Standard errors of fitted component means of normal mixtures

In this paper use consider the problem of providing standard errors of the component means in normal mixture models fitted to univariate or multivariate data by maximum likelihood via the EM algorithm. Two methods of estimation of the standard errors are considered: the standard information-based method and the computationally-intensive bootstrap method. They are compared empirically by their application to three real data sets and by a small-scale Monte Carlo experiment.

Synchronization of mutually coupled chaotic systems

We report on the experimental observation of both basic frequency locking synchronization and chaos synchronization between two mutually coupled chaotic subsystems. We show that these two kinds of synchronization are two stages of interaction between coupled chaotic systems. in particular the chaos synchronization could be understood as a state of phase locking between coupled chaotic oscillations.

Renal Cell Carcinoma: T1 and T2 Signal Intensity Characteristics of Papillary and Clear Cell Types Correlated with Pathology

OBJECTIVE. The objective of our study was to describe the T1 and T2 signal intensity characteristics of papillary renal cell carcinoma (RCC) and clear cell RCC with pathologic correlation. MATERIALS AND METHODS. Of 539 RCCs, 49 tumors (21 papillary RCCs and 28 clear cell RCCs) in 45 patients were examined with MRI. Two radiologists retrospectively and independently assessed each tumor`s T1 and T2 signal intensity qualitatively and quantitatively (i.e., the signal intensity [SI] ratio [tumor SI/renal cortex SI]). Of the 49 tumors, 37 (76%) were assessed for pathology features including tumor architecture and the presence of hemosiderin, ferritin, necrosis, and fibrosis. MRI findings and pathology features were correlated. Statistical methods included summary statistics and Wilcoxon`s rank sum test for signal intensity, contingency tables for assessing reader agreement, concordance rate between the two readers with 95% CIs, and Fisher`s exact test for independence, all stratified by RCC type. RESULTS. Papillary RCCs and clear cell RCCs had a similar appearance and signal intensity ratio on T1-weighted images. On T2-weighted images, most papillary RCCs were hypointense (reader 1, 13/21; reader 2, 14/21), with an average mean signal intensity ratio for both readers of 0.67 +/- 0.2, and none was hyperintense, whereas most clear cell RCCs were hyperintense (reader 1, 21/28; reader 2, 17/28), with an average mean signal intensity ratio for both readers of 1.41 +/- 0.4 (p < 0.05). A tumor T2 signal intensity ratio of <= 0.66 had a specificity of 100% and sensitivity of 54% for papillary RCC. Most T2 hypointense tumors exhibited predominant papillary architecture; most T2 hyperintense tumors had a predominant nested architecture (p < 0.05). CONCLUSION. On T2-weighted images, most papillary RCCs are hypointense and clear cell RCCs, hyperintense. The T2 hypointense appearance of papillary RCCs correlated with a predominant papillary architecture at pathology.