The Incompressibility Argument

The Incompressibility Method

Kolmogorov complexity is a modern notion of randomness dealing with the quantity of information in individual objects; that is, pointwise randomness rather than average randomness as produced by a random source. It was proposed by A.N. Kolmogorov in 1965 to quantify the randomness of individual objects in an objective and absolute manner. This is impossible for classical probability theory. Kol...

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...

Recurrence and Incompressibility

Incompressibility of Products

We show that the conjectural criterion of p-incompressibility for products of projective homogeneous varieties in terms of the factors, previously known in a few special cases only, holds in general. We identify the properties of projective homogeneous varieties actually needed for the proof to go through. For instance, generically split (nonhomogeneous) varieties also satisfy these properties....

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.