Equivariant Embeddings of Differentiable Spaces

Given a differentiable action of a compact Lie group G on a compact smooth manifold V , there exists [3] a closed embedding of V into a finite-dimensional real vector space E so that the action of G on V may be extended to a differentiable linear action (a linear representation) of G on E. We prove an analogous equivariant embedding theorem for compact differentiable spaces (∞-standard in the sense of [6, 7, 8]).

Embeddings of α-Modulation Spaces

2010 Mathematics Subject Classification: 42B35, 46E35.

Searching for Nearest Strings with Neural-Like String Embedding

We analyze an approach to a similarity preserving coding of symbol sequences based on neural distributed representations and show that it can be viewed as a metric embedding process.

Approaches to Sequence Similarity Representation

We discuss several approaches to similarity preserving coding of symbol sequences and possible connections of their distributed versions to metric embeddings. Interpreting sequence representation methods with embeddings can help develop an approach to their analysis and may lead to discovering useful properties.