Dynamic Word problems

Generating Mathematical Word Problems

This paper describes a prototype system that generates mathematical word problems from ontologies in unrestricted domains. It builds on an existing ontology verbaliser that renders logical statements written in Web Ontology Language (OWL) as English sentences. This kind of question is more complex than those normally attempted by question generation systems, since mathematical word problems con...

Word Problems By

Introduction. In studying fundamental groups of manifolds, Dehn [4] in 1911 investigated some special cases of a problem which is now known as the word problem for groups. Let G be a group generated by a finite set of elements a, b, c , . . . . Each element in G is a product of these generators and their inverses, for example, a~bacb~c. We call such expressions w(a, b, c,... ) words in the gene...

Polynomial-time Word Problems

We find polynomial-time solutions to the word problem for free-by-cyclic groups, the word problem for automorphism groups of free groups, and the membership problem for the handlebody subgroup of the mapping class group. All of these results follow from observing that automorphisms of the free group strongly resemble straight line programs, which are widely studied in the theory of compressed d...

Dynamic Word Embeddings

We present a probabilistic language model for time-stamped text data which tracks the semantic evolution of individual words over time. The model represents words and contexts by latent trajectories in an embedding space. At each moment in time, the embedding vectors are inferred from a probabilistic version of word2vec (Mikolov et al., 2013b). These embedding vectors are connected in time thro...

Word Problems for 2 - Homogeneous