Geometric methods for estimation of structured covariances

We consider problems of estimation of structured covariance matrices, and in particular of matrices with a Toeplitz structure. We follow a geometric viewpoint that is based on some suitable notion of distance. To this end, we overview and compare several alternatives metrics and divergence measures. We advocate a specific one which represents the Wasserstein distance between the corresponding Gaussians distributions and show that it coincides with the so-called Bures/Hellinger distance between covariance matrices as well. Most importantly, besides the physically appealing interpretation, computation of the metric requires solving a linear matrix inequality (LMI). As a consequence, computations scale nicely for problems involving large covariance matrices, and linear prior constraints on the covariance structure are easy to handle. We compare this transportation/Bures/Hellinger metric with the maximum likelihood and the Burg methods as to their performance with regard to estimation of power spectra with spectral lines on a representative case study from the literature.Comment: 12 pages, 3 figure

Insights into distinct regulatory modes of nucleosome positioning

<p>Abstract</p> <p>Background</p> <p>The nucleosome is the fundamental unit of eukaryotic genomes. Experimental evidence suggests that the genomic DNA sequence and a variety of protein factors contribute to nucleosome positioning <it>in vivo</it>. However, how nucleosome positioning is determined locally is still largely unknown.</p> <p>Results</p> <p>We found that transcription factor binding sites (TFBSs) with particular nucleosomal contexts show a preference to reside on specific chromosomes. We identified four typical gene classes associated with distinct regulatory modes of nucleosome positioning, and further showed that they are distinguished by transcriptional regulation patterns. The first mode involves the cooperativity between chromatin remodeling and stable transcription factor (TF)-DNA binding that is linked to high intrinsic DNA binding affinities, evicting nucleosomes from favorable DNA sequences. The second is the DNA-encoded low nucleosome occupancy that is associated with high gene activity. The third is through chromatin remodeling and histone acetylation, sliding nucleosomes along DNA. This mode is linked to more cryptic sites for TF binding. The last consists of the nucleosome-enriched organization driven by other factors that overrides nucleosome sequence preferences. In addition, we showed that high polymerase II (Pol II) occupancy is associated with high nucleosome occupancy around the transcription start site (TSS).</p> <p>Conclusions</p> <p>We identified four different regulatory modes of nucleosome positioning and gave insights into mechanisms that specify promoter nucleosome location. We suggest two distinct modes of recruitment of Pol II, which are selectively employed by different genes.</p

Two distinct modes of nucleosome modulation associated with different degrees of dependence of nucleosome positioning on the underlying DNA sequence

<p>Abstract</p> <p>Background</p> <p>The nucleosome is the fundamental unit of eukaryotic genomes. Its positioning plays a central role in diverse cellular processes that rely on access to genomic DNA. Experimental evidence suggests that the genomic DNA sequence is one important determinant of nucleosome positioning. Yet it is less clear whether the role of the underlying DNA sequence in nucleosome positioning varies across different promoters. Whether different determinants of nucleosome positioning have characteristic influences on nucleosome modulation also remains to be elucidated.</p> <p>Results</p> <p>We identified two typical promoter classes in yeast associated with high or low dependence of nucleosome positioning on the underlying DNA sequence, respectively. Importantly, the two classes have low or high intrinsic sequence preferences for nucleosomes, respectively. The two classes are further distinguished by multiple promoter features, including nucleosome occupancy, nucleosome fuzziness, H2A.Z occupancy, changes in nucleosome positions before and after transcriptional perturbation, and gene activity. Both classes have significantly high turnover rates of histone H3, but employ distinct modes of nucleosome modulation: The first class is characterized by hyperacetylation, whereas the second class is highly regulated by ATP-dependent chromatin remodelling.</p> <p>Conclusion</p> <p>Our results, coupled with the known features of nucleosome modulation, suggest that the two distinct modes of nucleosome modulation selectively employed by different genes are linked with the intrinsic sequence preferences for nucleosomes. The difference in modes of nucleosome modulation can account for the difference in the contribution of DNA sequence to nucleosome positioning between both promoter classes.</p

