Phylogenetic Distribution of Intron Positions in Alpha-Amylase Genes of Bilateria Suggests Numerous Gains and Losses

Most eukaryotes have at least some genes interrupted by introns. While it is well accepted that introns were already present at moderate density in the last eukaryote common ancestor, the conspicuous diversity of intron density among genomes suggests a complex evolutionary history, with marked differences between phyla. The question of the rates of intron gains and loss in the course of evolution and factors influencing them remains controversial. We have investigated a single gene family, alpha-amylase, in 55 species covering a variety of animal phyla. Comparison of intron positions across phyla suggests a complex history, with a likely ancestral intronless gene undergoing frequent intron loss and gain, leading to extant intron/exon structures that are highly variable, even among species from the same phylum. Because introns are known to play no regulatory role in this gene and there is no alternative splicing, the structural differences may be interpreted more easily: intron positions, sizes, losses or gains may be more likely related to factors linked to splicing mechanisms and requirements, and to recognition of introns and exons, or to more extrinsic factors, such as life cycle and population size. We have shown that intron losses outnumbered gains in recent periods, but that “resets” of intron positions occurred at the origin of several phyla, including vertebrates. Rates of gain and loss appear to be positively correlated. No phase preference was found. We also found evidence for parallel gains and for intron sliding. Presence of introns at given positions was correlated to a strong protosplice consensus sequence AG/G, which was much weaker in the absence of intron. In contrast, recent intron insertions were not associated with a specific sequence. In animal Amy genes, population size and generation time seem to have played only minor roles in shaping gene structures

Improved algorithms for the k-maximum subarray problem for small k

Abstract. The maximum subarray problem for a one- or two-dimensional array is to find the array portion that maiximizes the sum of array elements in it. The K-maximum subarray problem is to find the K subarrays with largest sums. We improve the time complexity for the one-dimensional case from O(min{K + n log 2 n, n √ K}) for 0 ≤ K ≤ n(n − 1)/2 to O(n log K + K 2) for K ≤ n. The latter is better when K ≤ √ n log n. If we simply extend this result to the two-dimensional case, we will have the complexity of O(n 3 log K + K 2 n 2).We improve this complexity to O(n 3) for K ≤ √ n.