Semigroups of finite-dimensional random projections

Ashs Theorem, Finite Nilpotent Semigroups, and One-Dimensional Tiling Semigroups

This is the manuscript for a talk given at CAUL (19 October, 2001) and also at Northern Illinois University (26 July, 2002). I am grateful to CAUL for their generous support during my visit there in October/November 2001) and to the Department of Mathematical Sciences at NIU (in particular to W.D. Blair) for the mini-conference on the occasion my my retirement.

Dynamics of Finite Semigroups

Dualisability of Finite Semigroups

We describe the inherently non-dualisable finite algebras from some semigroup related classes. The classes for which this problem is solved include the variety of bands, the pseudovariety of aperiodic monoids, commutative monoids, and (assuming a reasonable conjecture in the literature) the varieties of all finite monoids and finite inverse semigroups. The first example of an inherently non-dua...

Random projections of random manifolds

Interesting data often concentrate on low dimensional smooth manifolds inside a high dimensional ambient space. Random projections are a simple, powerful tool for dimensionality reduction of such data. Previous works have studied bounds on how many projections are needed to accurately preserve the geometry of these manifolds, given their intrinsic dimensionality, volume and curvature. However, ...

Decidability and Tameness in the Theory of Finite Semigroups