Independence Test for High Dimensional Random Vectors

This paper proposes a new mutual independence test for a large number of high dimensional random vectors. The test statistic is based on the characteristic function of the empirical spectral distribution of the sample covariance matrix. The asymptotic distributions of the test statistic under the null and local alternative hypotheses are established as dimensionality and the sample size of the data are comparable. We apply this test to examine multiple MA(1) and AR(1) models, panel data models with some spatial cross-sectional structures. In addition, in a flexible applied fashion, the proposed test can capture some dependent but uncorrelated structures, for example, nonlinear MA(1) models, multiple ARCH(1) models and vandermonde matrices. Simulation results are provided for detecting these dependent structures. An empirical study of dependence between closed stock prices of several companies from New York Stock Exchange (NYSE) demonstrates that the feature of cross-sectional dependence is popular in stock marketsIndependence test, cross-sectional dependence, empirical spectral distribution, characteristic function, Marcenko-Pastur Law

Flocculation of cyanobacterial cells using coal fly ash modified chitosan

Harmful algal blooms (HABs) have increasingly occurred worldwide, which pose serious threats to water environment safety. In this study, a compound flocculant (CFAL-Chitosan) was developed for HABs mitigation where chitosan was modified by coal fly ash leachate (CFAL). When using optimized dosage of CFAL-Chitosan flocculant, the zeta potential of Microcystis aeruginosa (M.A.) flocs stayed close to zero and the algal removal efficiency plateaued over 95 % in a wide dosage range from 3 to 6 mg/L. For chitosan without CFAL, the removal efficiency peaked at 3 mg/L with a maximum removal efficiency of 81% , which quickly decreased as the dosage increased (> 3 mg/L) due to the fast reversal of zeta potential. This indicated that CFAL-chitosan could maintain better removal efficiency over a wide dosage range due to improved property on charge neutralization than that of chitosan alone. The flocs of CFAL-Chitosan were larger and denser than that of chitosan without CFAL. However, excessive CFAL beyond the optimized dose inhibited M.A. removal due to the hydrolysis and declining of molecular weight of chitosan that weakened the bridging-netting property, where the surface charge reversal happened within a narrow dosage range and the removal-dosage curve became parabola. The pH and environmentally sensitive metal residuals in the algal solution were not significantly affected by the adding of optimized dosage of CAFL-chitosan. The study provides a possible way for HABs control using the cheap material of CFA. Further studies are needed to check the potential influence of leachable metals and persistent organic pollutants (pops) in CFA under a wide range of environmental condition