In linear regression with functional predictors and scalar responses, it may be advantageous, particularly if the function is thought to contain features at many scales, to restrict the coefficient function to the span of a wavelet basis, thereby converting the problem into one of variable selection. If the coefficient function is sparsely represented in the wavelet domain, we may employ the well-known LASSO to select a relatively small number of nonzero wavelet coefficients. This is a natural approach to take but to date, the properties of such an estimator have not been studied. In this article we describe the wavelet-based LASSO approach to regressing scalars on functions and investigate both its asymptotic convergence and its finite-sample performance through both simulation and real-data application. We compare the performance of this approach with existing methods and find that the wavelet-based LASSO performs relatively well, particularly when the true coefficient function is spiky. Source code to implement the method and datasets used in the study are provided as supplementary materials available online.

Abscisic acid (ABA) is a hormone that modulates a variety of agronomically important growth and developmental processes and various stresses responses, but its signal transduction pathways remain poorly understood. ROP10, a member of ROP small GTPases in Arabidopsis (Arabidopsis thaliana), is a plasma membrane-associated protein specifically involved in negative regulation of ABA responses. To dissect the ROP10-mediated ABA signaling, we carried out transcriptome analysis using the Arabidopsis full-genome chip. Our analysis revealed a total of 262 and 125 genes that were, respectively, up- and down-regulated (≥2-fold cutoff) by 1 μm ABA in wild type (Wassilewskija [Ws]); 42 up-regulated and 38 down-regulated genes have not been identified in other studies. Consistent with the nonpleiotropic phenotypes of rop10-1, only three genes were altered in rop10-1 in the absence of ABA treatment. In response to 1 μm ABA, 341 and 127 genes were, respectively, activated and repressed in rop10-1. Interestingly, a particular subset of 21 genes that were not altered by 1 μm ABA in Ws but only activated in rop10-1 was identified. Reverse transcription-polymerase chain reaction analysis revealed the existence of three distinct categories of ABA dose-response patterns. One novel category is characterized by their ABA unresponsiveness in Ws and activation in rop10-1 at 1 μm but not 10 and 100 μm of ABA. This indicates that ROP10 gates the expression of genes that are specific to low concentrations of ABA. Furthermore, almost all of these 21 genes are known to be highly induced by various biotic and abiotic stresses. Consequently, we found that rop10-1 enhanced the sensitivity of seed germination inhibition to mannitol and sodium chloride. Our results suggest that ROP10 negatively regulates ABA responses by specifically and differentially modulating the ABA sensitivity of a subset of genes including protein kinases and zinc-finger family proteins.

Huanglongbing (HLB) is arguably the most destructive disease for the citrus industry. HLB is caused by infection of the bacterium, Candidatus Liberibacter spp. Several citrus GeneChip studies have revealed thousands of genes that are up- or down-regulated by infection with Ca. Liberibacter asiaticus. However, whether and how these host genes act to protect against HLB remains poorly understood.