Institutes
Refine
Year of publication
Document Type
- Doctoral Thesis (91)
- Article (58)
- Bachelor Thesis (17)
- Book (13)
- Master's Thesis (10)
- Conference Proceeding (4)
- Contribution to a Periodical (4)
- Habilitation (2)
- Preprint (2)
- Diploma Thesis (1)
Has Fulltext
- yes (202)
Is part of the Bibliography
- no (202)
Keywords
- Machine Learning (5)
- NLP (4)
- ALICE (3)
- Annotation (3)
- Machine learning (3)
- Text2Scene (3)
- TextAnnotator (3)
- Virtual Reality (3)
- mathematics education (3)
- Artificial intelligence (2)
Institute
Proteins are biological macromolecules playing essential roles in all living organisms.
Proteins often bind with each other forming complexes to fulfill their function. Such protein complexes assemble along an ordered pathway. An assembled protein complex can often be divided into structural and functional modules. Knowing the order of assembly and the modules of a protein complex is important to understand biological processes and treat diseases related to misassembly.
Typical structures of the Protein Data Bank (PDB) contain two to three subunits and a few thousand atoms. Recent developments have led to large protein complexes being resolved. The increasing number and size of the protein complexes demand for computational assistance for the visualization and analysis. One such large protein complex is respiratory complex I accounting for 45 subunits in Homo sapiens.
Complex I is a well understood protein complex that served as case study to validate our methods.
Our aim was to analyze time-resolved Molecular Dynamics (MD) simulation data, identify modules of a protein complex and generate hypotheses for the assembly pathway of a protein complex. For that purpose, we abstracted the topology of protein complexes to Complex Graphs of the Protein Topology Graph Library (PTGL). The subunits are represented as vertices, and spatial contacts as edges. The edges are weighted with the number of contacts based on a distance threshold. This allowed us to apply graph-theoretic methods to visualize and analyze protein complexes.
We extended the implementations of two methods to achieve a computation of Complex Graphs in feasible runtimes. The first method skipped checks for contacts using the information which residues are sequential neighbors. We extended the method to protein complexes and structures containing ligands. The second method introduced spheres encompassing all atoms of a subunit and skipped the check for contacts if the corresponding spheres do not overlap. Both methods combined allowed skipping up to 93 % of the checks for contacts for sample complexes of 40 subunits compared to up to 10 % of the previous implementation. We showed that the runtime of the combined method scaled linearly with the number of atoms compared to a non-linear scaling of the previous implementation We implemented a third method fixing the assignment of an orientation to secondary structure elements. We placed a three-dimensional vector in each secondary structure element and computed the angle between secondary structure elements to assign an orientation. This method sped up the runtime especially for large structures, such as the capsid of human immunodeficiency virus, for which the runtime decreased from 43 to less than 9 hours.
The feasible runtimes allowed us to investigate two data sets of MD trajectories of respiratory complex I of Thermus thermophilus that we received. The data sets differ only by whether ubiquinone is bound to the complex. We implemented a pipeline, PTGLdynamics, to compute the contacts and Complex Graphs for all time steps of the trajectories. We investigated different methods to track changes of contacts during the simulation and created a heat map put onto the three-dimensional structure visualizing the changes. We also created line plots to visualize the changes of contacts over the course of the simulation. Both visualizations helped spotting outstandingly flexible or rigid regions of the structure or time points of the simulation in which major dynamics occur.
We introduced normalizations of the edge weights of Complex Graphs for identi-fying modules and predicting the assembly pathway. The idea is to normalize the number of contacts for the number of residues of a subunit. We defined five different normalizations.
To identify structural and functional modules, we applied the Leiden graph clustering algorithm to the Complex Graphs of respiratory complex I and the respiratory supercomplex. We examined the results for the different normalizations of the weights of the Complex Graphs. The absolute edge weight produced the best result identifying three of four modules that have been defined in the literature for respiratory complex I.
We applied agglomerative hierarchical clustering to the edges of a Complex Graph to create hypotheses of the assembly pathway. The rationale was that subunits with an extensive interface in the final structure assemble early. We tested our method against two existing methods on a data set of 21 proteins with reported assembly pathways. Our prediction outperformed the other methods and ran in feasible runtimes of a few minutes at most.
