Graph embeddings for low-stretch greedy routing

The simplest greedy geometric routing forwards packets to make most progress in terms of geometric distance within reach. Its notable advantages are low complexity, and the use of local information only. However, two problems of greedy routing are that delivery is not always guaranteed, and that the greedy routes may take more hops than the corresponding shortest paths. Additionally, in dynamic multihop networks, routing elements can join or leave during network operation or exhibit intermittent failures. Even a single link or node removal may invalidate the greedy routing success guarantees. Greedy embedding is a graph embedding that makes the simple greedy packet forwarding successful for every source-destination pair. In this dissertation, we consider the problems of designing greedy graph embeddings that also yield low hop stretch of the greedy paths over the shortest paths and can accommodate network dynamics. In the first part of the dissertation, we consider embedding and routing for arbitrary unweighted network graphs, based on greedy routing and utilizing virtual node coordinates. We propose an algorithm for online greedy graph embedding in the hyperbolic plane that enables incremental embedding of network nodes as they join the network, without disturbing the global embedding. As an alternative to frequent reembedding of temporally dynamic network graphs in order to retain the greedy embedding property, we propose a simple but robust generalization of greedy geometric routing called Gravity--Pressure (GP) routing. Our routing method always succeeds in finding a route to the destination provided that a path exists, even if a significant fraction of links or nodes is removed subsequent to the embedding. GP routing does not require precomputation or maintenance of special spanning subgraphs and is particularly suitable for operation in tandem with our proposed algorithm for online graph embedding. In the second part of the dissertation we study how topological and geometric properties of embedded graphs influence the hop stretch. Based on the obtained insights, we synthesize embedding heuristics that yield minimal hop stretch greedy embeddings. Finally, we verify their effectiveness on models of synthetic graphs as well as instances of several classes of real-world network graphs

Low Distortion Delaunay Embedding of Trees in Hyperbolic Plane

This paper considers the problem of embedding trees into the hyperbolic plane. We show that any tree can be realized as the Delaunay graph of its embedded vertices. Particularly, a weighted tree can be embedded such that the weight on each edge is realized as the hyperbolic distance between its embedded vertices. Thus the embedding preserves the metric information of the tree along with its topology. The distance distortion between non adjacent vertices can be made arbitrarily small – less than a (1 + ε) factor for any given ε. Existing results on low distortion of embedding discrete metrics into trees carry over to hyperbolic metric through this result. The Delaunay character implies useful properties such as guaranteed greedy routing and realization as minimum spanning trees

Information-theoretic environment modeling for mobile robot localization

To enhance robotic computational efficiency without degenerating accuracy, it is imperative to fit the right and exact amount of information in its simplest form to the investigated task. This thesis conforms to this reasoning in environment model building and robot localization. It puts forth an approach towards building maps and localizing a mobile robot efficiently with respect to unknown, unstructured and moderately dynamic environments. For this, the environment is modeled on an information-theoretic basis, more specifically in terms of its transmission property. Subsequently, the presented environment model, which does not specifically adhere to classical geometric modeling, succeeds in solving the environment disambiguation effectively. The proposed solution lays out a two-level hierarchical structure for localization. The structure makes use of extracted features, which are stored in two different resolutions in a single hybrid feature-map. This enables dual coarse-topological and fine-geometric localization modalities. The first level in the hierarchy describes the environment topologically, where a defined set of places is described by a probabilistic feature representation. A conditional entropy-based criterion is proposed to quantify the transinformation between the feature and the place domains. This criterion provides a double benefit of pruning the large dimensional feature space, and at the same time selecting the best discriminative features that overcome environment aliasing problems. Features with the highest transinformation are filtered and compressed to form a coarse resolution feature-map (codebook). Localization at this level is conducted through place matching. In the second level of the hierarchy, the map is viewed in high-resolution, as consisting of non-compressed entropy-processed features. These features are additionally tagged with their position information. Given the identified topological place provided by the first level, fine localization corresponding to the second level is executed using feature triangulation. To enhance the triangulation accuracy, redundant features are used and two metric evaluating criteria are employ-ed; one for dynamic features and mismatches detection, and another for feature selection. The proposed approach and methods have been tested in realistic indoor environments using a vision sensor and the Scale Invariant Feature Transform local feature extraction. Through experiments, it is demonstrated that an information-theoretic modeling approach is highly efficient in attaining combined accuracy and computational efficiency performances for localization. It has also been proven that the approach is capable of modeling environments with a high degree of unstructuredness, perceptual aliasing, and dynamic variations (illumination conditions; scene dynamics). The merit of employing this modeling type is that environment features are evaluated quantitatively, while at the same time qualitative conclusions are generated about feature selection and performance in a robot localization task. In this way, the accuracy of localization can be adapted in accordance with the available resources. The experimental results also show that the hybrid topological-metric map provides sufficient information to localize a mobile robot on two scales, independent of the robot motion model. The codebook exhibits fast and accurate topological localization at significant compression ratios. The hierarchical localization framework demonstrates robustness and optimized space and time complexities. This, in turn, provides scalability to large environments application and real-time employment adequacies

