Changes in the prevalence of chronic disability in the United States black and nonblack population above age 65 from 1982 to 1999

Survey evidence through the early 1990s generally suggests a reduction in disability in the elderly population of the United States. Because the evidence is not fully consistent, several authors have speculated about whether disability declines will continue. This paper reports results from the 1999 National Long-Term Care Survey on disability trends from 1982 through 1999. It is found that disability continued to decline in the 1994 to 1999 period, and that the decline was greater in the 1990s than in the 1980s. The disability decline from 1982 to 1989 was 0.26% per year, from 1989 to 1994 it was 0.38% per year, and from 1994 to 1999 it was 0.56% per year. In addition, disability declined by a greater percentage for blacks than for nonblacks over the 1989 to 1999 period.

New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan’s tau function

In this paper, we give two infinite families of explicit exact formulas that generalize Jacobi’s (1829) 4 and 8 squares identities to 4n2 or 4n(n + 1) squares, respectively, without using cusp forms. Our 24 squares identity leads to a different formula for Ramanujan’s tau function τ(n), when n is odd. These results arise in the setting of Jacobi elliptic functions, Jacobi continued fractions, Hankel or Turánian determinants, Fourier series, Lambert series, inclusion/exclusion, Laplace expansion formula for determinants, and Schur functions. We have also obtained many additional infinite families of identities in this same setting that are analogous to the η-function identities in appendix I of Macdonald’s work [Macdonald, I. G. (1972) Invent. Math. 15, 91–143]. A special case of our methods yields a proof of the two conjectured [Kac, V. G. and Wakimoto, M. (1994) in Progress in Mathematics, eds. Brylinski, J.-L., Brylinski, R., Guillemin, V. & Kac, V. (Birkhäuser Boston, Boston, MA), Vol. 123, pp. 415–456] identities involving representing a positive integer by sums of 4n2 or 4n(n + 1) triangular numbers, respectively. Our 16 and 24 squares identities were originally obtained via multiple basic hypergeometric series, Gustafson’s Cℓ nonterminating 6φ5 summation theorem, and Andrews’ basic hypergeometric series proof of Jacobi’s 4 and 8 squares identities. We have (elsewhere) applied symmetry and Schur function techniques to this original approach to prove the existence of similar infinite families of sums of squares identities for n2 or n(n + 1) squares, respectively. Our sums of more than 8 squares identities are not the same as the formulas of Mathews (1895), Glaisher (1907), Ramanujan (1916), Mordell (1917, 1919), Hardy (1918, 1920), Kac and Wakimoto, and many others.

Equilibrium distributions of microsatellite repeat length resulting from a balance between slippage events and point mutations

We describe and test a Markov chain model of microsatellite evolution that can explain the different distributions of microsatellite lengths across different organisms and repeat motifs. Two key features of this model are the dependence of mutation rates on microsatellite length and a mutation process that includes both strand slippage and point mutation events. We compute the stationary distribution of allele lengths under this model and use it to fit DNA data for di-, tri-, and tetranucleotide repeats in humans, mice, fruit flies, and yeast. The best fit results lead to slippage rate estimates that are highest in mice, followed by humans, then yeast, and then fruit flies. Within each organism, the estimates are highest in di-, then tri-, and then tetranucleotide repeats. Our estimates are consistent with experimentally determined mutation rates from other studies. The results suggest that the different length distributions among organisms and repeat motifs can be explained by a simple difference in slippage rates and that selective constraints on length need not be imposed.

Similarities and dissimilarities of phage genomes.

Genomic similarities and contrasts are investigated in a collection of 23 bacteriophages, including phages with temperate, lytic, and parasitic life histories, with varied sequence organizations and with different hosts and with different morphologies. Comparisons use relative abundances of di-, tri-, and tetranucleotides from entire genomes. We highlight several specific findings. (i) As previously shown for cellular genomes, each viral genome has a distinctive signature of short oligonucleotide abundances that pervade the entire genome and distinguish it from other genomes. (ii) The enteric temperate double-stranded (ds) phages, like enterobacteria, exhibit significantly high relative abundances of GpC = GC and significantly low values of TA, but no such extremes exist in ds lytic phages. (iii) The tetranucleotide CTAG is of statistically low relative abundance in most phages. (iv) The DAM methylase site GATC is of statistically low relative abundance in most phages, but not in P1. This difference may relate to controls on replication (e.g., actions of the host SeqA gene product) and to MutH cleavage potential of the Escherichia coli DAM mismatch repair system. (v) The enteric temperate dsDNA phages form a coherent group: they are relatively close to each other and to their bacteria] hosts in average differences of dinucleotide relative abundance values. By contrast, the lytic dsDNA phages do not form a coherent group. This difference may come about because the temperate phages acquire more sequence characteristics of the host because they use the host replication and repair machinery, whereas the analyzed lytic phages are replicated by their own machinery. (vi) The nonenteric temperate phages with mycoplasmal and mycobacterial hosts are relatively close to their respective hosts and relatively distant from any of the enteric hosts and from the other phages. (vii) The single-stranded RNA phages have dinucleotide relative abundance values closest to those for random sequences, presumably attributable to the mutation rates of RNA phages being much greater than those of DNA phages.

Major histocompatibility complex class II DR alleles DRB1*1501 and those encoding HLA-DR13 are preferentially associated with a diminution in maternally transmitted human immunodeficiency virus 1 infection in different ethnic groups: determination by an automated sequence-based typing method.

Transmission of human immunodeficiency virus 1 (HIV-1) from an infected women to her offspring during gestation and delivery was found to be influenced by the infant's major histocompatibility complex class II DRB1 alleles. Forty-six HIV-infected infants and 63 seroreverting infants, born with passively acquired anti-HIV antibodies but not becoming detectably infected, were typed by an automated nucleotide-sequence-based technique that uses low-resolution PCR to select either the simpler Taq or the more demanding T7 sequencing chemistry. One or more DR13 alleles, including DRB1*1301, 1302, and 1303, were found in 31.7% of seroreverting infants and 15.2% of those becoming HIV-infected [OR (odds ratio) = 2.6 (95% confidence interval 1.0-6.8); P = 0.048]. This association was influenced by ethnicity, being seen more strongly among the 80 Black and Hispanic children [OR = 4.3 (1.2-16.4); P = 0.023], with the most pronounced effect among Black infants where 7 of 24 seroreverters inherited these alleles with none among 12 HIV-infected infants (Haldane OR = 12.3; P = 0.037). The previously recognized association of DR13 alleles with some situations of long-term nonprogression of HIV suggests that similar mechanisms may regulate both the occurrence of infection and disease progression after infection. Upon examining for residual associations, only only the DR2 allele DRB1*1501 was associated with seroreversion in Caucasoid infants (OR = 24; P = 0.004). Among Caucasoids the DRB1*03011 allele was positively associated with the occurrence of HIV infection (P = 0.03).