Substitution principle for CLT of linear spectral statistics of high-dimensional sample covariance matrices with applications to hypothesis testing

published_or_final_versio

CLT for linear spectral statistics of a rescaled sample precision matrix

postprin

CLT for eigenvalue statistics of large-dimensional general Fisher matrices with applications

Random Fisher matrices arise naturally in multivariate statistical analysis and understanding the properties of its eigenvalues is of primary importance for many hypothesis testing problems like testing the equality between two covariance matrices, or testing the independence between sub-groups of a multivariate random vector. Most of the existing work on random Fisher matrices deals with a particular situation where the population covariance matrices are equal. In this paper, we consider general Fisher matrices with arbitrary population covariance matrices and develop their spectral properties when the dimensions are proportionally large compared to the sample size. The paper has two main contributions: first the limiting distribution of the eigenvalues of a general Fisher matrix is found and second, a central limit theorem is established for a wide class of functionals of these eigenvalues. Applications of the main results are also developed for testing hypotheses on high-dimensional covariance matrices.published_or_final_versio

Graphene-polyelectrolyte multilayer membranes with tunable structure and internal charge

One great advantage of graphene-polyelectrolyte multilayer (GPM) membranes is their tunable structure and internal charge for improved separation performance. In this study, we synthesized GO-dominant GPM membrane with internal negatively-charged domains, polyethyleneimine (PEI)-dominant GPM membrane with internal positively-charged domains and charge-balanced dense/loose GPM membranes by simply adjusting the ionic strength and pH of the GO and PEI solutions used in layer-by-layer membrane synthesis. A combined system of quartz crystal microbalance with dissipation (QCM-D) and ellipsometry was used to analyze the mass deposition, film thickness, and layer density of the GPM membranes. The performance of the GPM membranes were compared in terms of both permeability and selectivity to determine the optimal membrane structure and synthesis strategy. One effective strategy to improve the GPM membrane permeability-selectivity tradeoff is to assemble charge-balanced dense membranes under weak electrostatic interactions. This balanced membrane exhibits the highest MgCl2 selectivity (∼86%). Another effective strategy for improved cation removal is to create PEI-dominant membranes that provide internal positively-charged barrier to enhance cation selectivity without sacrificing water permeability. These findings shine lights on the development of a systematic approach to push the boundary of permeability-selectivity tradeoff for GPM membranes

Dynamic Covalent Synthesis of Crystalline Porous Graphitic Frameworks

Porous graphitic framework (PGF) is a two-dimensional (2D) material that has emerging energy applications. An archetype contains stacked 2D layers, the structure of which features a fully annulated aromatic skeleton with embedded heteroatoms and periodic pores. Due to the lack of a rational approach in establishing in-plane order under mild synthetic conditions, the structural integrity of PGF has remained elusive and ultimately limited its material performance. Here, we report the discovery of the unusual dynamic character of the C=N bonds in the aromatic pyrazine ring system under basic aqueous conditions, which enables the successful synthesis of a crystalline porous nitrogenous graphitic framework with remarkable in-plane order, as evidenced by powder X-ray diffraction studies and direct visualization using high-resolution transmission electron microscopy. The crystalline framework displays superior performance as a cathode material for lithium-ion batteries, outperforming the amorphous counterparts in terms of capacity and cycle stability. Insertion of well-defined, evenly spaced nanoscale pores into the two-dimensional (2D) layers of graphene invokes exciting properties due to the modulation of its electronic band gaps and surface functionalities. A bottom-up synthesis approach to such porous graphitic frameworks (PGFs) is appealing but also remains a great challenge. The current methods of building covalent organic frameworks rely on a small collection of thermodynamically reversible reactions. Such reactions are, however, inadequate in generating a fully annulated aromatic skeleton in PGFs. With the discovery of dynamic pyrazine formation, we succeeded in applying this linking chemistry to obtain a crystalline PGF material, which has displayed high electrical conductivity and remarkable performance as a cathode material for lithium-ion batteries. We envision that the demonstrated success will open the door to a wide array of fully annulated 2D porous frameworks, which hold immense potential for clean energy applications. We report the unusual dynamic characteristics of the C=N bonds in the pyrazine ring promoted under basic aqueous conditions, which enables the successful synthesis of two-dimensional porous graphitic frameworks (PGFs) featuring fully annulated aromatic skeletons and periodic pores. The PGF displayed high electrical conductivity and remarkable performance as a cathode material for lithium-ion batteries, far outperforming the amorphous counterparts in terms of capacity and cycle stability

DVL1 (dishevelled, dsh homolog 1 (Drosophila))

Review on DVL1 (dishevelled, dsh homolog 1 (Drosophila)), with data on DNA, on the protein encoded, and where the gene is implicated

Repeatability of Corneal Elevation Maps in Keratoconus Patients Using the Tomography Matching Method

To assess repeatability of corneal tomography in successive measurements by Pentacam in keratoconus (KC) and normal eyes based on the Iterative Closest Point (ICP) algorithm. The study involved 143 keratoconic and 143 matched normal eyes. ICP algorithm was used to estimate six single and combined misalignment (CM) parameters, the root mean square (RMS) of the difference in elevation data pre (PreICP-RMS) and post (PosICP-RMS) tomography matching. Corneal keratometry, expressed in the form of M, J0 and J45 (power vector analysis parameters), was used to evaluate the effect of misalignment on corneal curvature measurements. The PreICP-RMS and PosICP-RMS were statistically higher (P < 0.01) in KC than normal eyes. CM increased significantly (p = 0.00), more in KC (16.76 ± 20.88 μm) than in normal eyes (5.43 ± 4.08 μm). PreICP-RMS, PosICP-RMS and CM were correlated with keratoconus grade (p < 0.05). Corneal astigmatism J0 was different (p = 0.01) for the second tomography measurements with misalignment consideration (−1.11 ± 2.35 D) or not (−1.18 ± 2.35 D), while M and J45 kept similar. KC corneas consistently show higher misalignments between successive tomography measurements and lower repeatability compared with healthy eyes. The influence of misalignment is evidently clearer in the estimation of astigmatism than spherical curvature. These higher errors appear correlated with KC progression