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Let p , b ≥ 2 be two integers, and let D = p { 0 , 1 , ... , b − 1 }. It is well known that the self-similar measure μ p b , D generated by the iterated function system { τ d (x) = (p b) − 1 (x + d) } d ∈ D is a spectral measure with a spectrum Λ (p b , C) = ∑ j = 0 finite (p b) j c j : c j ∈ C = { 0 , 1 , ... , b − 1 } . In this paper, we study a class of primitive and composite numbers and their related properties. And we also explore the simple prime numbers and the properties related to their order. Based on these, let r be a positive integer, we give some conditions on the distinct prime numbers t 1 , t 2 , ... , t r such that the scaling set ∏ i = 1 r t i k i Λ (p b , C) is also a spectrum of μ p b , D for all k i ≥ 0. [ABSTRACT FROM AUTHOR]

A primitive tandem repeat α is a substring in string S if it can be expressed as two or more contiguous copies of β , where the base β cannot be expressed in terms of yet a shorter substring. Substring α is maximal if there is no copy of β to either its left or right. Tandem repeats (or arrays) are known to play an important role in biology, e.g. determining parentage. We present a deterministic algorithm that finds all the exact primitive maximal tandem arrays that occur in S , where at iteration k it discovers all the repeats with base length k . Our algorithm uses a simple list structure for all its operations. In theory, the algorithm scales well with the size of the alphabet. For strings over the alphabet Σ it has a complexity of O ( | S | + | Σ | ) in space, and O ( B | S | − B 2 / 2 ) in time, where B is the length of the longest primitive base of a tandem repeat in S . Experimental results on real biological sequences, randomly generated sequences using large sized alphabets, and Fibonacci strings, show that in practice the algorithm has indeed a linear complexity, both in space and time. [ABSTRACT FROM AUTHOR]

Single-celled parasites like Entamoeba, Trypanosoma, Phytophthora and Plasmodium wreak untold havoc on human habitat and health. Understanding the position of the various protistan pathogens in the larger context of eukaryotic diversity informs our study of how these parasites operate on a cellular level, as well as how they have evolved. Here, we review the literature that has brought our understanding of eukaryotic relationships from an idea of parasites as primitive cells to a crystallized view of diversity that encompasses 6 major divisions, or supergroups, of eukaryotes. We provide an updated taxonomic scheme (for 2011), based on extensive genomic, ultrastructural and phylogenetic evidence, with three differing levels of taxonomic detail for ease of referencing and accessibility (see supplementary material at Cambridge Journals On-line). Two of the most pressing issues in cellular evolution, the root of the eukaryotic tree and the evolution of photosynthesis in complex algae, are also discussed along with ideas about what the new generation of genome sequencing technologies may contribute to the field of eukaryotic systematics. We hope that, armed with this user's guide, cell biologists and parasitologists will be encouraged about taking an increasingly evolutionary point of view in the battle against parasites representing real dangers to our livelihoods and lives. [ABSTRACT FROM PUBLISHER]

The primitive neuroectodermal tumors (PNETs) of Hart and Earle constitute an important fraction of pediatric brain tumors that are clinically characterized by their aggressive behavior. In 1983, Rorke expanded the term 'PNET' to include all small cell embryonal neoplasms of neuroectodermal origin, regardless of the location of the tumor. More recently, Dehner also proposed the terms 'central' and 'peripheral' PNETs, and the provocative concept of 'PNET' has now come to encompass a diverse group of tumors in both the central and peripheral nervous systems. The acronym 'PNET' has thus become a confusing and controversial term in the diagnosis and classification of pediatric embryonal tumors. We reviewed ten papers concerning the various aspects of PNETs. [ABSTRACT FROM AUTHOR]