We study the minimal density of letters in infinite square-free words. First, we give some definitions of minimal density in infinite words and prove their equivalence. Further, we propose a method that allows to strongly reduce an exhaustive search for obtaining lower bounds for minimal density. Next, we develop a technique for constructing square-free morphisms with extremely small density fo...

Data stream classification poses many challenges, most of which are not addressed by the state-of-the-art. We present DXMiner, which addresses four major challenges to data stream classification, namely, infinite length, concept-drift, concept-evolution, and featureevolution. Data streams are assumed to be infinite in length, which necessitates single-pass incremental learning techniques. Conce...

In [Z] we defined the notion of an “inference method” which given a finite binary string guesses its continuation. We showed that a special class of these inference methods could be used to construct a very general theory of confirmation. In this paper we investigate the class of strings which are unpredictable with respect to these inference method-that is, infinite strings which are such that...

In a recent paper, Brlek, Jamet and Paquin showed that some extremal infinite smooth words are also infinite Lyndon words. This result raises a natural question: are they the only ones? If no, what do the infinite smooth words that are also Lyndon words look like? In this paper, we give the answer, proving that the only infinite smooth Lyndon words are m{a<b}, with a, b even, m{1<b} and ∆ −1 1 ...