The conditionally studentized test for high-dimensional parametric regressions

This paper studies model checking for general parametric regression models having no dimension reduction structures on the predictor vector. Using any U-statistic type test as an initial test, this paper combines the sample-splitting and conditional studentization approaches to construct a COnditionally Studentized Test (COST). Whether the initial test is global or local smoothing-based; the dimension of the predictor vector and the number of parameters are fixed or diverge at a certain rate, the proposed test always has a normal weak limit under the null hypothesis. When the dimension of the predictor vector diverges to infinity at faster rate than the number of parameters, even the sample size, these results are still available under some conditions. This shows the potential of our method to handle higher dimensional problems. Further, the test can detect the local alternatives distinct from the null hypothesis at the fastest possible rate of convergence in hypothesis testing. We also discuss the optimal sample splitting in power performance. The numerical studies offer information on its merits and limitations in finite sample cases including the setting where the dimension of predictor vector equals the sample size. As a generic methodology, it could be applied to other testing problems.Comment: 35 pages, 2 figure

Meibomian gland stem/progenitor cells: The hunt for gland renewal.

Meibomian glands (MGs) secrete lipid (meibum) onto the ocular surface to form the outermost layer of the tear film. Proper meibum secretion is essential for stabilizing the tear film, reducing aqueous tear evaporation, and maintaining the homeostasis of the ocular surface. Atrophy of MG as occurs with aging, leads to reduction of meibum secretion, loss of ocular surface homeostasis and evaporative dry eye disease (EDED). Since MGs are holocrine glands, secretion of meibum requires continuous self-renewal of lipid-secreting acinar meibocytes by stem/progenitor cells, whose proliferative potential is dramatically reduced with age leading to MG atrophy and an age-related meibomian gland dysfunction (ARMGD). Understanding the cellular and molecular mechanisms regulating meibocyte stem/progenitor cell maintenance and renewal may provide novel approaches to regenerating MG and treating EDED. Towards that end, recent label retaining cell and lineage-tracing experiments as well as knock-out transgenic mouse studies have begun to identify the location and identities of meibocyte progenitor cells and potential growth and transcription factors that may regulate meibocyte renewal. In addition, recent reports have shown that ARMGD may be reversed by novel therapeutics in mice. Herein, we discuss our current understanding of meibocyte stem/progenitor cells and the hunt for gland renewal

Successive vertex orderings of fully regular graphs

A graph G = (V,E) is called fully regular if for every independent set $I\subset V$ , the number of vertices in $V\setminus$ I that are not connected to any element of I depends only on the size of I. A linear ordering of the vertices of G is called successive if for every i, the first i vertices induce a connected subgraph of G. We give an explicit formula for the number of successive vertex orderings of a fully regular graph. As an application of our results, we give alternative proofs of two theorems of Stanley and Gao + Peng, determining the number of linear edge orderings of complete graphs and complete bipartite graphs, respectively, with the property that the first i edges induce a connected subgraph. As another application, we give a simple product formula for the number of linear orderings of the hyperedges of a complete 3-partite 3-uniform hypergraph such that, for every i, the first i hyperedges induce a connected subgraph. We found similar formulas for complete (non-partite) 3-uniform hypergraphs and in another closely related case, but we managed to verify them only when the number of vertices is small.Comment: 14 page

Effects of Shenque Moxibustion on Behavioral Changes and Brain Oxidative State in Apolipoprotein E-Deficient Mice

Purpose. To determine whether moxibustion influences the learning and memory behavior of ApoE−/− male mice, and investigate the mechanism of moxibustion on the alteration of oxidized proteins (glial fibrillary acidic protein, β-amyloid) in hippocampus. Methods. Thirty-three ApoE−/− mice were randomly divided into 3 groups (n=11/group): moxibustion, sham moxibustion, and no treatment control. Wild-type C57BL/6 mice n=13 were used for normal control. Moxibustion was performed with Shenque (RN8) moxibustion for 20 minutes per day, 6 days/week for 12 weeks. In sham control, the procedure was similar except burning of the moxa stick. Behavioral tests (step-down test and Morris water maze task) were conducted in the 13th week. The mice were then sacrificed and the tissues were harvested for immune-histochemical staining. Results. In the step-down test, the moxibustion group had shorter reaction time in training record and committed less mistakes compared to sham control. In immune-histochemical study, the moxibustion group expressed lower level of GFAP and less aggregation of β-amyloid in the hippocampus than the sham control. Conclusion. Our findings suggest that moxibustion may enhance learning capability of ApoE−/− mice. The mechanism may be via inhibiting oxidized proteins (GFAP and β-amyloid) in astrocytes

Modeling the Charging Behaviors for Electric Vehicles Based on Ternary Symmetric Kernel Density Estimation

The accurate modeling of the charging behaviors for electric vehicles (EVs) is the basis for the charging load modeling, the charging impact on the power grid, orderly charging strategy, and planning of charging facilities. Therefore, an accurate joint modeling approach of the arrival time, the staying time, and the charging capacity for the EVs charging behaviors in the work area based on ternary symmetric kernel density estimation (KDE) is proposed in accordance with the actual data. First and foremost, a data transformation model is established by considering the boundary bias of the symmetric KDE in order to carry out normal transformation on distribution to be estimated from all kinds of dimensions to the utmost extent. Then, a ternary symmetric KDE model and an optimum bandwidth model are established to estimate the transformed data. Moreover, an estimation evaluation model is also built to transform simulated data that are generated on a certain scale with the Monte Carlo method by means of inverse transformation, so that the fitting level of the ternary symmetric KDE model can be estimated. According to simulation results, a higher fitting level can be achieved by the ternary symmetric KDE method proposed in this paper, in comparison to the joint estimation method based on the edge KDE and the ternary t-Copula function. Moreover, data transformation can effectively eliminate the boundary effect of symmetric KDE. Document type: Articl