Target Informatics Net (TINet) is a readily extensible data integration system developed at GlaxoSmith- Kline (GSK), based on the Object-Protocol Model (OPM) multidatabase middleware system of Gene Logic Inc. Data sources currently integrated include: the Mouse Genome Database (MGD) and Gene Expression Database (GXD), GenBank, SwissProt, PubMed, GeneCards, the results of runtime BLAST and PROSITE searches, and GSK proprietary relational databases. Special-purpose class methods used to filter and augment query results include regular expression pattern-matching over BLAST HSP alignments and retrieving partial sequences derived from primary structure annotations. All data sources and methods are accessible through an SQL-like query language or a GUI, so that when new investigations arise no additional programming beyond query specification is required. The power and flexibility of this approach are illustrated in such integrated queries as: (1) 'find homologs in genomic sequence to all novel genes cloned and reported in the scientific literature within the past three months that are linked to the MeSH term 'neoplasms"; (2) 'using a neuropeptide precursor query sequence, return only HSPs where the target genomic sequences conserve the G[KR][KR] motif at the appropriate points in the HSP alignment'; and (3) 'of the human genomic sequences annotated with exon boundaries in GenBank, return only those with valid putative donor/acceptor sites and start/stop codons'.

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It is conjectured that for H°° the Bass stable rank (bsr) is 1 and the topological stable rank (tsr) is 2. bsr(H°°) = 1 if and only if for every (/i > fi) G H°° x H°° which is a corona pair (i.e., there exist g, , g2 e H°°s uch that f]g1 + f2g2 = 1) there exists age H°° such that /j + f2g e (Z/00)-, the invertibles in H°° ; however, it suffices to consider corona pairs (f\ < f-¡) where /, is a Blaschke product. It is also shown that there exists age H°° such that fx + f2g 6 exp(//°°) if and only if log/j can be boundedly, analytically defined on {z e B>: \f2(z)\ < 3} , for some ô > 0. tsr(//°°) = 2 if and only if the corona pairs are uniformly dense in H°° x H°° ; however, it suffices to show that the corona pairs are uniformly dense in pairs of Blaschke products. This condition would be satisfied if the interpolating Blaschke products were uniformly dense in the Blaschke products. For b an inner function, K = H 9 bH is an H°°-module via the compressed Toeplitz operators C, = PKTj-\K, for f e H°° , where T, is the Toeplitz operator Trg = fg , for g e H. Some stable rank questions can be recast as lifting questions: for (/])" C H°° , there exist (g,)" , (h¡)" C H°°s uch that S"=i (/; + bg¡)h¡ = 1 if and only if the compressed Toeplitz operators (Cj-)" may be lifted to Toeplitz operators (7"f)" which generate B(H2) as an ideal.

Abstract. It is conjectured that for H°° the Bass stable rank (bsr) is 1 and the topological stable rank (tsr) is 2 . bsr(H°°) = 1 if and only if for every (/i > fi) G H°° x H°° which is a corona pair (i.e., there exist g, , g2 e H°°s uch that f]g1 + f2g2 = 1 ) there exists age H°° such that /j + f2g e