When I offered to talk here, I asked myself if I had something suitable for a nice short 20 minute talk, and sent in an abstract about “cores of spaces and spectra”. However, since I have been given 50 minutes, I have decided to scrap that for something a little more substantial. It is brand new. I assume that I am among friends and that you won’t mind if some of what I say turns out to be nons...

In this paper we construct a pushforward-pullback adjoint pair for categories of quasi-coherent sheaves, along a morphism of algebraic stacks, which is represented in algebraic stacks over the site C = Affflat. The construction uses the characterization of algebraic stacks of [H3] and is based on the descent description of the category of quasi-coherent sheaves given in [H2]. We show that an es...

This paper reviews various optimization techniques available for training multi-layer perception (MLP) artificial neural networks for compression of images. These optimization techniques can be classified into two categories: Derivative-based and Derivative free optimization. The former is based on the calculation of gradient and includes Gradient Descent, Conjugate gradient, Quasi-Newton, Leve...

The (dual) Dold-Kan correspondence says that there is an equivalence of categories K : Ch → Ab between nonnegatively graded cochain complexes and cosimplicial abelian groups, which is inverse to the normalization functor. We show that the restriction of K to DG-rings can be equipped with an associative product and that the resulting functor DGR → Rings, although not itself an equivalence, does ...