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  6. Supervised dimensionality reduction for sequence data learns a transformation that maps the observations in sequences onto a low-dimensional subspace by maximizing the separability of sequences in different classes. It is typically more challenging than conventional dimensionality reduction for static data, because measuring the separability of sequences involves non-linear procedures to manipulate the temporal structures. In this paper, we propose a linear method, called Order-preserving Wasserstein Discriminant Analysis (OWDA), and its deep extension, namely DeepOWDA, to learn linear and non-linear discriminative subspace for sequence data, respectively. We construct novel separability measures between sequence classes based on the order-preserving Wasserstein (OPW) distancemore »to capture the essential differences among their temporal structures. Specifically, for each class, we extract the OPW barycenter and construct the intra-class scatter as the dispersion of the training sequences around the barycenter. The inter-class distance is measured as the OPW distance between the corresponding barycenters. We learn the linear and non-linear transformations by maximizing the inter-class distance and minimizing the intra-class scatter. In this way, the proposed OWDA and DeepOWDA are able to concentrate on the distinctive differences among classes by lifting the geometric relations with temporal constraints. Experiments on four 3D action recognition datasets show the effectiveness of OWDA and DeepOWDA.« less
  7. Sulfur modifications have been discovered on both DNA and RNA. Sulfur substitution of oxygen atoms at nucleobase or backbone locations in the nucleic acid framework led to a wide variety of sulfur-modified nucleosides and nucleotides. While the discovery, regulation and functions of DNA phosphorothioate (PS) modification, where one of the non-bridging oxygen atoms is replaced by sulfur on the DNA backbone, are important topics, this review focuses on the sulfur modification in natural cellular RNAs and therapeutic nucleic acids. The sulfur modifications on RNAs exhibit diversity in terms of modification locations and cellular functions, but the various sulfur modifications sharemore »common biosynthetic strategies across RNA species, cell types and all domains of life. The first section reviews the post-transcriptional sulfur modifications on nucleobase with emphasis on thiouridine on tRNA and phosphorothioate modification on RNA backbones, as well as the functions of the sulfur modifications on different species of cellular RNAs. The second section reviews the biosynthesis of different types of sulfur modifications and summarizes the general strategy for the biosynthesis of sulfur-containing RNA residues. One of the main goals of investigating the sulfur modifications is to enrich the genomic drug development pipeline and enhance our understandings of the rapidly growing nucleic acid-based gene therapy. The last section of the review focuses on the current drug development strategies employing sulfur substitution of oxygen atoms in therapeutic RNAs.« less