Data-Driven Determination of the Number of Jumps in Regression Curves

In nonparametric regression with jump discontinuities, one major challenge is to determine the number of jumps in a regression curve. Most existing methods to solve that problem are based on either a sequence of hypothesis tests or model selection, by introducing some extra tuning parameters that may not be easy to determine in practice. This article aims to develop a data-driven new methodology for determining the number of jumps, using an order-preserved sample-splitting strategy together with a cross-validation-based criterion. Statistical consistency of the determined number of jumps by our proposed method is established. More interestingly, the proposed method allows us to move beyond just point estimation, and it can quantify uncertainty of the proposed estimate. The key idea behind our method is the construction of a series of statistics with marginal symmetry property and this property can be used for choosing a data-driven threshold to control the false discovery rate of our method. The proposed method is computationally efficient. Numerical experiments indicate that it has a reliable performance in finite-sample cases. An R package jra is developed to implement the proposed method.</p

Double N,B-Type Bidentate Boryl Ligands Enabling a Highly Active Iridium Catalyst for C–H Borylation

Boryl ligands hold promise in catalysis due to their very high electron-donating property. In this communication double N,B-type boryl anions were designed as bidentate ligands to promote an sp² C–H borylation reaction. A symmetric pyridine-containing tetraamino­diborane(4) compound (<b>1</b>) was readily prepared as the ligand precursor that could be used, in combination with [Ir­(OMe)­(COD)]₂, to <i>in situ</i> generate a highly active catalyst for a broad range of (hetero)­arene substrates including highly electron-rich and/or sterically hindered ones. This work provides the first example of a bidentate boryl ligand in supporting homogeneous organometallic catalysis

Geometric interpretation of the Plücker correction Ls*=(us*T,vs*T)T.

<p>Geometric interpretation of the Plücker correction </p><p></p><p></p><p></p><p></p><p><mi>L</mi></p>s<mo>*</mo><p></p><mo>=</mo><p></p><p><mo stretchy="false">(</mo></p><p></p><p><mi>u</mi></p>s<p><mo>*</mo>T</p><p></p><mo>,</mo><p></p><p><mi>v</mi></p>s<p><mo>*</mo>T</p><p></p><mo stretchy="false">)</mo><p></p>T<p></p><p></p><p></p><p></p>.<p></p

Rotenone induced microglial activation via p38 MAPK.

<p>(A) BV2 cells were treated with different doses of rotenone for 6 hours or 1 µg/mL LPS for 1 hour and lysed in lysis buffer. The lysates were immunoblotted with the indicated antibodies. (B) Quantitative analysis of the data from (A), showing the density of pp38 relative to that of the loading control (tubulin). The data are presented as the mean ± S.E.M. n = 3, *p<0.05, one-way ANOVA. (C) BV2 cells were treated with 1 µM rotenone for 6 hours or 1 µg/mL LPS for 1 hour or co-treated with 5 mM NAC and either 1 µM rotenone for 6 hours or 1 µg/mL LPS for 1 hour. The cells were stained with an ROS indicator, DCFH-DA, for 30 minutes. The scale bar represents 10 µm. (D) BV2 cells were treated with rotenone or LPS in the same manner described in (C). The cells were lysed, and the lysates were immunoblotted with the indicated antibodies.</p

Eight 3D lines (in pink color) on two orthogonal planes used in the simulations, where the small pyramids stand for camera viewpoints.

<p>Eight 3D lines (in pink color) on two orthogonal planes used in the simulations, where the small pyramids stand for camera viewpoints.</p

Eight 3D lines (in pink color) on two orthogonal planes used in the simulations, where the small pyramids stand for camera viewpoints.

<p>Eight 3D lines (in pink color) on two orthogonal planes used in the simulations, where the small pyramids stand for camera viewpoints.</p

The optimal algorithm: OPTa-II.

<p>The optimal algorithm: OPTa-II.</p

The optimal algorithm: OPTa-I.

<p>The optimal algorithm: OPTa-I.</p

Distances between the edges on the unit cube by the three metrics.

<p>Distances between the edges on the unit cube by the three metrics.</p

Experimental results.

<p>(a) Calibration cube; (b) planar checkerboard; (c) model house; (d) corridor.</p