Is it fixed-parameter tractable to find an out-directed spanning tree of a given digraph with the maximum possible k of leaves? More precisely, consider a digraph D. An out-tree of D is a subtree in which all vertices but one have in-degree exactly 1. The vertices of out-degree 0 are called leaves. Let `(D) denote the maximum number of leaves of any out-tree in D. An out-branching of D is an ou...

Background: Screening and counselling is the most effective way to prevent the birth of children with thalassemia major. An accurate and relatively less time-consuming protocol is necessary to screen large populations. Separating iron deficiency anaemia from thalassemia trait based on blood cell parameters has been used by hematologists for many years. We aimed to design a new approach to scree...

The suffix tree — the compacted trie of all suffixes a string is most important and widely-used data structure in processing. We consider natural combinatorial question about trees: for S length n, how many nodes νS(d) can there be at (string) depth d its tree? prove ν(n,d)=maxS∈Σn⁡νS(d) O((n/d)log⁡(n/d)), show that this bound asymptotically tight, describing strings which Ω((n/d)log⁡(n/d)).

In this paper we provide an example of a modified antiferromagnetic Potts model which has uniqueness on the d-regular tree but does not have uniqueness on some infinite d-regular graphs. This example runs counter to the notion that the regular tree has the slowest decay of correlation amongst d-regular graphs. Sokal [7] conjectured that uniqueness in the hard-core model on the d-regular tree im...

An optimal three-dimensional (3-D) coefficient tree structure for 3-D zerotree wavelet video coding is considered in this paper. The 3-D zerotree wavelet video coding is inspired by the success of the two-dimensional (2-D) zerotree wavelet image coding. Existing 3-D zerotree wavelet video codecs use the either symmetric or symmetric-alike 3-D tree structure, which is a straightforward extension...

This chapter describes a novel ACO algorithm for the degree-constrained minimum spanning tree (d-MST) problem. Instead of constructing the d-MST directly on the construction graph, ants construct the encoded d-MST. Two well-known tree codings are used: the Prüfer code, and the more recent Blob code (Picciotto, 1999). Both of these tree codings are bijective because they represent each spanning ...

Recent epidemiologic studies assessing tree nut (almonds, Brazil nuts, cashews, hazelnuts, macadamia nuts, pecans, pine nuts, pistachios, and walnuts) consumption and the association with nutrient intake and diet quality are lacking. This study determined the association of tree nut consumption and nutrient intake and diet quality using a nationally representative sample of adults. Adults 19+ y...