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Geometric T-Duality
(2022)
From a physicists point of view T-duality is a relation connecting string
theories on different spacetimes. Mathematically speaking, T-duality should be a symmetric relation on
the space of toroidal string backgrounds. Such a background consists of: a smooth manifold M; a torus bundle E over M - the total space modelling spacetime; a Riemannian metric g on E - modelling the field of gravity; a U(1)-bundle gerbe G with connection over E - modelling the Kalb-
Ramond field.
But as of now no complete model for T-duality exists. The three most notable
approaches for T-duality are given by the differential approaches by Buscher in the form of the Buscher rules and by Bouwknegt, Evslin and Mathai in the form of T-duality with H-flux on the one hand, and by the topological approach given by Bunke, Rumpf and Schick which is known as topological T-duality. In this thesis we combine these different approaches to form the first model for T-duality over complete geometric toroidal string backgrounds and we will introduce an example for this geometric T-duality inspired by the Hopf bundle.
Discovering Latent Structure in High-Dimensional Healthcare Data: Toward Improved Interpretability
(2022)
This cumulative thesis describes contributions to the field of interpretable machine learning in the healthcare domain. Three research articles are presented that lie at the intersection of biomedical and machine learning research. They illustrate how incorporating latent structure can provide a valuable compression of the information hidden in complex healthcare data.
Methodologically, this thesis gives an overview of interpretable machine learning and the discovery of latent structure, including clusters, latent factors, graph structure, and hierarchical structure. Different workflows are developed and applied to two main types of complex healthcare data (cohort study data and time-resolved molecular data). The core result builds on Bayesian networks, a type of probabilistic graphical model. On the application side, we provide accurate predictive or discriminative models focusing on relevant medical conditions, related biomarkers, and their interactions.
Spatial variation in survival has individual fitness consequences and influences population dynamics. It proximately and ultimately impacts space use including migratory connectivity. Therefore, knowing spatial patterns of survival is crucial to understand demography of migrating animals. Extracting information on survival and space use from observation data, in particular dead recovery data, requires explicitly identifying the observation process. The main aim of this work is to establish a modeling framework which allows estimating spatial variation in survival, migratory connectivity and observation probability using dead recovery data. We provide some biological background on survival and migration and a short methodological overview of how similar situations are modeled in literature.
Afterwards, we provide REML-like estimators for discrete space and show identifiability of all three parameters using the characteristics of the multinomial distribution. Moreover, we formulate a model in continuous space using mixed binomial point processes. The continuous model assumes a constant recovery probability over space. To drop this strict assumption, we develop an optimization procedure combining the discrete and continuous space model. Therefore, we use penalized M-splines. In simulation studies we demonstrate the performance of the estimators for all three model approaches. Furthermore, we apply the models to real-world data sets of European robins \textit{Erithacus rubecula} and ospreys \textit{Pandion haliaetus}.
We discuss how this study can be embedded in the framework of animal movement and the capture mark recapture/recovery methodology. It can be seen as a contribution and an extension to distance sampling, local stationary everyday movement and dispersal. We emphasize the importance of having a mathematically clearly formulated modeling framework for applied methods. Moreover, we comment on model assumptions and their limits. In the future, it would be appealing to extend this framework to the full annual cycle and carry-over effects.
Anaplasma phagocytophilum and Anaplasma ovis–Emerging Pathogens in the German Sheep Population
(2021)
Knowledge on the occurrence of pathogenic tick-borne bacteria Anaplasma phagocytophilum and Anaplasma ovis is scarce in sheep from Germany. In 2020, owners from five flocks reported ill thrift lambs and ewes with tick infestation. Out of 67 affected sheep, 55 animals were clinically examined and hematological values, blood chemistry and fecal examinations were performed to investigate the underlying disease causes. Serological tests (cELISA, IFAT) and qPCR were applied to all affected sheep to rule out A. phagocytophilum and A. ovis as a differential diagnosis. Ticks were collected from selected pastures and tested by qPCR. Most animals (n = 43) suffered from selenium deficiency and endoparasites were detected in each flock. Anaplasma spp. antibodies were determined in 59% of examined sheep. Seventeen animals tested positive for A. phagocytophilum by qPCR from all flocks and A. phagocytophilum was also detected in eight pools of Ixodes ricinus. Anaplasma phagocytophilum isolates from sheep and ticks were genotyped using three genes (16S rRNA, msp4 and groEL). Anaplasma ovis DNA was identified in six animals from one flock. Clinical, hematological and biochemical changes were not significantly associated with Anaplasma spp. infection. The 16S rRNA analysis revealed known variants of A. phagocytophilum, whereas the msp4 and groEL showed new genotypes. Further investigations are necessary to evaluate the dissemination and health impact of both pathogens in the German sheep population particularly in case of comorbidities.
