Pursuing the study started by Rigo, Salimov and Vandomme, we use elementary number-theoretic techniques to characterize rotation words having a finite set of abelian returns to all prefixes. We also make the connection between the three gap theorem and the number of semi-abelian returns for Sturmian words, simplifying some arguments developed by Puzynina and Zamboni.

We use a weak Gibbs property and a weak form of specification to derive level-2 large deviations principles for symbolic systems equipped with a large class of reference measures. This has applications to a broad class of coded systems, including β-shifts, S-gap shifts, and their factors. Our techniques are suitable for adaptation beyond the symbolic setting.

Depending on temperature, the modified Hodgkin-Huxley (MHH) equations exhibit a variety of dynamical behaviors, including intrinsic chaotic firing. We analyze synchronization in a large ensemble of MHH neurons that are interconnected with gap junctions. By evaluating tangential Lyapunov exponents we clarify whether the synchronous state of neurons is chaotic or periodic. Then, we evaluate trans...

In this short and self contained paper we are proposing a simple penalty, which is a modification on the constraint set. We show that duality gap is eliminated under certain conditions.