Limiting spectral distribution of high-dimensional noncentral Fisher matrices and its analysis

Fisher matrix is one of the most important statistics in multivariate statistical analysis.Its eigenvalues are of primary importance for many applications,such as testing the equality of mean vectors,testing the equality of covariance matrices and signal detection problems.In this paper,we establish the limiting spectral distribution of high-dimensional noncentral Fisher matrices and investigate its analytic behavior.In particular,we show the determination criterion for the support of the limiting spectral distribution of the noncentral Fisher matrices,which is the base of investigating the high-dimensional problems concerned with noncentral Fisher matrices.

Transport of intensity diffraction tomography with non-interferometric synthetic aperture for three-dimensional label-free microscopy

We present a new label-free three-dimensional(3D)microscopy technique,termed transport of intensity diffraction tomography with non-interferometric synthetic aperture(TIDT-NSA).Without resorting to interferometric detection,TIDT-NSA retrieves the 3D refractive index(RI)distribution of biological specimens from 3D intensity-only measurements at various illumination angles,allowing incoherent-diffraction-limited quantitative 3D phase-contrast imaging.The unique combination of z-scanning the sample with illumination angle diversity in TIDT-NSA provides strong defocus phase contrast and better optical sectioning capabilities suitable for high-resolution tomography of thick biological samples.Based on an off-the-shelf bright-field microscope with a programmable light-emitting-diode(LED)illumination source,TIDT-NSA achieves an imaging resolution of 206 nm laterally and 520 nm axially with a high-NA oil immersion objective.We validate the 3D RI tomographic imaging performance on various unlabeled fixed and live samples,including human breast cancer cell lines MCF-7,human hepatocyte carcinoma cell lines HepG2,mouse macrophage cell lines RAW 264.7,Caenorhabditis elegans(C.elegans),and live Henrietta Lacks(HeLa)cells.These results establish TIDT-NSA as a new non-interferometric approach to optical diffraction tomography and 3D label-free microscopy,permitting quantitative characterization of cell morphology and time-dependent subcellular changes for widespread biological and medical applications.

Weighted estimating equation： modified GEE in longitudinal data analysis

The method of generalized estimating equations （GEE） introduced by K. Y. Liang and S. L. Zeger has been widely used to analyze longitudinal data. Recently, this method has been criticized for a failure to protect against misspecification of working correlation models, which in some cases leads to loss of efficiency or infeasibility of solutions. In this paper, we present a new method named as ＇weighted estimating equations （WEE）＇ for estimating the correlation parameters. The new estimates of correlation parameters are obtained as the solutions of these weighted estimating equations. For some commonly assumed correlation structures, we show that there exists a unique feasible solution to these weighted estimating equations regardless the correlation structure is correctly specified or not. The new feasible estimates of correlation parameters are consistent when the working correlation structure is correctly specified. Simulation results suggest that the new method works well in finite samples.