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Sonstige beteiligte Institutionen
- Johns Hopkins School of Medicine (15)
- Johns Hopkins University School of Medicine (5)
- Department of Biomedical Imaging, National Cerebral and Cardiovascular Research Center, Suita, Japan (2)
- Division of Medical Technology and Science, Department of Medical Physics and Engineering, Course of Health Science, Osaka University Graduate School of Medicine, Suita Japan (2)
- Institut for Molecular Biology and CMBI, Department of Genomics, Stem Cell Biology and Regenerative Medicine, Leopold-Franzens-University Innsbruck, Innsbruck, Austria (2)
- International Max Planck Research School Molecular Biology, University of Göttingen, Germany (2)
- Johns Hopkins School of Medicine, The Russell H Morgan Department of Radiology and Radiological Science, Baltimore, MD, USA (2)
- ACC GmbH Analytical Clinical Concepts (1)
- BMBF (1)
- Boehringer Ingelheim Pharma GmbH & Co. KG (1)
ResearcherID
- J-8841-2015 (1)
The main theme of this thesis is the development of multigrid and hierarchical matrix solution procedures with almost linear computational complexity for classes of partial integro-differential problems. An elliptic partial integro-differential equation, a convection-diffusion partial integro-differential equation and a convection-diffusion partial integro-differential optimality system are investigated. In the first part of this work, an efficient multigrid finite-differences scheme for solving an elliptic
Fredholm partial integro-differential equation (PIDE) is discussed. This scheme combines a second-order accurate finite difference discretization and a Simpson's quadrature rule to approximate the PIDE problem and a multigrid scheme and a fast
multilevel integration method of the Fredholm operator allowing the fast solution of the PIDE problem. Theoretical estimates of second-order accuracy and results of local Fourier analysis of convergence of the proposed multigrid scheme
are presented. Results of numerical experiments validate these estimates and demonstrate optimal computational complexity of the proposed framework that includes numerical experiments for elliptic PIDE problems with singular kernels. The experience gained in this part of the work is used for the investigation of convection diffusion partial-integro differential equations in the second part of this thesis.
Convection-diffusion PIDE problems are discretized using a finite volume scheme referred to as the Chang and Cooper (CC) scheme and a quadrature rule. Also for this class of PIDE problems and this numerical setting, a stability and accuracy analysis of the CC scheme combined with a Simpson's quadrature rule is presented proving second-order accuracy of the numerical solution. To extend and investigate the proposed approximation and solution strategy to the case of systems of convection-diffusion PIDE, an optimal control problem governed by this model is considered. In this case the research focus is the CC-Simpson's discretization of the optimality system and its solution by the proposed multigrid strategy. Second-order accuracy of the optimization solution is proved and results of local Fourier analysis are presented that provide sharp convergence estimates of the optimal computational complexity of the multigrid-fast integration technique.
While (geometric) multigrid techniques require ad-hoc implementation depending on the structure of the PIDE problem and on the dimensionality of the domain where the problem is considered, the hierarchical matrix framework allows a more general treatment that exploits the algebraic structure of the problem at hand. In this thesis, this framework is extended to the case of combined differential and integral problems considering the case of a convection-diffusion PIDE. In this case, the starting point is the CC discretization of the convection-diffusion operator combined with the trapezoidal quadrature rule. The hierarchical matrix approach exploits the algebraic nature of the hierarchical matrices for blockwise approximations by low-rank matrices of the sparse convection-diffusion approximation and enables data sparse representation of the fully populated matrix where all essential matrix operations are performed with at most logarithmic optimal complexity. The factorization of part of or the whole coefficient matrix is used as a preconditioner to the solution of the PIDE problem using a generalized minimum residual (GMRes) procedure as a solver.
Numerical analysis estimates of the accuracy of the
finite-volume and trapezoidal rule approximation are
presented and combined with estimates of the
hierarchical matrix approximation and with the
accuracy of the GMRes iterates. Results of numerical experiments are reported that
successfully validate the theoretical estimates and
the optimal computational complexity of the proposed hierarchical matrix
solution procedure. These results include an extension to higher dimensions and an application to the time evolution of the probability density function of a jump diffusion process.
