Honest confidence regions and optimality in high-dimensional precision matrix estimation

We propose methodology for estimation of sparse precision matrices and statistical inference for their low-dimensional parameters in a high-dimensional setting where the number of parameters p can be much larger than the sample size. We show that the novel estimator achieves minimax rates in supremum norm and the low-dimensional components of the estimator have a Gaussian limiting distribution. These results hold uniformly over the class of precision matrices with row sparsity of small order \(\sqrt{n}/\log p\) and spectrum uniformly bounded, under a sub-Gaussian tail assumption on the margins of the true underlying distribution. Consequently, our results lead to uniformly valid confidence regions for low-dimensional parameters of the precision matrix. Thresholding the estimator leads to variable selection without imposing irrepresentability conditions. The performance of the method is demonstrated in a simulation study and on real data.     

Bandwidth selection in kernel density estimation for interval-grouped data

When interval-grouped data are available, the classical Parzen–Rosenblatt kernel density estimator has to be modified to get a computable and useful approach in this context. The new nonparametric grouped data estimator needs of the choice of a smoothing parameter. In this paper, two different bandwidth selectors for this estimator are analyzed. A plug-in bandwidth selector is proposed and its relative rate of convergence obtained. Additionally, a bootstrap algorithm to select the bandwidth in this framework is designed. This method is easy to implement and does not require Monte Carlo. Both proposals are compared through simulations in different scenarios. It is observed that when the sample size is medium or large and grouping is not heavy, both bandwidth selection methods have a similar and good performance. However, when the sample size is large and under heavy grouping scenarios, the bootstrap bandwidth selector leads to better results.     

Stability and electronic properties of armchair boron nitride/carbon nanotubes

In this work are studied the electronic and structural properties of armchair boron nitride/carbon nanotubes using first principles calculations. The density functional within the generalized gradient approximation (HSEh1PBE-GGA) is used. For each composition, different bonding schemes for the construction of the hybrid systems were employed. Among them, structural stability with neutral charge was determined for the following compositions: T1: B₄₀N₃₅C₇₅H₂₀, T2: B₃₅N₄₀C₇₅H₂₀, T3: B₃₇N₃₈C₇₅H₂₀, T4 : B₃₇N₃₇C₇₆H₂₀, and T7: B₃₅N₃₅C₈₀H₂₀. All these hybrid nanotubes have high polarity; the T3, T4 and T7 are semiconductors: whereas T1 and T2 are conductor in character. The formers also have magnetic behavior. These properties together with a low-chemical potential suggest applications as nano-vehicle for drug delivery. These mixed nanotubes also have potential applications in the electronic devices based on the small work function.     

Photocatalytic activity of a new composite material of Fe (III) oxide nanoparticles wrapped by a matrix of polymeric carbon nitride and amorphous carbon

Polymeric carbon nitride was synthesized from urea and doped with Cu and Fe to act as co-catalysts. The material doped with Fe was a new composite material composed of Fe(III) oxides (acting as a co-catalyst) wrapped by the polymer layers and amorphous carbon. Furthermore, the copper doped material was described in a previous report. The photocatalytic degradation of the azo dye direct blue 1 (DB) was studied using as photocatalysts: pure carbon nitride (CN), carbon nitride doped with Cu (CN-Cu) and carbon nitride doped with Fe (CN-Fe). The catalysts were characterized by Fourier transform infrared (FTIR) spectroscopy, X-ray diffraction (XRD), by X-ray photoelectron spectroscopy (XPS) and Brunauer–Emmett–Teller method (BET), etc. The adsorption phenomenon was studied using the Langmuir and Freundlich models. For the kinetic study, a solution of 500 mg L^?1 of DB1 was treated with each catalyst, visible light and H₂O₂. The dye concentration was measured by spectrophotometry at the wavelength of 565 nm, and the removal of the total organic content (TOC) was quantified. BET analysis yielded surface areas of 60.029, 20.116 and 70.662 m²g^?1 for CN, CN-Cu and CN-Fe, respectively. The kinetics of degradation were pseudo-first order, whose constants were 0.093, 0.039 and 0.110 min^?1 for CN, CN-Cu and CN-Fe, respectively. The total organic carbon (TOC) removal reached the highest value of 14.46% with CN-Fe.     

Utilizing Iron's Attractive Chemical and Magnetic Properties in Microrocket Design,Extended Motion,and Unique Performance

All‐in‐one material for microrocket propulsion featuring acid‐based bubble generation and magnetic guidance is presented. Electrochemically deposited iron serves as both a propellant, toward highly efficient self‐propulsion in acidic environments, and as a magnetic component enabling complete motion control. The new microrockets display longer lifetime and higher propulsion efficiency compared to previously reported active metal zinc‐based microrockets due to the chemical properties of iron and the unique structure of the microrockets. These iron‐based microrockets also demonstrate unique and attractive cargo towing and autonomous release capabilities. The latter is realized upon loss of the magnetic properties due to acid‐driven iron dissolution. More interestingly, these bubble‐propelled microrockets assemble via magnetic interactions into a variety of complex configurations and train structures, which enrich the behavior of micromachines. Modeling of the magnetic forces during the microrocket assembly and cargo capture confirms these unique experimentally observed assembly and cargo‐towing behaviors. These findings provide a new concept of blending propellant and magnetic components into one, toward simplifying the design and fabrication of artificial micro/nanomachines, realizing new functions and capabilities for a variety of future applications.     

Hybrid Nanoscopy of Hybrid Nanomaterials

The combination of complementary techniques to characterize materials at the nanoscale is crucial to gain a more complete picture of their structure, a key step to design and fabricate new materials with improved properties and diverse functions. Here it is shown that correlative atomic force microscopy (AFM) and localization‐based super‐resolution microscopy is a useful tool that provides insight into the structure and emissive properties of fluorescent β‐lactoglobulin (βLG) amyloid‐like fibrils. These hybrid materials are made by functionalization of βLG with organic fluorophores and quantum dots, the latter being relevant for the production of 1D inorganic nanostructures templated by self‐assembling peptides. Simultaneous functionalization of βLG fibers by QD655 and QD525 allows for correlative AFM and two‐color super‐resolution fluorescence imaging of these hybrid materials. These experiments allow the combination of information about the topography and number of filaments that compose a fibril, as well as the emissive properties and nanoscale spatial distribution of the attached fluorophores. This study represents an important step forward in the characterization of multifunctionalized hybrid materials, a key challenge in nanoscience.