A preliminary set of experiments are described in which a biologically-inspired computer vision system (Serre, Wolf et al. 2005; Serre 2006; Serre, Oliva et al. 2006; Serre, Wolf et al. 2006) designed for visual object recognition was applied to the task of phonetic classification. During learning, the system processed 2-D wideband magnitude spectrograms directly as images, producing a set of 2...

the blow-up of |KC +D| along the image of C (which we will also denote by C). In contrast, the Serre correspondence is a morphism only when d ≤ 2, as it is undefined at points of C (and certain secant varieties) for larger values of d. The structure of the Serre correspondence for large d (particularly d > 2g − 2, in which case it is dominant) is, however, well understood now, due largely to re...

Spectral sequences are a powerful bookkeeping tool, used to handle large amounts of information. As such, they have become nearly ubiquitous in algebraic topology and algebraic geometry. In this paper, we take a few results on faith (i.e., without proof, pointing to books in which proof may be found) in order to streamline and simplify the exposition. From the exact couple formulation of spectr...

Let $$(\mathbf{U}, \mathbf{U}^\imath )$$ be a quantum symmetric pair of Kac–Moody type. The $$\imath $$ groups $$\mathbf{U}^\imath and the universal $$\widetilde{\mathbf{U}}^\imath can viewed as generalization Drinfeld doubles $$\widetilde{\mathbf{U}}$$ . In this paper we formulate establish Serre–Lusztig relations for in terms divided powers, which are an -analog Lusztig’s higher order Serre g...

We give some new examples for which the Serre problem is solvable by using invariant pseudodistances.

We demonstrate that commutativity of numerous one-dimensional subalgebras in W1+∞ algebra, i.e. the existence many non-trivial integrable systems described recent arXiv:2303.05273 follows from subset relations algebra known as Serre relations. No other are needed for commutativity. The survive deformation to affine Yangian Y(glˆ1), hence commutative do well. A special case parameters correspond...