We focus on Θ-rich and almost Θ-rich words over a finite alphabet A, where Θ is an involutive antimorphism over A∗. We show that any recurrent almost Θ-rich word u is an image of a recurrent Θ′-rich word under a suitable morphism, where Θ′ is also an involutive antimorphism. Moreover, if the word u is uniformly recurrent, we show that Θ′ can be set to the reversal mapping. We also treat one spe...

We study a transformation on terms consisting of applying an inverse deterministic rational mapping followed by an unfolding. Iterating these transformations from the regular terms gives a hierarchy of families of terms having a decidable monadic theory. In particular, the family at level 2 contains the morphic innnite words investigated by Carton and Thomas. We show that this hierarchy coincid...

A D0L-system is a triple (A,σ,w) where A is a finite alphabet, σ is an endomorphism of the free monoid over A, and w is a word over A. The D0L-sequence generated by (A,σ,w) is the sequence of words (w, σ(w), σ(σ(w)), σ(σ(σ(w))), . . . ). The corresponding sequence of lengths, i.e, the function mapping each integer n ≥ 0 to |σn(w)|, is called the growth function of (A,σ,w). In 1978, Salomaa and ...

We present a type-theoretic encoding of extensible objects and types. The ambient theory is a higher-order-calculus with poly-morphic types, recursive types and operators, and subtyping. Using this theory, we give a type preserving and computationally adequate translation of a full-edged object calculus that includes object extension and override. The translation specializes to calculi of nonex...

In this paper we study a generalization of the classical notions of bordered and unbordered words, motivated by DNA computing. DNA strands can be viewed as finite strings over the alphabet {A, G, C, T}, and are used in DNA computing to encode information. Due to the fact that A is Watson-Crick complementary to T and G to C, DNA single strands that are Watson-Crick complementary can bind to each...

Aword is called fair if it contains, for each pair of distinct symbols a, b, the same number of occurrences of the scattered subword ab as of ba. We prove that if the first k + 1 words in the sequence generated by a D0L system over a k-letter alphabet are fair then all words in the sequence are fair. © 2007 Elsevier B.V. All rights reserved.

This paper defines the q-analogue of a matroid and establishes several properties like duality, restriction and contraction. We discuss possible ways to define a q-matroid, and why they are (not) crypto-morphic. Also, we explain the motivation for studying q-matroids by showing that a rank metric code gives a q-matroid. This paper establishes the definition and several basic properties of q-mat...

PURPOSE Sophisticated small animal irradiators, incorporating cone-beam-CT image-guidance, have recently been developed which enable exploration of the efficacy of advanced radiation treatments in the preclinical setting. Microstereotactic-body-radiation-therapy (microSBRT) is one technique of interest, utilizing field sizes in the range of 1-15 mm. Verification of the accuracy of microSBRT tre...