Multiple Disjointness for Weakly Mixing Regular Minimal Flows

Disjointness of Mobius from Horocycle Flows

We formulate and prove a finite version of Vinogradov’s bilinear sum inequality.We use it together with Ratner’s joinings theorems to prove that the Mobius function is disjoint from discrete horocycle flows on Γ\SL2(R).

Multiple returns for some regular and mixing maps.

We study the distributions of the number of visits for some noteworthy dynamical systems, considering whether limit laws exist by taking domains that shrink around points of the phase space. It is well known that for highly mixing systems such limit distributions exhibit a Poissonian behavior. We analyze instead a skew integrable map defined on a cylinder that models a shear flow. Since almost ...

Characterizations of Regular Almost Periodicity in Compact Minimal Abelian Flows

Regular almost periodicity in compact minimal abelian flows was characterized for the case of discrete acting group by W. Gottschalk and G. Hedlund and for the case of 0-dimensional phase space by W. Gottschalk a few decades ago. In 1995 J. Egawa gave characterizations for the case when the acting group is R. We extend Egawa’s results to the case of an arbitrary abelian acting group and a not n...

Weakly Distance-regular Digraphs

Finding Minimal Multiple Generalization over Regular Patterns with Alphabet Indexing

We propose a learning algorithm that discovers a motif represented by patterns and an alphabet indexing from biosequences. From only positive examples with the help of an alphabet indexing, the algorithm nds k regular patterns as a k-minimal multiple generalization (k-mmg for short). The computational results for transmembrane domains indicate that the combination of k-mmg and alphabet indexing...