Recurrence and Incompressibility

Recurrence and Incompressibility

Incompressibility and Global Inversion

Given a local diffeomorphism f : R → R, we consider certain incompressibility conditions on the parallelepiped Df(x) ([0, 1]) which imply that the pre-image of an affine subspace is non-empty and has trivial homotopy groups. These conditions are then used to establish criteria for f to be globally invertible, generalizing in all dimensions the previous results of Sabatini.

Large Alphabets and Incompressibility

We briefly survey some concepts related to empirical entropy — normal numbers, de Bruijn sequences and Markov processes — and investigate how well it approximates Kolmogorov complexity. Our results suggest lth-order empirical entropy stops being a reasonable complexity metric for almost all strings of length m over alphabets of size n about when nl surpasses m.

Incompressibility and Least-area Surfaces

We show that if F is a smooth, closed, orientable surface embedded in a closed, orientable 3-manifold M such that for each Riemannian metric g on M , F is isotopic to a least-area surface F (g), then F is incompressible.

Modeling durational incompressibility

We show how incompressibility, a well-described property of some prosodic timing effects, can be accounted for in an optimization-based model of speech timing. Preliminary results of a corpus study are presented, replicating and generalizing previous findings on incompressibility as a function of increasing speaking rate. We then introduce the architecture of our model and present results of si...