New experimental methods have drastically accelerated the pace and quantity at which biological data is generated. High-throughput DNA sequencing is one of the pivotal new technologies. It offers a number of novel applications in various fields of biology, including ecology, evolution, and genomics. However, together with those opportunities many new challenges arise. Specialized algorithms and software are required to cope with the amount of data, often requiring substantial training in bioinformatic methods. Another way to make those data accessible to non-bioinformaticians is the development of programs with intuitive user interfaces.
In my thesis I developed analyses and programs to tackle current problems with high-throughput data in biology. In the field of ecology this covers the establishment of the bioinformatic workflow for pollen DNA meta-barcoding. Furthermore, I developed an application that facilitates the analysis of ecological communities in the context of their traits. Information from multiple public databases have been aggregated and can now be mapped automatically to existing community tables for interactive inspection. In evolution the new data are used to reconstruct phylogenetic trees from multiple genes. I developed the tool bcgTree to automate this process for bacteria. Many plant genomes have been sequenced in current years. Sequencing reads of those projects also contain data from the chloroplasts. The tool chloroExtractor supports the targeted extraction and analysis of the chloroplast genome. To compare the structure of multiple genomes specialized software is required for calculation and visualization of the relationships. I developed AliTV to address this. In contrast to existing programs for this task it allows interactive adjustments of produced graphics. Thus, facilitating the discovery of biologically relevant information. Another application I developed helps to analyze transcriptomes even if no reference genome is present. This is achieved by aggregating the different pieces of information, like functional annotation and expression level, for each transcript in a web platform. Scientists can then search, filter, subset, and visualize the transcriptome.
Together the methods and tools expedite insights into biological systems that were not possible before.
The sequencing of several ant genomes within the last six years open new research avenues for understanding not only the genetic basis of social species but also the complex systems such as immune responses in general. Similar to other social insects, ants live in cooperative colonies, often in high densities and with genetically identical or closely related individuals. The contact behaviours and crowd living conditions allow the disease to spread rapidly through colonies. Nevertheless, ants can efficiently combat infections by using diverse and effective immune mechanisms. However, the components of the immune system of carpenter ant Camponotus floridanus and also the factors in bacteria that facilitate infection are not well understood.
To form a better view of the immune repository and study the C. floridanus immune responses against the bacteria, experimental data from Illumina sequencing and mass-spectrometry (MS) data of haemolymph in normal and infectious conditions were analysed and integrated with the several bioinformatics approaches. Briefly, the tasks were accomplished in three levels. First, the C. floridanus genome was re-annotated for the improvement of the existing annotation using the computational methods and transcriptomics data. Using the homology based methods, the extensive survey of literature, and mRNA expression profiles, the immune repository of C. floridanus were established. Second, large-scale protein-protein interactions (PPIs) and signalling network of C. floridanus were reconstructed and analysed and further the infection induced functional modules in the networks were detected by mapping of the expression data over the networks. In addition, the interactions of the immune components with the bacteria were identified by reconstructing inter-species PPIs networks and the interactions were validated by literature. Third, the stage-specific MS data of larvae and worker ants were analysed and the differences in the immune response were reported.
Concisely, all the three omics levels resulted to multiple findings, for instance, re-annotation and transcriptome profiling resulted in the overall improvement of structural and functional annotation and detection of alternative splicing events, network analysis revealed the differentially expressed topologically important proteins and the active functional modules, MS data analysis revealed the stage specific differences in C. floridanus immune responses against bacterial pathogens.
Taken together, starting from re-annotation of C. floridanus genome, this thesis provides a transcriptome and proteome level characterization of ant C. floridanus, particularly focusing on the immune system responses to pathogenic bacteria from a biological and a bioinformatics point of view. This work can serve as a model for the integration of omics data focusing on the immuno-transcriptome of insects.