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We consider the problem of approximating smoothing spline estimators in a nonparametric regression model. When applied to a sample of size [Formula: see text] , the smoothing spline estimator can be expressed as a linear combination of [Formula: see text] basis functions, requiring [Formula: see text] computational time when the number [Formula: see text] 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 [Formula: see text] randomly selected basis functions, resulting in a computational cost of [Formula: see text]. It is known that these two estimators converge at the same rate when [Formula: see text] is of order [Formula: see text] , where [Formula: see text] depends on the true function and [Formula: see text] depends on the type of spline. Such a [Formula: see text] 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 [Formula: see text] to around [Formula: see text] when [Formula: see text]. Applications to synthetic and real-world datasets show that the proposed method leads to a smaller prediction error than other basis selection methods.

Very often for the same scientific question, there may exist different techniques or experiments that measure the same numerical quantity. Historically, various methods have been developed to exploit the information within each type of data independently. However, statistical data fusion methods that could effectively integrate multi-source data under a unified framework are lacking. In this paper, we propose a novel data fusion method, called B-scaling, for integrating multi-source data. Consider $K$ measurements that are generated from different sources but measure the same latent variable through some linear or nonlinear ways. We seek to find a representation of the latent variable, named B-mean, which captures the common information contained in the $K$ measurements while takes into account the nonlinear mappings between them and the latent variable. We also establish the asymptotic property of the B-mean and apply the proposed method to integrate multiple histone modifications and DNA methylation levels for characterizing epigenomic landscape. Both numerical and empirical studies show that B-scaling is a powerful data fusion method with broad applications., To be published in Annals of Applied Statistics

Atomic force microscopy-single-molecule force spectroscopy (AFM-SMFS) is a powerful methodology to probe intermolecular and intramolecular interactions in biological systems because of its operability in physiological conditions, facile and rapid sample preparation, versatile molecular manipulation, and combined functionality with high-resolution imaging. Since a huge number of AFM-SMFS force-distance curves are collected to avoid human bias and errors and to save time, numerous algorithms have been developed to analyze the AFM-SMFS curves. Nevertheless, there is still a need to develop new algorithms for the analysis of AFM-SMFS data since the current algorithms cannot specify an unbinding force to a corresponding/each binding site due to the lack of networking functionality to model the relationship between the unbinding forces. To address this challenge, herein, we develop an unsupervised method, i.e., a network-based automatic clustering algorithm (NASA), to decode the details of specific molecules, e.g., the unbinding force of each binding site, given the input of AFM-SMFS curves. Using the interaction of heparan sulfate (HS)-antithrombin (AT) on different endothelial cell surfaces as a model system, we demonstrate that NASA is able to automatically detect the peak and calculate the unbinding force. More importantly, NASA successfully identifies three unbinding force clusters, which could belong to three different binding sites, for both Ext1f/f and Ndst1f/f cell lines. NASA has great potential to be applied either readily or slightly modified to other AFM-based SMFS measurements that result in "saw-tooth"-shaped force-distance curves showing jumps related to the force unbinding, such as antibody-antigen interaction and DNA-protein interaction.

Summary Large samples are generated routinely from various sources. Classic statistical models, such as smoothing spline ANOVA models, are not well equipped to analyse such large samples because of high computational costs. In particular, the daunting computational cost of selecting smoothing parameters renders smoothing spline ANOVA models impractical. In this article, we develop an asympirical, i.e., asymptotic and empirical, smoothing parameters selection method for smoothing spline ANOVA models in large samples. The idea of our approach is to use asymptotic analysis to show that the optimal smoothing parameter is a polynomial function of the sample size and an unknown constant. The unknown constant is then estimated through empirical subsample extrapolation. The proposed method significantly reduces the computational burden of selecting smoothing parameters in high-dimensional and large samples. We show that smoothing parameters chosen by the proposed method tend to the optimal smoothing parameters that minimize a specific risk function. In addition, the estimator based on the proposed smoothing parameters achieves the optimal convergence rate. Extensive simulation studies demonstrate the numerical advantage of the proposed method over competing methods in terms of relative efficacy and running time. In an application to molecular dynamics data containing nearly one million observations, the proposed method has the best prediction performance.

Retinitis Pigmentosa (RP) is a mostly incurable inherited retinal degeneration affecting approximately 1 in 4000 individuals globally. The goal of this work was to identify drugs that can help patients suffering from the disease. To accomplish this, we screened drugs on a zebrafish autosomal dominant RP model. This model expresses a truncated human rhodopsin transgene (Q344X) causing significant rod degeneration by 7 days post-fertilization (dpf). Consequently, the larvae displayed a deficit in visual motor response (VMR) under scotopic condition. The diminished VMR was leveraged to screen an ENZO SCREEN-WELL REDOX library since oxidative stress is postulated to play a role in RP progression. Our screening identified a beta-blocker, carvedilol, that ameliorated the deficient VMR of the RP larvae and increased their rod number. Carvedilol may directly on rods as it affected the adrenergic pathway in the photoreceptor-like human Y79 cell line. Since carvedilol is an FDA-approved drug, our findings suggest that carvedilol can potentially be repurposed to treat autosomal dominant RP patients.

