Modeling and replicating statistical topology, and evidence for CMB non-homogeneity

Under the banner of `Big Data', the detection and classification of structure in extremely large, high dimensional, data sets, is, one of the central statistical challenges of our times. Among the most intriguing approaches to this challenge is `TDA', or `Topological Data Analysis', one of the primary aims of which is providing non-metric, but topologically informative, pre-analyses of data sets which make later, more quantitative analyses feasible. While TDA rests on strong mathematical foundations from Topology, in applications it has faced challenges due to an inability to handle issues of statistical reliability and robustness and, most importantly, in an inability to make scientific claims with verifiable levels of statistical confidence. We propose a methodology for the parametric representation, estimation, and replication of persistence diagrams, the main diagnostic tool of TDA. The power of the methodology lies in the fact that even if only one persistence diagram is available for analysis -- the typical case for big data applications -- replications can be generated to allow for conventional statistical hypothesis testing. The methodology is conceptually simple and computationally practical, and provides a broadly effective statistical procedure for persistence diagram TDA analysis. We demonstrate the basic ideas on a toy example, and the power of the approach in a novel and revealing analysis of CMB non-homogeneity

Transcription Impacts the Efficiency of mRNA Translation via Co-transcriptional N6-adenosine Methylation

Transcription and translation are two main pillars of gene expression. Due to the different timings, spots of action, and mechanisms of regulation, these processes are mainly regarded as distinct and generally uncoupled, despite serving a common purpose. Here, we sought for a possible connection between transcription and translation. Employing an unbiased screen of multiple human promoters, we identified a positive effect of TATA box on translation and a general coupling between mRNA expression and translational efficiency. Using a CRISPR-Cas9-mediated approach, genome-wide analyses, and in vitro experiments, we show that the rate of transcription regulates the efficiency of translation. Furthermore, we demonstrate that m6A modification of mRNAs is co-transcriptional and depends upon the dynamics of the transcribing RNAPII. Suboptimal transcription rates lead to elevated m6A content, which may result in reduced translation. This study uncovers a general and widespread link between transcription and translation that is governed by epigenetic modification of mRNAs

Correcting for Measurement Error in Segmented Cox Model

Measurement error in the covariate of main interest (e.g. the exposure variable, or the risk factor) is common in epidemiologic and health studies. It can effect the relative risk estimator or other types of coefficients derived from the fitted regression model. In order to perform a measurement error analysis, one needs information about the error structure. Two sources of validation data are an internal subset of the main data, and external or independent study. For the both sources, the true covariate is measured (that is, without error), or alternatively, its surrogate, which is error-prone covariate, is measured several times (repeated measures). This paper compares the precision in estimation via the different validation sources in the Cox model with a changepoint in the main covariate, using the bias correction methods RC and RR. The theoretical properties under each validation source is presented. In a simulation study it is found that the best validation source in terms of smaller mean square error and narrower confidence interval is the internal validation with measure of the true covariate in a common disease case, and the external validation with repeated measures of the surrogate for a rare disease case. In addition, it is found that addressing the correlation between the true covariate and its surrogate, and the value of the changepoint, is needed, especially in the rare disease case