Geodesic laminations is a remarkable abstraction (due to W. P. Thurston) of many otherwise unrelated phenomena occurring in differential geometry, complex analysis and geometric topology. In this article we focus on connections of geodesic laminations with the inductive limits of finite-dimensional semi-simple C-algebras (AF C-algebras). Our main result is a bijection between combinatorial pres...

Automated reasoning of inductive theorems is considered important in program verification. To verify inductive theorems automatically, several implicit induction methods like the inductionless induction and the rewriting induction methods have been proposed. In studying inductive theorems on higher-order rewritings, we found that the class of the theorems shown by known implicit induction metho...

We show that finitely generated subhomogeneous C∗-algebras have finite decomposition rank. As a consequence, any separable ASH C∗-algebra can be written as an inductive limit of subhomogeneous C∗-algebras each of which has finite decomposition rank. It then follows from work of H. Lin and of the second named author that the class of simple unital ASH algebras which have real rank zero and absor...

In plants of Sinapis alba and Arabidopsis thaliana, leaf exudate (phloem sap) was analysed during and after a single long day inducing flowering and in control short days. The amounts of carbohydrates and amino acids were measured to estimate the organic C : N ratio. In both species, the C : N ratio of the phloem sap increased markedly and early during the inductive treatment, suggesting that a...

We consider finite approximations of a topological space M by noncommutative lattices of points. These lattices are structure spaces of noncommutativeC∗-algebras which in turn approximate the algebra C(M) of continuous functions on M . We show how to recover the space M and the algebra C(M) from a projective system of noncommutative lattices and an inductive system of noncommutative C∗-algebras...

We show that unital simple C-algebras with tracial topological rank zero which are locally approximated by subhomogeneous C-algebras can be classified by their ordered K-theory. We apply this classification result to show that certain simple crossed products are isomorphic if they have the same ordered K-theory. In particular, irrational higher dimensional noncommutative tori of the form C(T)×θ...

This paper reviews our recent work on applying inductive logic programming to the construction of natural language processing systems. We have developed a system, Chill, that learns a parser from a training corpus of parsed sentences by inducing heuristics that control an initial overly-general shift-reduce parser. Chill learns syntactic parsers as well as ones that translate English database q...

We consider, in a quite general setting, inductive limits of weighted spaces holomorphic functions the unit ball $${{\mathbb {C}}}^n$$ . The relationship between sets uniqueness, weakly sufficient and sampling these is studied. In particular, equivalence sets, under some conditions weights, obtained.

Induction-induction is a principle for mutually defining data types A ∶ Set and B ∶ A→ Set. Both A and B are defined inductively, and the constructors for A can refer to B and vice versa. In addition, the constructor for B can refer to the constructor for A. Induction-induction occurs in a natural way when formalising dependent type theory in type theory. We give some examples of inductive-indu...