Background: Extensive clinical evidence suggests that a preventive screening of coronary heart disease (CHD) at an earlier stage can greatly reduce the mortality rate. We use 64 two-dimensional speckle tracking echocardiography (2D-STE) features and seven clinical features to predict whether one has CHD. Methods: We develop a machine learning approach that integrates a number of popular classification methods together by model stacking, and generalize the traditional stacking method to a two-step stacking method to improve the diagnostic performance. Results: By borrowing strengths from multiple classification models through the proposed method, we improve the CHD classification accuracy from around 70% to 87.7% on the testing set. The sensitivity of the proposed method is 0.903 and the specificity is 0.843, with an AUC of 0.904, which is significantly higher than those of the individual classification models. Conclusions: Our work lays a foundation for the deployment of speckle tracking echocardiography-based screening tools for coronary heart disease., 30 pages, 5 figures, 5 tables

Additional file 1: Figure S1. The largest separation between bacterial communities is spatial proximity to the root as revealed by PCoA plotted from wUniFrac metrics (Related to Fig. 1). [A] PCo 1 vs PCo 2. [B] PCo 2 vs PCo 3. [C] PCo 1 vs PCo 3. Figure S2. Microbe richness in different compartments reflects the selectivity of plants on root-associated microbes (Related to Fig. 1). [A] Numbers of observed OTUs in the different compartments. [B] Numbers of estimated OTUs based on the Chao1 estimator. [C] Shannon index of the microbe richness. Samples were rarefied to 23000 reads prior to the analysis. Soil1 is the initial bulk soil and Soil2 is the final bulk soil. Letters denote statistical significance (p ≤ 0.05, Wilcox test) compared to Soil 1. Figure S3. Taxonomic structure of Abundant Community members (ACM) is affected by compartments and plant genotype (Related to Fig. 1). [A] Relative abundance (RA) of the bacteria within the initial bulk soil (Soil 1) and the final bulk soil (Soil 2) as classified at the phylum level. [B] Relative abundance of the bacteria phyla that were identified within the rhizosphere samples. [C] Relative abundance of the bacteria phyla that were identified within the root samples. Figure S4. The dcl234 triple mutation alters Arabidopsis root microbiota (Related to Fig. 1). [A] Relative abundance of the top 5 abundant phyla in roots of the wild type Arabidopsis (Col-0) and the RdDM pathway mutants. Mean ± SE, n ≥ 3. Asterisks indicate significant difference (FDR ≤ 0.05) between the mutant and the wild type. Taxa with RA > 5% in at least one sample were included in the statistical analysis. [B] A heatmap showing the levels of OTUs with significantly different enrichment (FDR ≤ 0.05) in dcl234 compared to Col-0. Phyla are annotated on the left side of the heatmap; on the right side, OTUs are annotated to different levels, F, family, G, genus, O, order; NR, New Reference. Figure S5. Read counts of the metagenomic sequencing. Stacked bars are shown to indicate the read counts of both plant DNA and microbial DNA sequences in each sample. Mean ±SE, n = 4. * indicates p ≤ 0.05; NS, non-significant, student t-test. Figure S6. The dcl234 triple mutation causes alterations in Arabidopsis defense-related processes (Related to Fig. 2). [A] A heatmap of DEGs involved in phenylpropanoid production. [B] Root anthocyanin visualization and measurements in plants at 18 days after germination. Mean ± SE, n = 6 biological replicates. Each biological replicate consisted of roots from 3 plants. **, p ≤ 0.01, student t-test. [C] A heatmap of DEGs involved in sulfur metabolism. DEGs were identified in the mRNAseq transcriptome analysis. The two heatmaps use the same Z-Score color scale that is shown in panel C. Figure S7. The dcl234 mutant shows both decreased and increased accumulation of different sRNAs (Related to Fig. 3). [A] The MA plot of the sRNA population identified in Col-0 and dcl234. Y-axis displays fold changes (dcl234 vs Col-0) of sRNA abundance; X-axis displays average signal intensities of the sRNA in all samples. The red, purple, and black colors indicate sRNAs that were increased, decreased, or not changed in dcl234 compared to Col-0 based on FDR p ≤ 0.05. [B] A heatmap of miRNAs identified as increased or decreased in dcl234 compared to Col-0. [C] Examples of genetic loci where sRNA abundance was affected by the dcl234 triple mutation. Snapshot images were obtained from whole-genome sRNA sequencing results. Vertical gray bars indicate the sRNA sequencing coverage normalized to the same scale in Col-0 and dcl234. Figure S8. The dcl234 mutant shows altered expression of cell wall-associated genes (Related to Fig. 4). [A] A heatmap of DEGs related to cellulose synthesis. [B] Expression levels of DEGs related to callose synthesis and pectin metabolism. Snapshot images were obtained from whole-genome sRNA sequencing results. Vertical gray bars indicate the mRNA sequencing coverage normalized to the same scale in Col-0 and dcl234. [C] Quantitative RT-PCR measurements of two pectin-related DEGs. Mean ± SE, n=3 technical replicates. Two biological replicates were analyzed with similar results. * indicates p ≤ 0.05, student t-test. Figure S9. The dcl234 mutant shows altered transcription regulation of metabolism that potentially connects to alterations in root exudates (Related to Table 2). [A] Gas Chromatography-Mass Spectrometry (GC-MS) analysis of root exudates from Col-0 and dcl234. Representative profiles were shown. n =3 biological replicates. [B] A heatmap of gibberellin-related DEGs. [C] Expression levels of miR827 and its target gene BAH1. Snapshot images were obtained from whole-genome sRNA and mRNA sequencing results. Vertical gray bars indicate the sequencing coverage normalized to the same scale in Col-0 and dcl234.

