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In this research communication we used digital gene expression (DGE) analysis to identify differences in gene expression in the mammary glands of dairy cows between early lactation and the mid-dry period. A total of 741 genes were identified as being differentially expressed by DGE analysis. Compared with their expression in dry cows, 214 genes were up-regulated and 527 genes were down-regulated in lactating cow mammary glands. Gene Ontology analysis showed that lactation was supported by increased gene expression related to metabolic processes and nutrient transport and was associated with decreased gene expression related to cell proliferation. Pathway mapping using the Kyoto Encyclopedia of Genes and Genomes showed that 579 differentially expressed genes had pathway annotations related to 204 pathways. Metabolic pathway-related genes were the most significantly enriched. Genes and pathways identified by the present study provide insights into molecular events that occur in the mammary gland between early lactation and mid-dry period, which can be used to facilitate further investigation of the mechanisms underlying lactation and mammary tissue remodeling in dairy cows.
We show that the expected number of maximal empty axis-parallel boxes amidst n random points in the unit hypercube [0,1]d in
is (1 ± o(1))
n lnd−1n, if d is fixed. This estimate is relevant to analysis of the performance of exact algorithms for computing the largest empty axis-parallel box amidst n given points in an axis-parallel box R, especially the algorithms that proceed by examining all maximal empty boxes. Our method for bounding the expected number of maximal empty boxes also shows that the expected number of maximal empty orthants determined by n random points in
is (1 ± o(1)) lnd−1n, if d is fixed. This estimate is related to the expected number of maximal (or minimal) points amidst random points, and has application to algorithms for coloured orthogonal range counting.
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