Abstract
Cellular stress has been associated with inflammation, yet precise underlying mechanisms remain elusive. In this study, various unrelated stress inducers were employed to screen for sensors linking altered cellular homeostasis and inflammation. We identified the intracellular pattern recognition receptors NOD1/2, which sense bacterial peptidoglycans, as general stress sensors detecting perturbations of cellular homeostasis. NOD1/2 activation upon such perturbations required generation of the endogenous metabolite sphingosine‐1‐phosphate (S1P). Unlike peptidoglycan sensing via the leucine‐rich repeats domain, cytosolic S1P directly bound to the nucleotide binding domains of NOD1/2, triggering NF‐κB activation and inflammatory responses. In sum, we unveiled a hitherto unknown role of NOD1/2 in surveillance of cellular homeostasis through sensing of the cytosolic metabolite S1P. We propose S1P, an endogenous metabolite, as a novel NOD1/2 activator and NOD1/2 as molecular hubs integrating bacterial and metabolic cues.
Phytopathogenic Verticillia cause Verticillium wilt on numerous economically important crops. Plant infection begins at the roots, where the fungus is confronted with rhizosphere inhabiting bacteria. The effects of different fluorescent pseudomonads, including some known biocontrol agents of other plant pathogens, on fungal growth of the haploid Verticillium dahliae and/or the amphidiploid Verticillium longisporum were compared on pectin-rich medium, in microfluidic interaction channels, allowing visualization of single hyphae, or on Arabidopsis thaliana roots. We found that the potential for formation of bacterial lipopeptide syringomycin resulted in stronger growth reduction effects on saprophytic Aspergillus nidulans compared to Verticillium spp. A more detailed analyses on bacterial-fungal co-cultivation in narrow interaction channels of microfluidic devices revealed that the strongest inhibitory potential was found for Pseudomonas protegens CHA0, with its inhibitory potential depending on the presence of the GacS/GacA system controlling several bacterial metabolites. Hyphal tip polarity was altered when V. longisporum was confronted with pseudomonads in narrow interaction channels, resulting in a curly morphology instead of straight hyphal tip growth. These results support the hypothesis that the fungus attempts to evade the bacterial confrontation. Alterations due to co-cultivation with bacteria could not only be observed in fungal morphology but also in fungal transcriptome. P. protegens CHA0 alters transcriptional profiles of V. longisporum during 2 h liquid media co-cultivation in pectin-rich medium. Genes required for degradation of and growth on the carbon source pectin were down-regulated, whereas transcripts involved in redox processes were up-regulated. Thus, the secondary metabolite mediated effect of Pseudomonas isolates on Verticillium species results in a complex transcriptional response, leading to decreased growth with precautions for self-protection combined with the initiation of a change in fungal growth direction. This interplay of bacterial effects on the pathogen can be beneficial to protect plants from infection, as shown with A. thaliana root experiments. Treatment of the roots with bacteria prior to infection with V. dahliae resulted in a significant reduction of fungal root colonization. Taken together we demonstrate how pseudomonads interfere with the growth of Verticillium spp. and show that these bacteria could serve in plant protection.
Abstract
The expected signature is an analogue of the Laplace transform for probability measures on rough paths. A key question in the area has been to identify a general condition to ensure that the expected signature uniquely determines the measures. A sufficient condition has recently been given by Chevyrev and Lyons and requires a strong upper bound on the expected signature. While the upper bound was verified for many well‐known processes up to a deterministic time, it was not known whether the required bound holds for random time. In fact, even the simplest case of Brownian motion up to the exit time of a planar disc was open. For this particular case we answer this question using a suitable hyperbolic projection of the expected signature. The projection satisfies a three‐dimensional system of linear PDEs, which (surprisingly) can be solved explicitly, and which allows us to show that the upper bound on the expected signature is not satisfied.