This past October, I published an editorial (Blatt, 2015) appraising the social media phenomenon of PubPeer. I raised several issues with the Web site that I maintain do not serve the scientific community and will only entrench many of the underlying attitudes and behaviors that PubPeer claims it seeks to counter. The response tomyeditorial exceededall expectations— in 18 days it garnered 348 c...

An infinite permutation α is a linear ordering of N. We study properties of infinite permutations analogous to those of infinite words and showing some resemblance and some difference between permutations and words. In this paper, we define maximal pattern complexity pα(n) for infinite permutations and show that this complexity function is ultimately constant if and only if the permutation is u...

By the famous theorem of Morse and Hedlund, a word is ultimately periodic if and only if it has bounded subword complexity, i.e., for sufficiently large n, the number of factors of length n is constant. In this paper we consider relational periods and relationally periodic sequences, where the relation is a similarity relation on words induced by a compatibility relation on letters. We investig...

We call a one-way innnite word w over a nite alphabet (; p)-repetitive if all long enough preexes of w contain as a suux a th power (or more generally a repetition of order) of a word of length at most p. We show that each (2; 4)-repetitive word is ultimately periodic, as well as that there exist nondenumerably many, and hence also nonultimately periodic, (2; 5)-repetitive words. Further we cha...

According to biological strategy for pest control, we investigate the dynamic behavior of a pest management SEI model with nonlinear incidence concerning impulsive strategyperiodic releasing infected pests at fixed times. We prove that all solutions of the system are uniformly ultimately bounded and there exists a globally asymptotically attractive pest-eradication periodic solution when the im...

Let C be a class of relational structures. We denote by fC(n) the number of structures in C over the labeled set {0, . . . , n − 1}. For any C definable in monadic second order logic with unary and binary relation symbols only, E. Specker and C. Blatter showed that for every m ∈ N, the function fC satisfies a linear recurrence relation modulo m, and hence it is ultimately periodic modulo m. The...

To extend a natural concept of equivalence of sequences to two-sided infinite sequences, the notion of permutation transducer is introduced. Requiring the underlying automaton to be deterministic in two directions, it provides the means to rewrite bi-infinite sequences. The first steps in studying the ensuing hierarchy of equivalence classes of bi-infinite sequences are taken, by describing the...

Given an integer base b > 1, a set of integers is represented in base b by a language over {0, 1, ..., b − 1}. The set is said to be b-recognisable if its representation is a regular language. It is known that ultimately periodic sets are b-recognisable in every base b, and Cobham’s theorem implies the converse: no other set is b-recognisable in every base b. We are interested in deciding wheth...