We also tested our method on respiratory complex I, the respiratory supercomplex and the respiratory megacomplex. We compared the results for the different normalizations with an assembly pathway of respiratory complex I described in the literature. We transformed the assembly pathways to dendrograms and compared the predictions to the reference using the Robinson-Foulds distance and clustering information distance. We analyzed the landscape of the clustering information distance by generating random dendrograms and showed that our result is far better than expected at random. We showed in a detailed analysis that the assembly prediction using one normalization was able to capture key features of the assembly pathway that has been proposed in the literature.
In conclusion, we presented different applications of graph theory to automatically analyze the topology of protein complexes. Our programs run in feasible runtimes even for large complexes. We showed that graph-theoretic modeling of the protein structure can be used to analyze MD simulation data, identify modules of protein complexes and predict assembly pathways.
The present paper is concerned with the half-space Dirichlet problem [...] where ℝ𝑁+:={𝑥∈ℝ𝑁:𝑥𝑁>0} for some 𝑁≥1 and 𝑝>1, 𝑐>0 are constants. We analyse the existence, non-existence and multiplicity of bounded positive solutions to (𝑃𝑐). We prove that the existence and multiplicity of bounded positive solutions to (𝑃𝑐) depend in a striking way on the value of 𝑐>0 and also on the dimension N. We find an explicit number 𝑐𝑝∈(1,𝑒√), depending only on p, which determines the threshold between existence and non-existence. In particular, in dimensions 𝑁≥2, we prove that, for 0<𝑐<𝑐𝑝, problem (𝑃𝑐) admits infinitely many bounded positive solutions, whereas, for 𝑐>𝑐𝑝, there are no bounded positive solutions to (𝑃𝑐).
Goal-Conditioned Reinforcement Learning (GCRL) is a popular framework for training agents to solve multiple tasks in a single environment. It is cru- cial to train an agent on a diverse set of goals to ensure that it can learn to generalize to unseen downstream goals. Therefore, current algorithms try to learn to reach goals while simultaneously exploring the environment for new ones (Aubret et al., 2021; Mendonca et al., 2021). This creates a form of the prominent exploration-exploitation dilemma. To relieve the pres- sure of a single agent having to optimize for two competing objectives at once, this thesis proposes the novel algorithm family Goal-Conditioned Re- inforcement Learning with Prior Intrinsic Exploration (GC-π), which sep- arates exploration and goal learning into distinct phases. In the first ex- ploration phase, an intrinsically motivated agent explores the environment and collects a rich dataset of states and actions. This dataset is then used to learn a representation space, which acts as the distance metric for the goal- conditioned reward signal. In the final phase, a goal-conditioned policy is trained with the help of the representation space, and its training goals are randomly sampled from the dataset collected during the exploration phase. Multiple variations of these three phases have been extensively evaluated in the classic AntMaze MuJoCo environment (Nachum et al., 2018). The fi- nal results show that the proposed algorithms are able to fully explore the environment and solve all downstream goals while using every dimension of the state space for the goal space. This makes the approach more flexible compared to previous GCRL work, which only ever uses a small subset of the dimensions for the goals (S. Li et al., 2021a; Pong et al., 2020).
Nowadays, digitalization has an immense impact on the landscape of jobs. This technological revolution creates new industries and professions, promises greater efficiency and improves the quality of working life. However, emerging technologies such as robotics and artificial intelligence (AI) are reducing human intervention, thus advancing automation and eliminating thousands of jobs and whole occupational images. To prepare employees for the changing demands of work, adequate and timely training of the workforce and real-time support of workers in new positions is necessary. Therefore, it is investigated whether user-oriented technologies, such as augmented reality (AR) and virtual reality (VR) can be applied “on-the-job” for such training and support—also known as intelligence augmentation (IA). To address this problem, this work synthesizes results of a systematic literature review as well as a practically oriented search on augmented reality and virtual reality use cases within the IA context. A total of 150 papers and use cases are analyzed to identify suitable areas of application in which it is possible to enhance employees' capabilities. The results of both, theoretical and practical work, show that VR is primarily used to train employees without prior knowledge, whereas AR is used to expand the scope of competence of individuals in their field of expertise while on the job. Based on these results, a framework is derived which provides practitioners with guidelines as to how AR or VR can support workers at their job so that they can keep up with anticipated skill demands. Furthermore, it shows for which application areas AR or VR can provide workers with sufficient training to learn new job tasks. By that, this research provides practical recommendations in order to accompany the imminent distortions caused by AI and similar technologies and to alleviate associated negative effects on the German labor market.