Towards Quantitative Endoscopy with Vision Intelligence

In this thesis, we work on topics related to quantitative endoscopy with vision-based intelligence. Specifically, our works revolve around the topic of video reconstruction in endoscopy, where many challenges exist, such as texture scarceness, illumination variation, multimodality, etc., and these prevent prior works from working effectively and robustly. To this end, we propose to combine the strength of expressivity of deep learning approaches and the rigorousness and accuracy of non-linear optimization algorithms to develop a series of methods to confront such challenges towards quantitative endoscopy. We first propose a retrospective sparse reconstruction method that can estimate a high-accuracy and density point cloud and high-completeness camera trajectory from a monocular endoscopic video with state-of-the-art performance. To enable this, replacing the role of a hand-crafted local descriptor, a deep image feature descriptor is developed to boost the feature matching performance in a typical sparse reconstruction algorithm. A retrospective surface reconstruction pipeline is then proposed to estimate a textured surface model from a monocular endoscopic video, where self-supervised depth and descriptor learning and surface fusion technique is involved. We show that the proposed method performs superior to a popular dense reconstruction method and the estimate reconstructions are in good agreement with the surface models obtained from CT scans. To align video-reconstructed surface models with pre-operative imaging such as CT, we introduce a global point cloud registration algorithm that is robust to resolution mismatch that often happens in such multi-modal scenarios. Specifically, a geometric feature descriptor is developed where a novel network normalization technique is used to help a 3D network produce more consistent and distinctive geometric features for samples with different resolutions. The proposed geometric descriptor achieves state-of-the-art performance, based on our evaluation. Last but not least, a real-time SLAM system that estimates a surface geometry and camera trajectory from a monocular endoscopic video is developed, where deep representations for geometry and appearance and non-linear factor graph optimization are used. We show that the proposed SLAM system performs favorably compared with a state-of-the-art feature-based SLAM system

Handbook of Mathematical Geosciences

This Open Access handbook published at the IAMG's 50th anniversary, presents a compilation of invited path-breaking research contributions by award-winning geoscientists who have been instrumental in shaping the IAMG. It contains 45 chapters that are categorized broadly into five parts (i) theory, (ii) general applications, (iii) exploration and resource estimation, (iv) reviews, and (v) reminiscences covering related topics like mathematical geosciences, mathematical morphology, geostatistics, fractals and multifractals, spatial statistics, multipoint geostatistics, compositional data analysis, informatics, geocomputation, numerical methods, and chaos theory in the geosciences

Using MapReduce Streaming for Distributed Life Simulation on the Cloud

Distributed software simulations are indispensable in the study of large-scale life models but often require the use of technically complex lower-level distributed computing frameworks, such as MPI. We propose to overcome the complexity challenge by applying the emerging MapReduce (MR) model to distributed life simulations and by running such simulations on the cloud. Technically, we design optimized MR streaming algorithms for discrete and continuous versions of Conway’s life according to a general MR streaming pattern. We chose life because it is simple enough as a testbed for MR’s applicability to a-life simulations and general enough to make our results applicable to various lattice-based a-life models. We implement and empirically evaluate our algorithms’ performance on Amazon’s Elastic MR cloud. Our experiments demonstrate that a single MR optimization technique called strip partitioning can reduce the execution time of continuous life simulations by 64%. To the best of our knowledge, we are the first to propose and evaluate MR streaming algorithms for lattice-based simulations. Our algorithms can serve as prototypes in the development of novel MR simulation algorithms for large-scale lattice-based a-life models.https://digitalcommons.chapman.edu/scs_books/1014/thumbnail.jp