Recently developed spatial gene expression technologies such as the SpatialTranscriptomics and Visium platforms allow for comprehensive measurement of transcriptomic profiles while retaining spatial context. However, existing methods for analyzing spatial gene expression data often do not efficiently leverage the spatial information and fail to address the limited resolution of the technology. Here, we introduce BayesSpace, a fully Bayesian statistical method for clustering analysis and resolution enhancement of spatial transcriptomics data that seamlessly integrates into current transcriptomics analysis workflows. We show that BayesSpace improves the identification of transcriptionally distinct tissues from spatial transcriptomics samples of the brain, of melanoma, and of squamous cell carcinoma. In particular, BayesSpace's improved resolution allows the identification of tissue structure that is not detectable at the original resolution and thus not recovered by other methods. Using an in silico dataset constructed from scRNA-seq, we demonstrate that BayesSpace can spatially resolve expression patterns to near single-cell resolution without the need for external single-cell sequencing data.In all, our results illustrate the utility BayesSpace has in facilitating the discovery of biological insights from a variety of spatial transcriptomics datasets.

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An implicit finite-difference procedure for unsteady three-dimensional flow capable of handling arbitrary geometry through the use of general coordinate transformations is described. Viscous effects are optionally incorporated with a "thin-layer" approximation of the Navier-Stokes equations. An implicit approximate factorization technique is employed so that the small grid sizes required for spatial accuracy and viscous resolution do not impose stringent stability limitations. Results obtained from the program include transonic inviscid or viscous solutions about simple body configurations. Comparisons with existing theories and experiments are made. Numerical accuracy and the effect of three-dimensional coordinate singularities are also discussed.

A gradient-based Newton-Krylov algorithm is presented for the aerodynamic shape optimization of single-and multi-element airfoil configurations. The flow is governed by the compressible Navier-Stokes equations in conjunction with a one-equation transport turbulence model. The preconditioned generalized minimal residual method is applied to solve the discrete-adjoint equation, which leads to a fast computation of accurate objective function gradients. Optimization constraints are enforced through a penalty formulation, and the resulting unconstrained problem is solved via a quasi-Newton method. The new algorithm is evaluated for several design examples, including the lift enhancement of a takeoff configuration and a lift-constrained drag minimization at multiple transonic operating points. Furthermore, the new algorithm is used to compute a Pareto front based on competing objectives, and the results are validated using a genetic algorithm. Overall, the new algorithm provides an efficient approach for addressing the issues of complex aerodynamic design.