We present a symmetry result to solutions of equations involving the fractional Laplacian in a domain with at least two perpendicular symmetries. We show that if the solution is continuous, bounded, and odd in one direction such that it has a fixed sign on one side, then it will be symmetric in the perpendicular direction. Moreover, the solution will be monotonic in the part where it is of fixed sign. In addition, we present also a class of examples in which our result can be applied.
Motivated by Gröbner basis theory for finite point configurations, we define and study the class of standard complexes associated to a matroid. Standard complexes are certain subcomplexes of the independence complex that are invariant under matroid duality. For the lexicographic term order, the standard complexes satisfy a deletion-contraction-type recurrence. We explicitly determine the lexicographic standard complexes for lattice path matroids using classical bijective combinatorics.
For an abeloid variety A over a complete algebraically closed field extension K of Qp, we construct a p-adic Corlette–Simpson correspondence, namely an equivalence between finite-dimensional continuous K-linear representations of the Tate module and a certain subcategory of the Higgs bundles on A. To do so, our central object of study is the category of vector bundles for the v-topology on the diamond associated to A. We prove that any pro-finite-étale v-vector bundle can be built from pro-finite-étale v-line bundles and unipotent v-bundles. To describe the latter, we extend the theory of universal vector extensions to the v-topology and use this to generalise a result of Brion by relating unipotent v-bundles on abeloids to representations of vector groups.
Nodular lymphocyte-predominant Hodgkin lymphoma (NLPHL) can show variable histological growth patterns and present remarkable overlap with T-cell/histiocyte-rich large B-cell lymphoma (THRLBCL). Previous studies suggest that NLPHL histological variants represent progression forms of NLPHL and THRLBCL transformation in aggressive disease. Since molecular studies of both lymphomas are limited due to the low number of tumor cells, the present study aimed to learn if a better understanding of these lymphomas is possible via detailed measurements of nuclear and cell size features in 2D and 3D sections. Whereas no significant differences were visible in 2D analyses, a slightly increased nuclear volume and a significantly enlarged cell size were noted in 3D measurements of the tumor cells of THRLBCL in comparison to typical NLPHL cases. Interestingly, not only was the size of the tumor cells increased in THRLBCL but also the nuclear volume of concomitant T cells in the reactive infiltrate when compared with typical NLPHL. Particularly CD8+ T cells had frequent contacts to tumor cells of THRLBCL. However, the nuclear volume of B cells was comparable in all cases. These results clearly demonstrate that 3D tissue analyses are superior to conventional 2D analyses of histological sections. Furthermore, the results point to a strong activation of T cells in THRLBCL, representing a cytotoxic response against the tumor cells with unclear effectiveness, resulting in enhanced swelling of the tumor cell bodies and limiting proliferative potential. Further molecular studies combining 3D tissue analyses and molecular data will help to gain profound insight into these ill-defined cellular processes.
Through the glasses of didactic reduction, we consider a (periodic) tessellation Δ of either Euclidean or hyperbolic 𝑛-space 𝑀. By a piecewise isometric rearrangement of Δ we mean the process of cutting 𝑀 along corank-1 tile-faces into finitely many convex polyhedral pieces, and rearranging the pieces to a new tight covering of the tessellation Δ. Such a rearrangement defines a permutation of the (centers of the) tiles of Δ, and we are interested in the group of 𝑃𝐼(Δ) all piecewise isometric rearrangements of Δ. In this paper, we offer (a) an illustration of piecewise isometric rearrangements in the visually attractive hyperbolic plane, (b) an explanation on how this is related to Richard Thompson's groups, (c) a section on the structure of the group pei(ℤ𝑛) of all piecewise Euclidean rearrangements of the standard cubically tessellated ℝ𝑛, and (d) results on the finiteness properties of some subgroups of pei(ℤ𝑛).
