Example of an Order 16 Non Symplectic Action on a K3 Surface

We exhibit an example of a K3 surface of Picard rank 14 with a non-symplectic automorphism of order 16 which fixes a rational curve and 10 isolated points. This settles the existence problem for the last case of Al Tabbaa, Sarti and Taki\u27s classification

On Some Order 6 Non-Symplectic Automorphisms of Elliptic K3 Surfaces

We classify primitive non-symplectic automorphisms of order 6 on K3 surfaces. We show how their study can be reduced to the study of non-symplectic automorphisms of order 3 and to a local analysis of the fixed loci. In particular, we determine the possible fixed loci and show that when the Picard lattice is fixed, K3 surfaces come in mirror pairs

Higher dimensional Calabi-Yau manifolds of Kummer type

Based on Cynk-Hulek method we construct complex Calabi-Yau varieties of arbitrary dimensions using elliptic curves with automorphism of order 6. Also we give formulas for Hodge numbers of varieties obtained from that construction. We shall generalize result of Katsura and Sch\"utt to obtain arbitrarily dimensional Calabi-Yau manifolds which are Zariski in any characteristic $p\not\equiv 1\pmod{12}.$Comment: 13 pages, 2 figure

Generalized Borcea-Voisin Construction

C. Voisin and C. Borcea have constructed mirror pairs of families of Calabi-Yau threefolds by taking the quotient of the product of an elliptic curve with a K3 surface endowed with a non-symplectic involution. In this paper, we generalize the construction of Borcea and Voisin to any prime order and build three and four dimensional Calabi-Yau orbifolds. We classify the topological types that are obtained and show that, in dimension 4, orbifolds built with an involution admit a crepant resolution and come in topological mirror pairs. We show that for odd primes, there are generically no minimal resolutions and the mirror pairing is lost.Comment: 15 pages, 2 figures. v2: typos corrected & references adde

Gene dispersion is the key determinant of the read count bias in differential expression analysis of RNA-seq data

Background: In differential expression analysis of RNA-sequencing (RNA-seq) read count data for two sample groups, it is known that highly expressed genes (or longer genes) are more likely to be differentially expressed which is called read count bias (or gene length bias). This bias had great effect on the downstream Gene Ontology over-representation analysis. However, such a bias has not been systematically analyzed for different replicate types of RNA-seq data. Results: We show that the dispersion coefficient of a gene in the negative binomial modeling of read counts is the critical determinant of the read count bias (and gene length bias) by mathematical inference and tests for a number of simulated and real RNA-seq datasets. We demonstrate that the read count bias is mostly confined to data with small gene dispersions (e.g., technical replicates and some of genetically identical replicates such as cell lines or inbred animals), and many biological replicate data from unrelated samples do not suffer from such a bias except for genes with some small counts. It is also shown that the sample-permuting GSEA method yields a considerable number of false positives caused by the read count bias, while the preranked method does not. Conclusion: We showed the small gene variance (similarly, dispersion) is the main cause of read count bias (and gene length bias) for the first time and analyzed the read count bias for different replicate types of RNA-seq data and its effect on gene-set enrichment analysis

Improving gene-set enrichment analysis of RNA-Seq data with small replicates

Deregulated pathways identified from transcriptome data of two sample groups have played a key role in many genomic studies. Gene-set enrichment analysis (GSEA) has been commonly used for pathway or functional analysis of microarray data, and it is also being applied to RNA-seq data. However, most RNA-seq data so far have only small replicates. This enforces to apply the gene-permuting GSEA method (or preranked GSEA) which results in a great number of false positives due to the inter-gene correlation in each gene-set. We demonstrate that incorporating the absolute gene statistic in one-tailed GSEA considerably improves the false-positive control and the overall discriminatory ability of the gene-permuting GSEA methods for RNA-seq data. To test the performance, a simulation method to generate correlated read counts within a gene-set was newly developed, and a dozen of currently available RNA-seq enrichment analysis methods were compared, where the proposed methods outperformed others that do not account for the inter-gene correlation. Analysis of real RNA-seq data also supported the proposed methods in terms of false positive control, ranks of true positives and biological relevance. An efficient R package (AbsFilterG- SEA) coded with C++ (Rcpp) is available from CRAN.open

Normalizing single-cell RNA sequencing data: challenges and opportunities

Single-cell transcriptomics is becoming an important component of the molecular biologist's toolkit. A critical step when analyzing data generated using this technology is normalization. However, normalization is typically performed using methods developed for bulk RNA sequencing or even microarray data, and the suitability of these methods for single-cell transcriptomics has not been assessed. We here discuss commonly used normalization approaches and illustrate how these can produce misleading results. Finally, we present alternative approaches and provide recommendations for single-cell RNA sequencing users

Benchmarking of cell type deconvolution pipelines for transcriptomics data

Many computational methods have been developed to infer cell type proportions from bulk transcriptomics data. However, an evaluation of the impact of data transformation, pre-processing, marker selection, cell type composition and choice of methodology on the deconvolution results is still lacking. Using five single-cell RNA-sequencing (scRNA-seq) datasets, we generate pseudo-bulk mixtures to evaluate the combined impact of these factors. Both bulk deconvolution methodologies and those that use scRNA-seq data as reference perform best when applied to data in linear scale and the choice of normalization has a dramatic impact on some, but not all methods. Overall, methods that use scRNA-seq data have comparable performance to the best performing bulk methods whereas semi-supervised approaches show higher error values. Moreover, failure to include cell types in the reference that are present in a mixture leads to substantially worse results, regardless of the previous choices. Altogether, we evaluate the combined impact of factors affecting the deconvolution task across different datasets and propose general guidelines to maximize its performance. Inferring cell type proportions from transcriptomics data is affected by data transformation, normalization, choice of method and the markers used. Here, the authors use single-cell RNAseq datasets to evaluate the impact of these factors and propose guidelines to maximise deconvolution performance