Good metric spaces without good parameterizations

When Do Good Parameterizations Exist?

Good recognition is non-metric

Recognition is the fundamental task of visual cognition, yet how to formalize the general recognition problem for computer vision remains an open issue. The problem is sometimes reduced to the simplest case of recognizing matching pairs, often structured to allow for metric constraints. However, visual recognition is broader than just pair matching – especially when we consider multi-class trai...

Good Representations and Homogeneous Spaces

Remark. The word generic cannot be replaced by all. We show this in Example 6. Theorem 1 is proven first for complex groups then deduced for real groups. It is not known at this time, to the author, whether or not these results hold true for more general algebraic groups. Our proof exploits Weyl’s Unitarian Trick. Before proving this theorem, we present some corollaries to demonstrate its value...

Good-Turing Smoothing Without Tears

The performance of statistically based techniques for many tasks such as spelling correction, sense disambiguation, and translation is improved if one can estimate a probability for an object of interest which has not been seen before. Good-Turing methods are one means of estimating these probabilities for previously unseen objects. However, the use of Good-Turing methods requires a smoothing s...

Formal GAGA for good moduli spaces

We prove formal GAGA for good moduli space morphisms under an assumption of “enough vector bundles” (which holds for instance for quotient stacks). This supports the philosophy that though they are non-separated, good moduli space morphisms largely behave like proper morphisms.