Conditional Sums-of-AM/GM-Exponentials (conditional SAGE) is a decomposition method to prove nonnegativity of a signomial or polynomial over some subset X of real space. In this article, we undertake the first structural analysis of conditional SAGE signomials for convex sets X. We introduce the X-circuits of a finite subset A⊂Rn , which generalize the simplicial circuits of the affine-linear matroid induced by A to a constrained setting. The X-circuits serve as the main tool in our analysis and exhibit particularly rich combinatorial properties for polyhedral X, in which case the set of X-circuits is comprised of one-dimensional cones of suitable polyhedral fans. The framework of X-circuits transparently reveals when an X-nonnegative conditional AM/GM-exponential can in fact be further decomposed as a sum of simpler X-nonnegative signomials. We develop a duality theory for X-circuits with connections to geometry of sets that are convex according to the geometric mean. This theory provides an optimal power cone reconstruction of conditional SAGE signomials when X is polyhedral. In conjunction with a notion of reduced X-circuits, the duality theory facilitates a characterization of the extreme rays of conditional SAGE cones. Since signomials under logarithmic variable substitutions give polynomials, our results also have implications for nonnegative polynomials and polynomial optimization.
In this article, we prove the Hodge conjecture for a desingularization of the moduli space of rank 2, semi-stable, torsion-free sheaves with fixed odd degree determinant over a very general irreducible nodal curve of genus at least 2. We also compute the algebraic Poincaré polynomial of the associated cohomology ring.
Background: The ability to approximate intra-operative hemoglobin loss with reasonable precision and linearity is prerequisite for determination of a relevant surgical outcome parameter: This information enables comparison of surgical procedures between different techniques, surgeons or hospitals, and supports anticipation of transfusion needs. Different formulas have been proposed, but none of them were validated for accuracy, precision and linearity against a cohort with precisely measured hemoglobin loss and, possibly for that reason, neither has established itself as gold standard. We sought to identify the minimal dataset needed to generate reasonably precise and accurate hemoglobin loss prediction tools and to derive and validate an estimation formula.
Methods: Routinely available clinical and laboratory data from a cohort of 401 healthy individuals with controlled hemoglobin loss between 29 and 233 g were extracted from medical charts. Supervised learning algorithms were applied to identify a minimal data set and to generate and validate a formula for calculation of hemoglobin loss.
Results: Of the classical supervised learning algorithms applied, the linear and Ridge regression models performed at least as well as the more complex models. Most straightforward to analyze and check for robustness, we proceeded with linear regression. Weight, height, sex and hemoglobin concentration before and on the morning after the intervention were sufficient to generate a formula for estimation of hemoglobin loss. The resulting model yields an outstanding R2 of 53.2% with similar precision throughout the entire range of volumes or donor sizes, thereby meaningfully outperforming previously proposed medical models.
Conclusions: The resulting formula will allow objective benchmarking of surgical blood loss, enabling informed decision making as to the need for pre-operative type-and-cross only vs. reservation of packed red cell units, depending on a patient’s anemia tolerance, and thus contributing to resource management.
The novel coronavirus (SARS-CoV-2), identified in China at the end of December 2019 and causing the disease COVID-19, has meanwhile led to outbreaks all over the globe with about 2.2 million confirmed cases and more than 150,000 deaths as of April 17, 2020 [37]. In view of most recent information on testing activity [32], we present here an update of our initial work [4]. In this work, mathematical models have been developed to study the spread of COVID-19 among the population in Germany and to asses the impact of non-pharmaceutical interventions. Systems of differential equations of SEIR type are extended here to account for undetected infections, as well as for stages of infections and age groups. The models are calibrated on data until April 5, data from April 6 to 14 are used for model validation. We simulate different possible strategies for the mitigation of the current outbreak, slowing down the spread of the virus and thus reducing the peak in daily diagnosed cases, the demand for hospitalization or intensive care units admissions, and eventually the number of fatalities. Our results suggest that a partial (and gradual) lifting of introduced control measures could soon be possible if accompanied by further increased testing activity, strict isolation of detected cases and reduced contact to risk groups.