Embedded graph invariants in Chern-Simons theory

Chern-Simons gauge theory, since its inception as a topological quantum field theory, has proved to be a rich source of understanding for knot invariants. In this work the theory is used to explore the definition of the expectation value of a network of Wilson lines - an embedded graph invariant. Using a slight generalization of the variational method, lowest-order results for invariants for arbitrary valence graphs are derived; gauge invariant operators are introduced; and some higher order results are found. The method used here provides a Vassiliev-type definition of graph invariants which depend on both the embedding of the graph and the group structure of the gauge theory. It is found that one need not frame individual vertices. Though, without a global projection of the graph, there is an ambiguity in the relation of the decomposition of distinct vertices. It is suggested that framing may be seen as arising from this ambiguity - as a way of relating frames at distinct vertices.Comment: 20 pages; RevTex; with approx 50 ps figures; References added, introduction rewritten, version to be published in Nuc. Phys.

SemTab 2019: Resources to Benchmark Tabular Data to Knowledge Graph Matching Systems

Tabular data to Knowledge Graph matching is the process of assigning semantic tags from knowledge graphs (e.g., Wikidata or DBpedia) to the elements of a table. This task is a challenging problem for various reasons, including the lack of metadata (e.g., table and column names), the noisiness, heterogeneity, incompleteness and ambiguity in the data. The results of this task provide significant insights about potentially highly valuable tabular data, as recent works have shown, enabling a new family of data analytics and data science applications. Despite significant amount of work on various flavors of this problem, there is a lack of a common framework to conduct a systematic evaluation of state-of-the-art systems. The creation of the Semantic Web Challenge on Tabular Data to Knowledge Graph Matching (SemTab) aims at filling this gap. In this paper, we report about the datasets, infrastructure and lessons learned from the first edition of the SemTab challenge

Robust Component-based Network Localization with Noisy Range Measurements

Accurate and robust localization is crucial for wireless ad-hoc and sensor networks. Among the localization techniques, component-based methods advance themselves for conquering network sparseness and anchor sparseness. But component-based methods are sensitive to ranging noises, which may cause a huge accumulated error either in component realization or merging process. This paper presents three results for robust component-based localization under ranging noises. (1) For a rigid graph component, a novel method is proposed to evaluate the graph's possible number of flip ambiguities under noises. In particular, graph's \emph{MInimal sepaRators that are neaRly cOllineaR (MIRROR)} is presented as the cause of flip ambiguity, and the number of MIRRORs indicates the possible number of flip ambiguities under noise. (2) Then the sensitivity of a graph's local deforming regarding ranging noises is investigated by perturbation analysis. A novel Ranging Sensitivity Matrix (RSM) is proposed to estimate the node location perturbations due to ranging noises. (3) By evaluating component robustness via the flipping and the local deforming risks, a Robust Component Generation and Realization (RCGR) algorithm is developed, which generates components based on the robustness metrics. RCGR was evaluated by simulations, which showed much better noise resistance and locating accuracy improvements than state-of-the-art of component-based localization algorithms.Comment: 9 pages, 15 figures, ICCCN 2018, Hangzhou, Chin