Smoothing splines have been used pervasively in nonparametric regressions. However, the computational burden of smoothing splines is significant when the sample size n is large. When the number of predictors d���2, the computational cost for smoothing splines is at the order of O(n3) using the standard approach. Many methods have been developed to approximate smoothing spline estimators by using q basis functions instead of n ones, resulting in a computational cost of the order O(nq2). These methods are called the basis selection methods. Despite algorithmic benefits, most of the basis selection methods require the assumption that the sample is uniformly distributed on a hypercube. These methods may have deteriorating performance when such an assumption is not met. To overcome the obstacle, we develop an efficient algorithm that is adaptive to the unknown probability density function of the predictors. Theoretically, we show the proposed estimator has the same convergence rate as the full-basis estimator when q is roughly at the order of O[n2d/{(pr+1)(d+2)}], where p���[1,2] and r���4 are some constants depend on the type of the spline. Numerical studies on various synthetic datasets demonstrate the superior performance of the proposed estimator in comparison with mainstream competitors. Supplementary files for this article are available online.

Optimal transport has been one of the most exciting subjects in mathematics, starting from the eighteenth century. As a powerful tool to transport between two probability measures, optimal transport methods have been reinvigorated nowadays in a remarkable proliferation of modern data science applications. To meet the big data challenges, various computational tools have been developed in the recent decade to accelerate the computation for optimal transport methods. In this review, we present some cutting-edge computational optimal transport methods with a focus on the regularization-based methods and the projection-based methods. We discuss their real-world applications in biomedical research.

Background: Extensive clinical evidence suggests that a preventive screening of coronary heart disease (CHD) at an earlier stage can greatly reduce the mortality rate. We use 64 two-dimensional speckle tracking echocardiography (2D-STE) features and seven clinical features to predict whether one has CHD. Methods: We develop a machine learning approach that integrates a number of popular classification methods together by model stacking, and generalize the traditional stacking method to a two-step stacking method to improve the diagnostic performance. Results: By borrowing strengths from multiple classification models though the proposed method, we improve the CHD classification accuracy from around 70% to 87.7% on the testing set. The sensitivity of the proposed method is 0.903 and the specificity is 0.843, with an AUC of 0.904, which is significantly higher than those of the individual classification models. Conclusions: Our work lays a foundation for the deployment of speckle tracking echocardiography-based screening tools for coronary heart disease.

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.

Retinitis Pigmentosa (RP) is an incurable inherited retinal degeneration affecting approximately 1 in 4,000 individuals globally. The goal of this work was to identify drugs that can help patients suffering from the disease. To accomplish this, we screened drugs on a zebrafish RP model. This model expresses a truncated human rhodopsin transgene (Tg(rho:Hsa.RH1_Q344X)) causing significant rod degeneration by 7 days post-fertilization (dpf). Consequently, the larvae displayed a deficit in visual motor response (VMR) under scotopic condition. The diminished VMR was leveraged to screen an ENZO SCREEN-WELL® REDOX library since oxidative stress is postulated to play a role in RP progression. Our screening identified a beta-blocker, carvedilol, that ameliorated the deficient VMR of the RP larvae and increased their rod number. Carvedilol can act directly on rods as it affected the adrenergic pathway in a rod-like human Y79 cell line. Since carvedilol is an FDA-approved drug, our findings suggest that carvedilol can potentially be repurposed to treat RP patients.Summary StatementThis paper presents the utilization of zebrafish visual behavior, a novel paradigm to screen and identify drugs to treat retinitis pigmentosa, an incurable retinal-degenerative disease.

Upon a drastic change in environmental illumination, zebrafish larvae display a rapid locomotor response. This response can be simultaneously tracked from larvae arranged in multi-well plates. The resulting data have provided new insights into neuro-behaviour. The features of these data, however, present a challenge to traditional statistical tests. For example, many larvae display little or no movement. Thus, the larval responses have many zero values and are imbalanced. These responses are also measured repeatedly from the same well, which results in correlated observations. These analytical issues were addressed in this study by the generalized linear mixed model (GLMM). This approach deals with binary responses and characterizes the correlation of observations in the same group. It was used to analyze a previously reported dataset. Before applying the GLMM, the activity values were transformed to binary responses (movement vs. no movement) to reduce data imbalance. Moreover, the GLMM estimated the variations among the effects of different well locations, which would eliminate the location effects when two biological groups or conditions were compared. By addressing the data-imbalance and location-correlation issues, the GLMM effectively quantified true biological effects on zebrafish locomotor response.