Granularrules have been extensively used for classification in fuzzy datasets to promote the advancement of artificial intelligence. However, due diversity data types, how improve readability extracted granular rules while ensuring efficiency is always a challenge. Since reduct computing (GrC) can simplify real complex problem and dataset, this article carries out rule learning from perspective...

Metastatic cutaneous Crohn's disease is a rare entity first described by McCallum et al. in 1976. It is diagnosed when histologically characteristic granulomata are seen at a site not contiguous with inflammatory disease in the gastrointestinal tract. We herein report presentation, diagnosis and management of a 28 year old lady with disabling, symptomatic cutaneous Crohn's of the buttocks and n...

Consider the smooth projective models C of curves y = f(x) with f(x) ∈ Z[x] monic and separable of degree 2g + 1. We prove that for g ≥ 3, a positive fraction of these have only one rational point, the point at infinity. We prove a lower bound on this fraction that tends to 1 as g → ∞. Finally, we show that C(Q) can be algorithmically computed for such a fraction of the curves. The method can b...

This report introduces QEPCAD B, a program for computing with real algebraic sets using cylindrical algebraic decomposition (CAD). QEPCAD B both extends and improves upon the QEPCAD system for quantifier elimination by partial cylindrical algebraic decomposition written by Hoon Hong in the early 1990s. This paper briefly discusses some of the improvements in the implementation of CAD and quanti...

By representing words with probability densities rather than point vectors, probabilistic word embeddings can capture rich and interpretable semantic information and uncertainty (Vilnis & McCallum, 2014; Athiwaratkun & Wilson, 2017). The uncertainty information can be particularly meaningful in capturing entailment relationships – whereby general words such as “entity” correspond to broad distr...

Incorporating distant information via manually selected skip chain templates has been shown to be beneficial for the performance of conditional random field models in contrast to a simple linear chain based structure (Sutton and McCallum, 2007; Galley, 2006; Liu et al., 2010). The set of properties to be captured by a template is typically manually chosen with respect to the application domain....

The concept of rules for monetary policy has been more and more critized in recent years. The Deutsche Bundesbank is also urged to give up monetary targeting. The idea is that the economic performance could be improved if monetary policy became more pragmatic and was more concerned about slow growth and high unemployment. In reality, however, monetary policy in the past decades has been highly ...