The direction of outlyingness is crucial to describing the centrality of multivariate functional data. Motivated by this idea, classical depth is generalized to directional outlyingness for functional data. Theoretical properties of functional directional outlyingness are investigated and the total outlyingness can be naturally decomposed into two parts: magnitude outlyingness and shape outlyingness which represent the centrality of a curve for magnitude and shape, respectively. This decomposition serves as a visualization tool for the centrality of curves. Furthermore, an outlier detection procedure is proposed based on functional directional outlyingness. This criterion applies to both univariate and multivariate curves and simulation studies show that it outperforms competing methods. Weather and electrocardiogram data demonstrate the practical application of our proposed framework.
This paper proposes a new graphical tool, the magnitude-shape (MS) plot, for visualizing both the magnitude and shape outlyingness of multivariate functional data. The proposed tool builds on the recent notion of functional directional outlyingness, which measures the centrality of functional data by simultaneously considering the level and the direction of their deviation from the central region. The MS-plot intuitively presents not only levels but also directions of magnitude outlyingness on the horizontal axis or plane, and demonstrates shape outlyingness on the vertical axis. A dividing curve or surface is provided to separate non-outlying data from the outliers. Both the simulated data and the practical examples confirm that the MS-plot is superior to existing tools for visualizing centrality and detecting outliers for functional data.
Functional data analysis can be seriously impaired by abnormal observations, which can be classified as either magnitude or shape outliers based on their way of deviating from the bulk of data. Identifying magnitude outliers is relatively easy, while detecting shape outliers is much more challenging. We propose turning the shape outliers into magnitude outliers through data transformation and detecting them using the functional boxplot. Besides easing the detection procedure, applying several transformations sequentially provides a reasonable taxonomy for the flagged outliers. A joint functional ranking, which consists of several transformations, is also defined here. Simulation studies are carried out to evaluate the performance of the proposed method using different functional depth notions. Interesting results are obtained in several practical applications.
Schisandrin B (SchB) is one of the most abundant bioactive dibenzocyclooctadiene derivatives found in the fruit of Schisandra chinensis. Here, we investigated the potential therapeutic effects of SchB on non-alcoholic fatty-liver disease (NAFLD). In lipidomic study, ingenuity pathway analysis highlighted palmitate biosynthesis metabolic pathway in the liver samples of SchB-treated high-fat-diet-fed mice. Further experiments showed that the SchB treatment reduced expression and activity of fatty acid synthase, expressions of hepatic mature sterol regulatory element binding protein-1 and tumor necrosis factor-α, and hepatic level of palmitic acid which is known to promote progression of steatosis to steatohepatitis. Furthermore, the treatment also reduced hepatic fibrosis, activated nuclear factor-erythroid-2-related factor-2 which is known to attenuate the progression of NASH-related fibrosis. Interestingly, in fasting mice, a single high-dose SchB induced transient lipolysis and increased the expressions of adipose triglyceride lipase and phospho-hormone sensitive lipase. The treatment also increased plasma cholesterol levels and 3-hydroxy-3-methylglutaryl-CoA reductase activity, reduced the hepatic low-density-lipoprotein receptor expression in these mice. Our data not only suggest SchB is a potential therapeutic agent for NAFLD, but also provided important information for a safe consumption of SchB because SchB overdosed under fasting condition will have adverse effects on lipid metabolism.
Inflammatory bowel disease (IBD) is a refractory disorder characterized by chronic and recurrent inflammation. The progression and pathogenesis of IBD is closely related to oxidative stress and irregularly high concentrations of reactive oxygen species (ROS). A new oxidation-responsive nano prodrug was constructed from a phenylboronic esters-modified carboxylmethyl chitosan (OC-B) conjugated with berberine (BBR) that degrades selectively in response to ROS. The optimized micelles exhibited well-controlled physiochemical properties and stability in a physiological environment. OC-B-BBR micelles could effectively encapsulate the anti-inflammatory drug berberine and exhibit ideal H2O2-triggered release behavior as confirmed by in vitro drug loading and release studies. The in vivo anti-inflammatory effect and regulation of gut microbiota caused by it were explored in mice with colitis induced by dextran sodium sulfate (DSS). The results showed that OC-B-BBR significantly ameliorated colitis symptoms and colon damage by regulating the expression levels of IL-6 and remodeling gut microbiota. In summary, this study exhibited a novel BBR-loaded Carboxylmethyl Chitosan nano delivery system which may represent a promising approach for improving IBD treatment.
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