Third-order tensors are widely used as a mathematical tool for modeling physical properties of media in solid state physics. In most cases, they arise constitutive proportionality between basic physics quantities. The tensor can be considered complete set parameters medium. algebraic features the seen proper identification natural material, crystals, and design artificial nano-materials with pr...

We present algorithms for higher-order dependency parsing that are “third-order” in the sense that they can evaluate substructures containing three dependencies, and “efficient” in the sense that they require only O(n4) time. Importantly, our new parsers can utilize both sibling-style and grandchild-style interactions. We evaluate our parsers on the Penn Treebank and Prague Dependency Treebank,...