Optimal Error Bounds for Convergents of a Family of Continued Fractions

AbstractLet F be the family of continued fractionsK(ap/1), wherea1=−g1,ap=(1−gp−1)gpxp,p=2,3,…, with 0≤gp≤1,gpfixed, and |xp|≤1,p=2,3,…. In this work, we derive upper bounds on the errors in the convergents ofK(ap/1) that are uniform for F, and optimal in the sense that they are attained by some continued fraction in F. For the special casegi=g<1/2,i=1,2,…, this bound turns out to be especially simple, and forgi=g=1/2,i=1,2,…, the known best form of the theorem of Worpitzki is obtained as an immediate corollary

An automatic multigrid method for the solution of sparse linear systems

An automatic version of the multigrid method for the solution of linear systems arising from the discretization of elliptic PDE's is presented. This version is based on the structure of the algebraic system solely, and does not use the original partial differential operator. Numerical experiments show that for the Poisson equation the rate of convergence of our method is equal to that of classical multigrid methods. Moreover, the method is robust in the sense that its high rate of convergence is conserved for other classes of problems: non-symmetric, hyperbolic (even with closed characteristics) and problems on non-uniform grids. No double discretization or special treatment of sub-domains (e.g. boundaries) is needed. When supplemented with a vector extrapolation method, high rates of convergence are achieved also for anisotropic and discontinuous problems and also for indefinite Helmholtz equations. A new double discretization strategy is proposed for finite and spectral element schemes and is found better than known strategies

Preconditioning spectral element schemes for definite and indefinite problems

Spectral element schemes for the solution of elliptic boundary value problems are considered. Preconditioning methods based on finite difference and finite element schemes are implemented. Numerical experiments show that inverting the preconditioner by a single multigrid iteration is most efficient and that the finite difference preconditioner is superior to the finite element one for both definite and indefinite problems. A multigrid preconditioner is also derived from the finite difference preconditioner and is found suitable for the CGS acceleration method. It is pointed out that, for the finite difference and finite element preconditioners, CGS does not always converge to the accurate algebraic solution

Combining mouse mammary gland gene expression and comparative mapping for the identification of candidate genes for QTL of milk production traits in cattle

<p>Abstract</p> <p>Background</p> <p>Many studies have found segregating quantitative trait loci (QTL) for milk production traits in different dairy cattle populations. However, even for relatively large effects with a saturated marker map the confidence interval for QTL location by linkage analysis spans tens of map units, or hundreds of genes. Combining mapping and arraying has been suggested as an approach to identify candidate genes. Thus, gene expression analysis in the mammary gland of genes positioned in the confidence interval of the QTL can bridge the gap between fine mapping and quantitative trait nucleotide (QTN) determination.</p> <p>Results</p> <p>We hybridized Affymetrix microarray (MG-U74v2), containing 12,488 murine probes, with RNA derived from mammary gland of virgin, pregnant, lactating and involuting C57BL/6J mice in a total of nine biological replicates. We combined microarray data from two additional studies that used the same design in mice with a total of 75 biological replicates. The same filtering and normalization was applied to each microarray data using GeneSpring software. Analysis of variance identified 249 differentially expressed probe sets common to the three experiments along the four developmental stages of puberty, pregnancy, lactation and involution. 212 genes were assigned to their bovine map positions through comparative mapping, and thus form a list of candidate genes for previously identified QTLs for milk production traits. A total of 82 of the genes showed mammary gland-specific expression with at least 3-fold expression over the median representing all tissues tested in GeneAtlas.</p> <p>Conclusion</p> <p>This work presents a web tool for candidate genes for QTL (cgQTL) that allows navigation between the map of bovine milk production QTL, potential candidate genes and their level of expression in mammary gland arrays and in GeneAtlas. Three out of four confirmed genes that affect QTL in livestock (<it>ABCG2</it>, <it>DGAT1</it>, <it>GDF8, IGF2</it>) were over expressed in the target organ. Thus, cgQTL can be used to determine priority of candidate genes for QTN analysis based on differential expression in the target organ.</p

Association between CTL Precursor Frequency to HLA-C Mismatches and HLA-C Antigen Cell Surface Expression

Previous studies showed the relevance of the cytotoxic T-cell precursor (CTLp) frequency assay for prediction of the outcome of HLA mismatched hematopoietic cell transplantation (HCT). Recently, it has been shown that HLA-C cell surface expression is correlated with virus specific cytotoxic T-cell responses and viremia control in HIV patients. The aim of the current study was to investigate the association between HLA-C antigen expression and the CTLp frequency to the mismatched HLA-C antigen. In total 115 recipient–donor pairs, for whom a successful CTLp assay was performed, were evaluated for this pilot study. All donor–recipient pairs were matched at 9/10 alleles with a single mismatch at the HLA-C locus. Antigen expression level of the mismatched HLA-C allele for each recipient and donor was based on the mean fluorescence intensity (MFI) values as described by Apps et al. (1). The cell surface expression of recipient’s mismatched HLA-C antigen was significantly lower among CTLp negative (n = 59) compared to CTLp positive (n = 56) pairs (154 and 193 MFI units, respectively, p = 0.0031). This difference was more pronounced in donor–recipient pairs that were mismatched for amino-acid residue-116 located in the groove of the HLA-C antigen, suggesting that the importance of peptide binding in the allo-recognition. Furthermore, in the particular case of low expression of the recipient mismatched HLA-C antigen (MFI < 115), CTLp reactivity depended on HLA-C expression level in the donor, the median MFI of donor’s mismatched HLA-C antigen was 114 in CTLp negative cases (n = 26), while in CTLp positive cases (n = 15) the median MFI of donor’s HLA-C antigen was 193 (p = 0.0093). We conclude that the expression level of the donor and recipient mismatched HLA-C antigens affect CTLp outcome. HLA-C antigen expression levels in combination with the CTLp assay may prove useful for the prediction of the clinical outcome of HLA-C mismatched HCT