In this article, a novel technique for reducing settling error and noise in switched-capacitor amplifiers is presented. The technique combines Correlated Level Shifting (CLS) with Bandwidth Switching to achieve improved performance. Closed-loop amplification with CLS can provide true rail-to-rail performance and reduce settling error from finite opamp gain and limited opamp output swing. The purpose of CLS is to remove the signal from the output of the opamp by sampling the estimated signal in the first phase of CLS. Bandwidth switching is used to reduce the final output noise of amplification by changing the noise bandwidth during settling. The common feature of CLS and Bandwidth switching is multi-phase operation. Therefore, the proposed closed-loop amplification operation can integrate CLS with bandwidth switching without extra clock phase overhead. From simulation results, the proposed technique improves SFDR from 51 dB to 88 dB and reduces the output noise from 583.3 uV to 450.8 uV for 80 mV input voltage.

MOTIVATION: In the context of sample (e.g. tumor) classifications with microarray gene expression data, many methods have been proposed. However, almost all the methods ignore existing biological knowledge and treat all the genes equally a priori. On the other hand, because some genes have been identified by previous studies to have biological functions or to be involved in pathways related to the outcome (e.g. cancer), incorporating this type of prior knowledge into a classifier can potentially improve both the predictive performance and interpretability of the resulting model. RESULTS: We propose a simple and general framework to incorporate such prior knowledge into building a penalized classifier. As two concrete examples, we apply the idea to two penalized classifiers, nearest shrunken centroids (also called PAM) and penalized partial least squares (PPLS). Instead of treating all the genes equally a priori as in standard penalized methods, we group the genes according to their functional associations based on existing biological knowledge or data, and adopt group-specific penalty terms and penalization parameters. Simulated and real data examples demonstrate that, if prior knowledge on gene grouping is indeed informative, our new methods perform better than the two standard penalized methods, yielding higher predictive accuracy and screening out more irrelevant genes.

MOTIVATION: Discriminant analysis for high-dimensional and low-sample-sized data has become a hot research topic in bioinformatics, mainly motivated by its importance and challenge in applications to tumor classifications for high-dimensional microarray data. Two of the popular methods are the nearest shrunken centroids, also called predictive analysis of microarray (PAM), and shrunken centroids regularized discriminant analysis (SCRDA). Both methods are modifications to the classic linear discriminant analysis (LDA) in two aspects tailored to high-dimensional and low-sample-sized data: one is the regularization of the covariance matrix, and the other is variable selection through shrinkage. In spite of their usefulness, there are potential limitations with each method. The main concern is that both PAM and SCRDA are possibly too extreme: the covariance matrix in the former is restricted to be diagonal while in the latter there is barely any restriction. Based on the biology of gene functions and given the feature of the data, it may be beneficial to estimate the covariance matrix as an intermediate between the two; furthermore, more effective shrinkage schemes may be possible. RESULTS: We propose modified LDA methods to integrate biological knowledge of gene functions (or variable groups) into classification of microarray data. Instead of simply treating all the genes independently or imposing no restriction on the correlations among the genes, we group the genes according to their biological functions extracted from existing biological knowledge or data, and propose regularized covariance estimators that encourages between-group gene independence and within-group gene correlations while maintaining the flexibility of any general covariance structure. Furthermore, we propose a shrinkage scheme on groups of genes that tends to retain or remove a whole group of the genes altogether, in contrast to the standard shrinkage on individual genes. We show that one of the proposed methods performed better than PAM and SCRDA in a simulation study and several real data examples.