Feature Selection for Longitudinal Data by Using Sign Averages to Summarize Gene Expression Values over Time

With the rapid evolution of high-throughput technologies, time series/longitudinal high-throughput experiments have become possible and affordable. However, the development of statistical methods dealing with gene expression profiles across time points has not kept up with the explosion of such data. The feature selection process is of critical importance for longitudinal microarray data. In this study, we proposed aggregating a gene’s expression values across time into a single value using the sign average method, thereby degrading a longitudinal feature selection process into a classic one. Regularized logistic regression models with pseudogenes (i.e., the sign average of genes across time as predictors) were then optimized by either the coordinate descent method or the threshold gradient descent regularization method. By applying the proposed methods to simulated data and a traumatic injury dataset, we have demonstrated that the proposed methods, especially for the combination of sign average and threshold gradient descent regularization, outperform other competitive algorithms. To conclude, the proposed methods are highly recommended for studies with the objective of carrying out feature selection for longitudinal gene expression data.

Consolidation by Prefabricated Vertical Drains with a Threshold Gradient

This paper shows the development of an approximate analytical solution of radial consolidation by prefabricated vertical drains with a threshold gradient. To understand the effect of the threshold gradient on consolidation, a parametric analysis was performed using the present solution. The applicability of the present solution was demonstrated in two cases, wherein the comparisons with Hansbo’s results and observed data were conducted. It was found that (1) the flow with the threshold gradient would not occur instantaneously throughout the whole unit cell. Rather, it gradually occurs from the vertical drain to the outside; (2) the moving boundary would never reach the outer radius of influence ifR+1<n, whereas it will reach the outer radius of influence at some time; (3) the excess pore pressure will not be dissipated completely, but it will maintain a long-term stable value at the end of consolidation; (4) the larger the threshold gradient is, the greater the long-term excess pore pressure will be; and (5) the present solution could predict the consolidation behavior in soft clay better than previous methods.