Variable-Dependent Partial Dimension Reduction

Sufficient dimension reduction reduces the dimension of a regression model without loss of information by replacing the original predictor with its lower-dimensional linear combinations. Partial (sufficient) dimension reduction arises when the predictors naturally fall into two sets X and W, and pursues a partial dimension reduction of X. Though partial dimension reduction is a very general problem, only very few research results are available when W is continuous. To the best of our knowledge, none can deal with the situation where the reduced lower-dimensional subspace of X varies with W. To address such issue, we in this paper propose a novel variable-dependent partial dimension reduction framework and adapt classical sufficient dimension reduction methods into this general paradigm. The asymptotic consistency of our method is investigated. Extensive numerical studies and real data analysis show that our variable-dependent partial dimension reduction method has superior performance compared to the existing methods

Finding combinatorial histone code by semi-supervised biclustering

Abstract Background Combinatorial histone modification is an important epigenetic mechanism for regulating chromatin state and gene expression. Given the rapid accumulation of genome-wide histone modification maps, there is a pressing need for computational methods capable of joint analysis of multiple maps to reveal combinatorial modification patterns. Results We present the Semi-Supervised Coherent and Shifted Bicluster Identification algorithm (SS-CoSBI). It uses prior knowledge of combinatorial histone modifications to guide the biclustering process. Specifically, co-occurrence frequencies of histone modifications characterized by mass spectrometry are used as probabilistic priors to adjust the similarity measure in the biclustering process. Using a high-quality set of transcriptional enhancers and associated histone marks, we demonstrate that SS-CoSBI outperforms its predecessor by finding histone modification and genomic locus biclusters with higher enrichment of enhancers. We apply SS-CoSBI to identify multiple cell-type-specific combinatorial histone modification states associated with human enhancers. We show enhancer histone modification states are correlated with the expression of nearby genes. Further, we find that enhancers with the histone mark H3K4me1 have higher levels of DNA methylation and decreased expression of nearby genes, suggesting a functional interplay between H3K4me1 and DNA methylation that can modulate enhancer activities. Conclusions The analysis presented here provides a systematic characterization of combinatorial histone codes of enhancers across three human cell types using a novel semi-supervised biclustering algorithm. As epigenomic maps accumulate, SS-CoSBI will become increasingly useful for understanding combinatorial chromatin modifications by taking advantage of existing knowledge. Availability and implementation SS-CoSBI is implemented in C. The source code is freely available at http://www.healthcare.uiowa.edu/labs/tan/SS-CoSBI.gz.</p

Variable-Dependent Partial Dimension Reduction

Sufficient dimension reduction reduces the dimension of a regression model without loss of information by replacing the original predictor with its lower-dimensional linear combinations. Partial (sufficient) dimension reduction arises when the predictors naturally fall into two sets X and W, and pursues a partial dimension reduction of X. Though partial dimension reduction is a very general problem, only very few research results are available when W is continuous. To the best of our knowledge, none can deal with the situation where the reduced lower-dimensional subspace of X varies with W. To address such issue, we in this paper propose a novel variable-dependent partial dimension reduction framework and adapt classical sufficient dimension reduction methods into this general paradigm. The asymptotic consistency of our method is investigated. Extensive numerical studies and real data analysis show that our variable-dependent partial dimension reduction method has superior performance compared to the existing methods

Two surgical treatment methods for open angle glaucoma and cataract

AIM: To compare the curative effects of two surgical treatment methods for open angle glaucoma and cataract patients.<p>METHODS: Totally 69 patients with primary open angle glaucoma and cataract were divided into two groups: group A and group B. Thirty-four patients(34 eyes)in group A underwent small incision non-phacoemulsification cataract surgery combined with trabeculectomy, just combined operations, 35 patients(35 eyes)in group B underwent small incision non-phacoemulsification cataract surgery beyond 6mo after trabeculectomy, just two stage operations. Postoperative intraocular pressure at 1wk and 3mo, postoperative corrected visual acuity and filtering bleb at 3mo were observed, and intraoperative and postoperative complications were compared. All the patients were followed up for 3-6mo.<p>RESULTS: All the visual acuity were increased compared with that before surgery in two groups, the difference was not statistically significant. All the intraocular pressure was controlled in two groups, the difference was not statistically significant, and the difference about the filtering bleb was neither statistically significant(<i>P</i>>0.05). There were no serious intraoperative and postoperative complications in two groups.<p>CONCLUSION: The two stage operations and the combined operations both can control theintraocular pressure and improved visual acuity of open angle glaucoma and cataract. The two stage operations may prevent a second operation for post trabeculectomy cataract, allowing earlier visual rehabilitation

Pre-configured Error Pattern Ordered Statistics Decoding for CRC-Polar Codes

In this paper, we propose a pre-configured error pattern ordered statistics decoding (PEPOSD) algorithm and discuss its application to short cyclic redundancy check (CRC)-polar codes. Unlike the traditional OSD that changes the most reliable independent symbols, we regard the decoding process as testing the error patterns, like guessing random additive noise decoding (GRAND). Also, the pre-configurator referred from ordered reliability bits (ORB) GRAND can better control the range and testing order of EPs. Offline-online structure can accelerate the decoding process. Additionally, we also introduce two orders to optimize the search order for testing EPs. Compared with CRC-aided OSD and list decoding, PEPOSD can achieve a better trade-off between accuracy and complexity