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Knowledge of locations and activities ofcis-regulatory elements (CREs) is needed to decipher basic mechanisms of gene regulation and to understand the impact of genetic variants on complex traits. Previous studies identified candidate CREs (cCREs) using epigenetic features in one species, making comparisons difficult between species. In contrast, we conducted an interspecies study defining epigenetic states and identifying cCREs in blood cell types to generate regulatory maps that are comparable between species, using integrative modeling of eight epigenetic features jointly in human and mouse in our Validated Systematic Integration (VISION) Project. The resulting catalogs of cCREs are useful resources for further studies of gene regulation in blood cells, indicated by high overlap with known functional elements and strong enrichment for human genetic variants associated with blood cell phenotypes. The contribution of each epigenetic state in cCREs to gene regulation, inferred from a multivariate regression, was used to estimate epigenetic state regulatory potential (esRP) scores for each cCRE in each cell type, which were used to categorize dynamic changes in cCREs. Groups of cCREs displaying similar patterns of regulatory activity in human and mouse cell types, obtained by joint clustering on esRP scores, harbor distinctive transcription factor binding motifs that are similar between species. An interspecies comparison of cCREs revealed both conserved and species-specific patterns of epigenetic evolution. Finally, we show that comparisons of the epigenetic landscape between species can reveal elements with similar roles in regulation, even in the absence of genomic sequence alignment. 

Summary Sequential Monte Carlo algorithms are widely accepted as powerful computational tools for making inference with dynamical systems. A key step in sequential Monte Carlo is resampling, which plays the role of steering the algorithm towards the future dynamics. Several strategies have been used in practice, including multinomial resampling, residual resampling, optimal resampling, stratified resampling and optimal transport resampling. In one-dimensional cases, we show that optimal transport resampling is equivalent to stratified resampling on the sorted particles, and both strategies minimize the resampling variance as well as the expected squared energy distance between the original and resampled empirical distributions. For general $$d$$-dimensional cases, we show that if the particles are first sorted using the Hilbert curve, the variance of stratified resampling is $$O(m^{-(1+2/d)})$$, an improvement over the best previously known rate of $$O(m^{-(1+1/d)})$$, where $$m$$ is the number of resampled particles. We show that this improved rate is optimal for ordered stratified resampling schemes, as conjectured in Gerber et al. (2019). We also present an almost-sure bound on the Wasserstein distance between the original and Hilbert-curve-resampled empirical distributions. In light of these results, we show that for dimension $d>1$ the mean square error of sequential quasi-Monte Carlo with $$n$$ particles can be $$O(n^{-1-4/\{d(d+4)\}})$$ if Hilbert curve resampling is used and a specific low-discrepancy set is chosen. To our knowledge, this is the first known convergence rate lower than $$o(n^{-1})$$.