Quasi-complementary sequence sets (QCSSs) have attracted sustained research interests due to the ability to support more users compared to complete complementary codes (CCCs) in multi-carrier code division multiple access (MC-CDMA) systems. In this paper, two classes of aperiodic QCSSs are constructed over the finite rings, which have new parameters in terms of the length of constituent sequences and set size respectively. Most notably, the length of constituent sequences of QCSS derived from the first construction is$ p^{n} + 1$, where p is a prime and n is a positive integer, which has not been covered in the literature. In the second construction, the set size of the proposed binary QCSS is$2^{n+1}$larger than the existing binary QCSS. In addition, both the proposed aperiodic QCSSs are asymptotically optimal with respect to the correlation lower bound.

Prognostic tests using expression profiles of several dozen genes help provide treatment choices for prostate cancer (PCa). However, these tests require improvement to meet the clinical need for resolving overtreatment, which continues to be a pervasive problem in PCa management. Genomic selection (GS) methodology, which utilizes whole-genome markers to predict agronomic traits, was adopted in this study for PCa prognosis. We leveraged The Cancer Genome Atlas (TCGA) database to evaluate the prediction performance of six GS methods and seven omics data combinations, which showed that the Best Linear Unbiased Prediction (BLUP) model outperformed the other methods regarding predictability and computational efficiency. Leveraging the BLUP-HAT method, an accelerated version of BLUP, we demonstrated that using expression data of a large number of disease-relevant genes and with an integration of other omics data (i.e. miRNAs) significantly increased outcome predictability when compared with panels consisting of a small number of genes. Finally, we developed a novel stepwise forward selection BLUP-HAT method to facilitate searching multiomics data for predictor variables with prognostic potential. The new method was applied to the TCGA data to derive mRNA and miRNA expression signatures for predicting relapse-free survival of PCa, which were validated in six independent cohorts. This is a transdisciplinary adoption of the highly efficient BLUP-HAT method and its derived algorithms to analyze multiomics data for PCa prognosis. The results demonstrated the efficacy and robustness of the new methodology in developing prognostic models in PCa, suggesting a potential utility in managing other types of cancer.

MOTIVATION: Genome-wide association studies (GWAS) are still the primary steps toward gene discovery. The urgency is more obvious in the big data era when GWAS are conducted simultaneously for thousand traits, e.g. transcriptomic and metabolomic traits. Efficient mixed model association (EMMA) and genome-wide efficient mixed model association (GEMMA) are the widely used methods for GWAS. An algorithm with high computational efficiency is badly needed. It is interesting to note that the test statistics of the ordinary ridge regression (ORR) have the same patterns across the genome as those obtained from the EMMA method. However, ORR has never been used for GWAS due to its severe shrinkage on the estimated effects and the test statistics. RESULTS: We introduce a degree of freedom for each marker effect obtained from ORR and use it to deshrink both the estimated effect and the standard error so that the Wald test of ORR is brought back to the same level as that of EMMA. The new method is called deshrinking ridge regression (DRR). By evaluating the methods under three different model sizes (small, medium and large), we demonstrate that DRR is more generalized for all model sizes than EMMA, which only works for medium and large models. Furthermore, DRR detect all markers in a simultaneous manner instead of scanning one marker at a time. As a result, the computational time complexity of DRR is much simpler than EMMA and about m (number of genetic variants) times simpler than that of GEMMA when the sample size is way smaller than the number of markers. CONTACT: [email protected]. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Genomic scanning approaches that detect one locus at a time are subject to many problems in genome-wide association studies and quantitative trait locus mapping. The problems include large matrix inversion, over-conservativeness for tests after Bonferroni correction and difficulty in evaluation of the total genetic contribution to a trait's variance. Targeting these problems, we take a further step and investigate a multiple locus model that detects all markers simultaneously in a single model. RESULTS: We developed a sparse Bayesian learning (SBL) method for quantitative trait locus mapping and genome-wide association studies. This new method adopts a coordinate descent algorithm to estimate parameters (marker effects) by updating one parameter at a time conditional on current values of all other parameters. It uses an L2 type of penalty that allows the method to handle extremely large sample sizes (>100 000). Simulation studies show that SBL often has higher statistical powers and the simulated true loci are often detected with extremely small P-values, indicating that SBL is insensitive to stringent thresholds in significance testing. AVAILABILITY AND IMPLEMENTATION: An R package (sbl) is available on the comprehensive R archive network (CRAN) and https://github.com/MeiyueComputBio/sbl/tree/master/R%20packge. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.