Note on islands in path-length sequences of binary trees

An earlier characterization of topologically ordered (lexicographic) path-length sequences of binary trees is reformulated in terms of an integrality condition on a scaled Kraft sum of certain subsequences (full segments, or islands). The scaled Kraft sum is seen to count the set of ancestors at a certain level of a set of topologically consecutive leaves is a binary tree.Comment: 4 page

Wings

https://digitalcommons.library.umaine.edu/mmb-vp/7380/thumbnail.jp

When You And I Were Seventeen

With ukulele arrangement. Contains advertisements and/or short musical examples of pieces being sold by publisher.https://digitalcommons.library.umaine.edu/mmb-vp/6836/thumbnail.jp

Embedding the affine complement of three intersecting lines in a finite projective plane

An (r, 1)–design is a pair (V, F) where V is a ν–set and F is a family of non-null subsets of V (b in number) which satisfy the following. (1) Every pair of distinct members of V is contained in precisely one member of F. (2) Every member of V occurs in precisely r members of F. A pseudo parallel complement PPC(n, α) is an (n+1, 1)–design with ν=n2−αn and b≦n2+n−α in which there are at least n−α a blocks of size n. A pseudo intersecting complement PIC(n, α) is an (n+1, 1)–design with ν=n2−αn+α−1 and b≦n2+n−α in which there are at least n−α+1 blocks of size n−1. It has previously been shown that for α≦4, every PIC(n, α) can be embedded in a PPC(n, α−1) and that for n>(α4−2α3+2α2+α−2)/2, every PPC(n, α) can be embedded in a finite projective plane of order n. In this paper we investigate the case of α=3 and show that any PIC(n, 3) is embeddable in a PPC(n,2) provided n≧14

You\u27re In Kentucky Sure As You\u27re Born

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Model-based iterative reconstruction in paediatric head computed tomography : a pilot study on dose reduction in children

Purpose: To evaluate the potential of model-based iterative reconstruction (MBIR) on dose reduction and image quality in children undergoing computed tomography (CT) head examinations. Material and methods: This prospective study was approved by the institutional ethics committee. A total of 88 children (age range of 5 to 16 years) with a history of seizures underwent contrast-enhanced CT scan. Forty-one children underwent CT study according to the MBIR technique, while 47 children underwent CT of the head with the non-MBIR protocol. Images were reviewed by 2 blinded paediatric radiologists in a random order. Mean dose-length product, CT dose index (CTDI) volume, and mean effective dose were recorded for both groups. Image quality, image noise, and diagnostic acceptability of 2 image sets were also recorded. Results: In the MBIR group, the mean dose-length product was reduced by 79.8%; the mean CTDI volume was reduced by 88.5%, while the mean effective dose was reduced by 81% when compared to the non-MBIR group. No significant difference was seen in diagnostic acceptability, image noise, and image quality between the 2 groups. Conclusions: MBIR technique is highly effective in reducing radiation dose in paediatric head CT examinations without any significant difference in image quality, image noise, and diagnostic acceptability