Abstract. We use the Chebyshev knot diagram model of Koseleff and Pecker in order to introduce a random knot diagram model by assigning the crossings to be positive or negative uniformly at random. We give a formula for the probability of choosing a knot at random among all knots with bridge index at most 2. Restricted to this class, we define internal and external reduction moves that decrease the number of crossings of the diagram. We make calculations based on our formula, showing the numerics in graphs and providing evidence for our conjecture that the probability of any knot K appearing in this model decays to zero as the number of crossings goes to infinity.
The ability to create and interact with large-scale domainspecific knowledge bases from unstructured/semi-structured data is the foundation for many industry-focused cognitive systems. We will demonstrate the Content Services system that provides cloud services for creating and querying highquality domain-specific knowledge bases by analyzing and integrating multiple (un/semi)structured content sources. We will showcase an instantiation of the system for a financial domain. We will also demonstrate both cross-lingual natural language queries and programmatic API calls for interacting with this knowledge base.
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