Chromosome 19 has the highest gene density of all human chromosomes, more than double the genome-wide average. The large clustered gene families, corresponding high G1C content, CpG islands and density of repetitive DNA indicate a chromosome rich in biological and evolutionary significance. Here we describe 55.8 million base pairs of highly accurate finished sequence representing 99.9% of the euchromatin portion of the chromosome. Manual curation of gene loci reveals 1,461 protein-coding genes and 321 pseudogenes. Among these are genes directly implicated in mendelian disorders, including familial hypercholesterolaemia and insulin-resistant diabetes. Nearly one-quarter of these genes belong to tandemly arranged families, encompassing more than 25% of the chromosome. Comparative analyses show a fascinating picture of conservation and divergence, revealing large blocks of gene orthology with rodents, scattered regions with more recent gene family expansions and deletions, and segments of coding and non-coding conservation with the distant fish species Takifugu.
The problem classically titled “The Examination Schedule Problem” takes various forms in the literature. Most of these formulations can be presented in the terminology of classical Network Theory. One such formulation is: Given a nondirected network, partition its nodes into a minimal number of subsets such that no two members of the same subset are connected by an arc.
An obvious lower limit to this number is the size of the largest strongly connected subgraph. Kirchgassner proved that an upper limit is this size plus one.
One logical extension of the previous work is the introduction of variable length examinations where W(I) is the number of periods for exam I. The object of this paper is to generalize the definition of largest strongly connected subgraph to include the weighting of nodes, to present an approximate algorithm which usually finds the largest strongly connected subgraph, and to discuss the application of this algorithm to the solution of school scheduling and exam scheduling problems.
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