference between seasons, with the isotropic Brown-Resnick model showing considerable loss of skill for the winter maxima. We conclude that the assumptions commonly made when using the Brown-Resnick model are appropriate for modeling summer (i.e., convective) events, but further work should be done for modeling other types of precipitation regimes.Item Open Access Is minimally invasive multi-vessel off-pump coronary surgery as safe and effective as MIDCAB?(2024) Rufa, Magdalena I.; Ursulescu, Adrian; Dippon, Juergen; Aktuerk, Dincer; Nagib, Ragi; Albert, Marc; Franke, Ulrich F. W.The safety and efficacy of minimally invasive direct coronary artery bypass (MIDCAB) surgery has been confirmed in numerous reports. However, minimally invasive multi-vessel off-pump coronary artery bypass grafting (MICS CABG) has lower uptake and has not yet gained widespread adoption. The study aimed to investigate the non-inferiority of MICS CABG to MIDCAB in long-term follow-up for several clinical outcomes, including angina pectoris, major adverse cardiac and cerebrovascular events (MACCE) and overall survival. Methods This is an observational, retrospective, single center study of 1,149 patients who underwent either MIDCAB (n= 626) or MICS CABG (n= 523) at our institution between 2007 and 2018. The left internal thoracic artery and portions of the radial artery and saphenous vein were used for the patients’ single-, double-, or triple-vessel revascularization procedures. We used gradient boosted propensity-score estimation to account for possible interactions between variables. After propensity-score adjustment, the two groups were similar in terms of preoperative demographics and risk profile. Long-term follow-up (mean 5.87, median 5.6 years) was available for 1,089 patients (94.8%). Results A total of 626, 454 and 69 patients underwent single, double and triple coronary revascularization, respectively. The long-term outcomes of freedom from angina pectoris, acute myocardial infarction, and revascularization rate were similar between the two groups. During follow-up, there were 123 deaths in the MIDCAB group and 96 in the MICS CABG group. The 1-, 3-, 5-, and 10-year survival rates were 97%, 92%, 85%, and 69% for the MIDCAB group and 97%, 93%, 89%, and 74% for the MICS CABG group, respectively. The hazard ratio of overall survival for patients with two or more bypass grafts compared to those with one bypass graft was 1.190 (p -value = 0.234, 95% CI: 0.893-1.586). This indicates that there was no significant difference in survival between the two groups. Furthermore, if we consider a hazard ratio of 1.2 to be clinically non-relevant, surgery with two or more grafts was significantly non-inferior to surgery with just one graft (p-value = 0.0057). Conclusion In experienced hands, MICS CABG is a safe and effective procedure. Survival and durability are comparable with MIDCAB.Item Open Access On the distances within cliques in a soft random geometric graph(2024) Sönmez, Ercan; Stegehuis, ClaraWe study the distances of vertices within cliques in a soft random geometric graph on a torus, where the vertices are points of a homogeneous Poisson point process, and far-away points are less likely to be connected than nearby points. We obtain the scaling of the maximal distance between any two points within a clique of size k . Moreover, we show that asymptotically in all cliques with large distances, there is only one remote point and all other points are nearby. Furthermore, we prove that a re-scaled version of the maximal k-clique distance converges in distribution to a Fréchet distribution. Thereby, we describe the order of magnitude according to which the largest distance between two points in a clique decreases with the clique size.Item Open Access Reproducing kernel Hilbert spaces cannot contain all continuous functions on a compact metric space(2024) Steinwart, IngoGiven an uncountable, compact metric space X, we show that there exists no reproducing kernel Hilbert space that contains the space of all continuous functions on X .Item Open Access A sphingolipid rheostat controls apoptosis versus apical cell extrusion as alternative tumour-suppressive mechanisms(2024) Armistead, Joy; Höpfl, Sebastian; Goldhausen, Pierre; Müller-Hartmann, Andrea; Fahle, Evelin; Hatzold, Julia; Franzen, Rainer; Brodesser, Susanne; Radde, Nicole E.; Hammerschmidt, MatthiasEvasion of cell death is a hallmark of cancer, and consequently the induction of cell death is a common strategy in cancer treatment. However, the molecular mechanisms regulating different types of cell death are poorly understood. We have formerly shown that in the epidermis of hypomorphic zebrafish hai1a mutant embryos, pre-neoplastic transformations of keratinocytes caused by unrestrained activity of the type II transmembrane serine protease Matriptase-1 heal spontaneously. This healing is driven by Matriptase-dependent increased sphingosine kinase (SphK) activity and sphingosine-1-phosphate (S1P)-mediated keratinocyte loss via apical cell extrusion. In contrast, amorphic hai1afr26 mutants with even higher Matriptase-1 and SphK activity die within a few days. Here we show that this lethality is not due to epidermal carcinogenesis, but to aberrant tp53-independent apoptosis of keratinocytes caused by increased levels of pro-apoptotic C16 ceramides, sphingolipid counterparts to S1P within the sphingolipid rheostat, which severely compromises the epidermal barrier. Mathematical modelling of sphingolipid rheostat homeostasis, combined with in vivo manipulations of components of the rheostat or the ceramide de novo synthesis pathway, indicate that this unexpected overproduction of ceramides is caused by a negative feedback loop sensing ceramide levels and controlling ceramide replenishment via de novo synthesis. Therefore, despite their initial decrease due to increased conversion to S1P, ceramides eventually reach cell death-inducing levels, making transformed pre-neoplastic keratinocytes die even before they are extruded, thereby abrogating the normally barrier-preserving mode of apical live cell extrusion. Our results offer an in vivo perspective of the dynamics of sphingolipid homeostasis and its relevance for epithelial cell survival versus cell death, linking apical cell extrusion and apoptosis. Implications for human carcinomas and their treatments are discussed.