Railway Timetable Optimization

In this cumulative dissertation, we study several aspects of railway timetable optimization. The first contributions cover Practical Applications of Automatic Railway Timetabling. In particular, for the problem of simultaneously scheduling all freight trains in Germany such that there are no conflicts between them, we propose a novel column generation approach. Each train can choose from an iteratively growing set of possible routes and times, so called slots. For the task of choosing maximally many slots without conflicts, we present and apply the heuristic algorithm Conflict Resolving (CR). With these two methods, we are able to schedule more than 5000 trains simultaneously, exceeding the scopes of other studies. A second practical application that we study is measuring the capacity increase in the railway network when equipping freight trains with electro-pneumatic brakes and middle buffer couplings. Methodically, we propose to explicitly construct as many slots as possible for such trains and measure the capacity as the number of constructed slots. Furthermore, we contribute to the field of Algorithms and Computability in Timetable Generation. We present two heuristic solution algorithms for the Maximum Satisfiability Problem (MaxSAT). In the literature, it has been proposed to encode different NP-complete problems that occur in railway timetabling in MaxSAT. In numerical experiments, we prove that our algorithms are competitive to state-of-the-art MaxSAT solvers. Moreover, we study the parameterized complexity status of periodic scheduling and give proofs that the problem is NP-complete for input graphs of bounded treewidth, branchwidth and carvingwidth. Finally, we propose a framework for analyzing Delay Propagation in Railway Networks. More precisely, we develop delay transmission rules based on different correlation measures that can be derived from historical operations data. What is more, we apply SHAP values from Explainable AI to the problem of discerning primary delays that occur stochastically in the operations, to secondary follow-up delays. Transmission rules that are derived from the secondary delays indicate where timetable adjustments are needed. In our last contribution in this field, we apply such adjustment rules for black-box optimization of timetables in a simulation environment

Opto-mechanical probe for combining atomic force microscopy and optical near-field surface analysis

We have developed a new easy-to-use probe that can be used to combine atomic force microscopy (AFM) and scanning near-field optical microscopy (SNOM). We show that, using this device, the evanescent field, obtained by total internal reflection conditions in a prism, can be visualized by approaching the surface with the scanning tip. Furthermore, we were able to obtain simultaneous AFM and SNOM images of a standard test grating in air and in liquid. The lateral resolution in AFM and SNOM mode was estimated to be 45 and 160 nm, respectively. This new probe overcomes a number of limitations that commercial probes have, while yielding the same resolution. (C) 2014 Optical Society of Americ

Using strong shape priors for stereo

Abstract. This paper addresses the problem of obtaining an accurate 3D reconstruction from multiple views. Taking inspiration from the recent successes of using strong prior knowledge for image segmentation, we propose a framework for 3D reconstruction which uses such priors to overcome the ambiguity inherent in this problem. Our framework is based on an object-specific Markov Random Field (MRF)[10]. It uses a volumetric scene representation and integrates conventional reconstruction measures such as photo-consistency, surface smoothness and visual hull membership with a strong object-specific prior. Simple parametric models of objects will be used as strong priors in our framework. We will show how parameters of these models can be efficiently estimated by performing inference on the MRF using dynamic graph cuts [7]. This procedure not only gives an accurate object reconstruction, but also provides us with information regarding the pose or state of the object being reconstructed. We will show the results of our method in reconstructing deformable and articulated objects.

A SAT approach to branchwidth

Branch decomposition is a prominent method for structurally decomposing a graph, a hypergraph, or a propositional formula in conjunctive normal form. The width of a branch decomposition provides a measure of how well the object is decomposed. For many applications, it is crucial to computing a branch decomposition whose width is as small as possible. We propose an approach based on Boolean Satisfiability (SAT) to finding branch decompositions of small width. The core of our approach is an efficient SAT encoding that determines with a single SAT-call whether a given hypergraph admits a branch decomposition of a certain width. For our encoding, we propose a natural partition-based characterization of branch decompositions. The encoding size imposes a limit on the size of the given hypergraph. To break through this barrier and to scale the SAT approach to larger instances, we develop a new heuristic approach where the SAT encoding is used to locally improve a given candidate decomposition until a fixed-point is reached. This new SAT-based local improvement method scales now to instances with several thousands of vertices and edges

Real-time content-aware video retargeting on the Android platform for tunnel vision assistance

As mobile devices continue to rise in popularity, advances in overall mobile device processing power lead to further expansion of their capabilities. This, coupled with the fact that many people suffer from low vision, leaves substantial room for advancing mobile development for low vision assistance. Computer vision is capable of assisting and accommodating individuals with blind spots or tunnel vision by extracting the necessary information and presenting it to the user in a manner they are able to visualize. Such a system would enable individuals with low vision to function with greater ease. Additionally, offering assistance on a mobile platform allows greater access. The objective of this thesis is to develop a computer vision application for low vision assistance on the Android mobile device platform. Specifically, the goal of the application is to reduce the effects tunnel vision inflicts on individuals. This is accomplished by providing an in-depth real-time video retargeting model that builds upon previous works and applications. Seam carving is a content-aware retargeting operator which defines 8-connected paths, or seams, of pixels. The optimality of these seams is based on a specific energy function. Discrete removal of these seams permits changes in the aspect ratio while simultaneously preserving important regions. The video retargeting model incorporates spatial and temporal considerations to provide effective image and video retargeting. Data reduction techniques are utilized in order to generate an efficient model. Additionally, a minimalistic multi-operator approach is constructed to diminish the disadvantages experienced by individual operators. In the event automated techniques fail, interactive options are provided that allow for user intervention. Evaluation of the application and its video retargeting model is based on its comparison to existing standard algorithms and its ability to extend itself to real-time. Performance metrics are obtained for both PC environments and mobile device platforms for comparison

On Structures of Large Rooted Graphs

A rooted graph is a pair (G,R), where G is a graph and R⊆V(G). There are two research topics in this thesis. One is about unavoidable substructures in sufficiently large rooted graphs. The other is about characterizations of rooted graphs excluding specific large graphs. The first topic of this thesis is motivated by Ramsey Theorem, which states that K_n and ¯(K_n ) are unavoidable induced subgraphs in every sufficiently large graph. It is also motivated by a classical result of Oporowski, Oxley, and Thomas, which determines unavoidable large 3-connected minors. We first determine unavoidable induced subgraphs, and unavoidable subgraphs in connected graphs with sufficiently many roots. We also extend this result to generalized rooted connected graphs. Secondly, we extend these results to rooted graphs of higher connectivity. In particular, we determine unavoidable subgraphs of sufficiently large rooted 2- connected graphs. Again, this result is extended to generalized rooted 2-connected graphs. The second topic of this dissertation is motivated by two results of Robertson and Seymour, let’s only talk about path and star. In the first result they established that graphs without a long path subgraph are precisely those that can be constructed using a specific operation within a bounded number of iterations, starting from the trivial graph. In the second result they showed that graphs without a large star minor are those that are subdivisions of graphs with bounded number vertices. We consider similar problems for path, star and comb. We have some theorems on characterizations of rooted connected graphs excluding a heavy path, a large (nicely) confined comb, a large (nicely) confined star, which are similar to those of Robertson and Seymour. Moreover, our results strengthen their related results