Affine transformation with zero entropy and nilsystems

Zero - Entropy Affine Maps on Homogeneous Spaces

IPr -recurrence and nilsystems

By a result due to Furstenberg, a homeomorphism T of a compact space is distal if and only if it possesses the property of IP-recurrence, meaning that for any x0 ∈ X, for any open neighborhood U of x0, and for any sequence (ni) in Z, the set RU (x0) = {n ∈ Z : T x0 ∈ U} has a non-trivial intersection with the set of finite sums {ni1 +ni2 + · · ·+nis : i1 < i2 < . . . < is, s ∈ N}. We show that ...

Extractors for Affine Sources with Polylogarithmic Entropy

We give the first explicit construction of deterministic extractors for affine sources over F2, with entropy k ≥ log n for some large enough constant C, where n is the length of the source. Previously the best known results are by Bourgain [Bou07], Yehudayoff [Yeh11] and Li [Li11b], which require the affine source to have entropy at least Ω(n/ √ log log n). Our extractor outputs one bit with er...

Automatic Detection of Signs with Affine Transformation

In this paper, we propose an approach for detecting signs from natural scenes. The approach efficiently embeds multi-resolution, adaptive search, and affine rectification algorithms in a hierarchical framework, with different emphases at each layer. We combine multi-resolution and multi-scale edge detection techniques to effectively detect text in different sizes. Different from the existing ap...

Complexity of infinite sequences with zero entropy

The complexity function of an infinite word w on a finite alphabet A is the sequence counting, for each nonnegative n, the number of words of lenght n on the alphabet A that are factors of the infinite word w. The goal of this work is to estimate the number of words of lenght n on the alphabet A that are factors of an infinite word w with a complexity function bounded by a given function f with...