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A roadmap of the spine During spinal cord surgery, intraoperative neuromonitoring (IONM) is used to reduce the risk of damage. Electrodes on muscles or scalp record the response to large-amplitude electrical stimuli delivered to the spinal cord. However, this method does not allow precise spatiotemporal characterization of spinal cord neurophysiology. Now, Russman et al. developed a microelectrode array that can be placed on the spinal cord during surgery and record with high spatiotemporal definition and high sensitivity the electrophysiological response to low-current stimulation, providing precise maps of spinal cord electrophysiology. These maps can be used during surgery to improve IONM. 

Summary We consider the problem of approximating smoothing spline estimators in a nonparametric regression model. When applied to a sample of size $$n$$, the smoothing spline estimator can be expressed as a linear combination of $$n$$ basis functions, requiring $O(n^3)$ computational time when the number $$d$$ of predictors is two or more. Such a sizeable computational cost hinders the broad applicability of smoothing splines. In practice, the full-sample smoothing spline estimator can be approximated by an estimator based on $$q$$ randomly selected basis functions, resulting in a computational cost of $O(nq^2)$. It is known that these two estimators converge at the same rate when $$q$$ is of order $$O\{n^{2/(pr+1)}\}$$, where $$p\in [1,2]$$ depends on the true function and $r > 1$ depends on the type of spline. Such a $$q$$ is called the essential number of basis functions. In this article, we develop a more efficient basis selection method. By selecting basis functions corresponding to approximately equally spaced observations, the proposed method chooses a set of basis functions with great diversity. The asymptotic analysis shows that the proposed smoothing spline estimator can decrease $$q$$ to around $$O\{n^{1/(pr+1)}\}$$ when $$d\leq pr+1$$. Applications to synthetic and real-world datasets show that the proposed method leads to a smaller prediction error than other basis selection methods. 

Abstract Background Plants are naturally associated with root microbiota, which are microbial communities influential to host fitness. Thus, it is important to understand how plants control root microbiota. Epigenetic factors regulate the readouts of genetic information and consequently many essential biological processes. However, it has been elusive whether RNA-directed DNA methylation (RdDM) affects root microbiota assembly. Results By applying 16S rRNA gene sequencing, we investigated root microbiota of Arabidopsis mutants defective in the canonical RdDM pathway, including dcl234 that harbors triple mutation in the Dicer-like proteins DCL3, DCL2, and DCL4, which produce small RNAs for RdDM. Alpha diversity analysis showed reductions in microbe richness from the soil to roots, reflecting the selectivity of plants on root-associated bacteria. The dcl234 triple mutation significantly decreases the levels of Aeromonadaceae and Pseudomonadaceae , while it increases the abundance of many other bacteria families in the root microbiota. However, mutants of the other examined key players in the canonical RdDM pathway showed similar microbiota as Col-0, indicating that the DCL proteins affect root microbiota in an RdDM-independent manner. Subsequently gene analysis by shotgun sequencing of root microbiome indicated a selective pressure on microbial resistance to plant defense in the dcl234 mutant. Consistent with the altered plant-microbe interactions, dcl234 displayed altered characters, including the mRNA and sRNA transcriptomes that jointly highlighted altered cell wall organization and up-regulated defense, the decreased cellulose and callose deposition in root xylem, and the restructured profile of root exudates that supported the alterations in gene expression and cell wall modifications. Conclusion Our findings demonstrate an important role of the DCL proteins in influencing root microbiota through integrated regulation of plant defense, cell wall compositions, and root exudates. Our results also demonstrate that the canonical RdDM is dispensable for Arabidopsis root microbiota. These findings not only establish a connection between root microbiota and plant epigenetic factors but also highlight the complexity of plant regulation of root microbiota. 

A popular method for flexible function estimation in nonparametric models is the smoothing spline. When applying the smoothing spline method, the nonparametric function is estimated via penalized least squares, where the penalty imposes a soft constraint on the function to be estimated. The specification of the penalty functional is usually based on a set of assumptions about the function. Choosing a reasonable penalty function is the key to the success of the smoothing spline method. In practice, there may exist multiple sets of widely accepted assumptions, leading to different penalties, which then yield different estimates. We refer to this problem as the problem of ambiguous penalties. Neglecting the underlying ambiguity and proceeding to the model with one of the candidate penalties may produce misleading results. In this article, we adopt a Bayesian perspective and propose a fully Bayesian approach that takes into consideration all the penalties as well as the ambiguity in choosing them. We also propose a sampling algorithm for drawing samples from the posterior distribution. Data analysis based on simulated and real‐world examples is used to demonstrate the efficiency of our proposed method.