Time series data is ubiquitous in research as well as in a wide variety of industrial applications. Effectively analyzing the available historical data and providing insights into the far future allows us to make effective decisions. Recent research has witnessed the superior performance of transformer-based architectures, especially in the regime of far horizon time series forecasting. However, the current state of the art sparse Transformer architectures fail to couple down-and upsampling procedures to produce outputs in a similar resolution as the input. We propose the Yformer model, based on a novel Y-shaped encoder-decoder architecture that (1) uses direct connection from the downscaled encoder layer to the corresponding upsampled decoder layer in a U-Net inspired architecture, (2) Combines the downscaling/upsampling with sparse attention to capture long-range effects, and (3) stabilizes the encoder-decoder stacks with the addition of an auxiliary reconstruction loss. Extensive experiments have been conducted with relevant baselines on four benchmark datasets, demonstrating an average improvement of 19.82, 18.41 percentage MSE and 13.62, 11.85 percentage MAE in comparison to the current state of the art for the univariate and the multivariate settings respectively.
Amine transaminases (ATAs) are powerful biocatalysts for the stereoselective synthesis of chiral amines. Machine learning provides a promising approach for protein engineering, but activity prediction models for ATAs remain elusive due to the difficulty of obtaining high-quality training data. Thus, we first created variants of the ATA from Ruegeria sp. (3FCR) with improved catalytic activity (up to 2000-fold) as well as reversed stereoselectivity by a structure-dependent rational design and collected a high-quality dataset in this process. Subsequently, we designed a modified one-hot code to describe steric and electronic effects of substrates and residues within ATAs. Finally, we built a gradient boosting regression tree predictor for catalytic activity and stereoselectivity, and applied this for the datadriven design of optimized variants which then showed improved activity (up to 3-fold compared to the best variants previously identified). We also demonstrated that the model can predict the catalytic activity for ATA variants of another origin by retraining with a small set of additional data.
We consider the quasiconformal dilatation of projective transformations of the real projective plane. For non-affine transformations, the contour lines of dilatation form a hyperbolic pencil of circles, and these are the only circles that are mapped to circles. We apply this result to analyze the dilatation of the circumcircle preserving piecewise projective interpolation between discretely conformally equivalent triangulations. We show that another interpolation scheme, angle bisector preserving piecewise projective interpolation, is in a sense optimal with respect to dilatation. These two interpolation schemes belong to a one-parameter family.
30C62, 52C26
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.