Genome-wide analysis of the effect of histone modifications on the coexpression of neighboring genes in Saccharomyces cerevisiae

<p>Abstract</p> <p>Background</p> <p>Neighboring gene pairs in the genome of <it>Saccharomyces cerevisiae </it>have a tendency to be expressed at the same time. The distribution of histone modifications along chromatin fibers is suggested to be an important mechanism responsible for such coexpression. However, the extent of the contribution of histone modifications to the coexpression of neighboring genes is unclear.</p> <p>Results</p> <p>We investigated the similarity of histone modification between neighboring genes using autocorrelation analysis and composite profiles. Our analysis showed that neighboring genes had similar levels or changes of histone modifications, especially those transcribed in the same direction. The similarities, however, were restricted to 1 or 2 neighboring genes. Moreover, the expression of a gene was significantly correlated with histone modification of its neighboring gene(s), but this was limited to only 1 or 2 neighbors. Using a hidden Markov model (HMM), we found more than 2000 chromatin domains with similar acetylation changes as the cultures changed and a considerable number of these domains covered 2-4 genes. Gene pairs within domains exhibited a higher level of coexpression than random pairs and shared similar functions.</p> <p>Conclusions</p> <p>The results of this study suggest that similar histone modifications occur within only a small local chromatin region in yeast. The modifications generally have an effect on coexpression with only 1 or 2 neighboring genes. Some blocking mechanism(s) might strictly restrain the distribution of histone modifications in yeast.</p

Genome-wide analysis of interactions between ATP-dependent chromatin remodeling and histone modifications

<p>Abstract</p> <p>Background</p> <p>ATP-dependent chromatin remodeling and the covalent modification of histones play central roles in determining chromatin structure and function. Although several specific interactions between these two activities have been elaborated, the global landscape remains to be elucidated.</p> <p>Results</p> <p>In this paper, we have developed a computational method to generate the first genome-wide landscape of interactions between ATP-dependent chromatin remodeling and the covalent modification of histones in <it>Saccharomyces cerevisiae</it>. Our method succeeds in identifying known interactions and uncovers many previously unknown interactions between these two activities. Analysis of the genome-wide picture revealed that transcription-related modifications tend to interact with more chromatin remodelers. Our results also demonstrate that most chromatin remodeling-modification interactions act via interactions of remodelers with both histone-modifying enzymes and histone residues. We also found that the co-occurrence of both modification and remodeling has significantly different influences on multiple gene features (e.g. nucleosome occupancy) compared with the presence of either one.</p> <p>Conclusion</p> <p>We gave the first genome-wide picture of ATP-dependent chromatin remodeling-histone modification interactions. We also revealed how these two activities work together to regulate chromatin structure and function. Our results suggest that distinct strategies for regulating chromatin activity are selectively employed by genes with different properties.</p

A novel approach to melt purification of magnesium alloys

AbstractA novel low-cost method for melt purification of magnesium alloys, the melt self-purifying technology (MSPT), has been developed successfully based on a low temperature melt treatment (LTMT) without adding any fluxes. The iron solubility in the molten liquid of magnesium and its alloys, and the settlement velocity of iron particles were calculated. It is shown that the low temperature melt treatment is an effective method to decrease the impurity Fe content in magnesium and its alloys. Without any additions, the Fe content in the AZ31 alloy was reduced to 15 ppm from the initial 65 ppm, and the Fe content in the AZ61 melt was decreased to 20 ppm from the initial 150 ppm after the low temperature melt treatment. The results also showed that the Fe content in AM60 and AM50 dropped to 15 and 18 ppm, respectively, from the initial 150 ppm after the low temperature melt treatment. For ZK 60, the Fe content in the melt down to less than 5 ppm was achieved. After the low temperature melt treatment, the Si content in the above alloys was also decreased obviously