MOTIVATION Recently, a range of new statistics have become available for the alignment-free comparison of two sequences based on k-tuple word content. Here, we extend these statistics to the simultaneous comparison of more than two sequences. Our suite of statistics contains, first, C(*)1 and C(S)1, extensions of statistics for pairwise comparison of the joint k-tuple content of all the sequenc...

A vector space partition of a finite vector space V over the field of q elements is a collection of subspaces whose union is all of V and whose pairwise intersections are trivial. While a number of necessary conditions have been proved for certain types of vector space partitions to exist, the problem of the existence of partitions meeting these conditions is still open. In this note, we consid...

A seminal result of Reed et al. [15] in 1996 states that the Erdős-Pósa property holds for directed cycles, i.e. for every integer n there is an integer t such that every directed graph G has n pairwise vertex disjoint directed cycles or contains a set T ⊆ V (G) of at most t vertices such that G−T contains no directed cycle. In this paper, we consider the Erdős-Pósa property for directed cycles...

An independent dominating set of a graph, also known as maximal set, is S pairwise non-adjacent vertices such that every vertex not in adjacent to some S. We prove for Δ=4 or Δ≥6, connected n-vertex graph maximum degree at most Δ has an size (1−Δ⌊Δ2/4⌋+Δ)(n−1)+1. In addition, we characterize all graphs having the equality and show other have (1−Δ⌊Δ2/4⌋+Δ)n.

Background and Aim: Previous studies have shown that some dyes used in photodynamic therapy (PDT) have a low pH and may cause root demineralization and remove the smear layer. This study aimed to assess and compare the effects of root biomodification with citric acid and PDT on the adhesion and proliferation of human gingival fibroblasts (HGFs). Materials and Methods: In this in vitro experime...

We introduce a new approach to compare DNA primary sequences. The core of our method is a new measure of pairwise distances among sequences. Using the primitive discrimination substrings of sequence S and Q, a discrimination measure DM(S, Q) is defined for the similarity analysis of them. The proposed method does not require multiple alignments and is fully automatic. To illustrate its utility,...

While it was noted by R. Hardy and proved in a famous paper by C. A. Micchelli that radial basis function interpolants s(x) = ∑ λjφ(‖x − xj‖) exist uniquely for the multiquadric radial function φ(r) = √ r2 + c2 as soon as the (at least two) centres are pairwise distinct, the error bounds for this interpolation problem always demanded an added constant to s. By using Pontryagin native spaces, we...