Computation and visualization of cell-cell signaling topologies in single-cell systems data using Connectome.

Single-cell RNA-sequencing data has revolutionized our ability to understand of the patterns of cell-cell and ligand-receptor connectivity that influence the function of tissues and organs. However, the quantification and visualization of these patterns in a way that informs tissue biology are major computational and epistemological challenges. Here, we present Connectome, a software package for R which facilitates rapid calculation and interactive exploration of cell-cell signaling network topologies contained in single-cell RNA-sequencing data. Connectome can be used with any reference set of known ligand-receptor mechanisms. It has built-in functionality to facilitate differential and comparative connectomics, in which signaling networks are compared between tissue systems. Connectome focuses on computational and graphical tools designed to analyze and explore cell-cell connectivity patterns across disparate single-cell datasets and reveal biologic insight. We present approaches to quantify focused network topologies and discuss some of the biologic theory leading to their design.

Efficient multilevel eigensolvers with applications to data analysis tasks.

Multigrid solvers proved very efficient for solving massive systems of equations in various fields. These solvers are based on iterative relaxation schemes together with the approximation of the "smooth" error function on a coarser level (grid). We present two efficient multilevel eigensolvers for solving massive eigenvalue problems that emerge in data analysis tasks. The first solver, a version of classical algebraic multigrid (AMG), is applied to eigenproblems arising in clustering, image segmentation, and dimensionality reduction, demonstrating an order of magnitude speedup compared to the popular Lanczos algorithm. The second solver is based on a new, much more accurate interpolation scheme. It enables calculating a large number of eigenvectors very inexpensively.

Geometry of intensive scalar dissipation events in turbulence.

The maxima of the scalar dissipation rate in turbulence appear in the form of sheets and correspond to the potentially most intensive scalar mixing events. Their cross section extension determines a locally varying diffusion scale of the mixing process and extends the classical Batchelor picture of one mean diffusion scale. The distribution of the local diffusion scales is analyzed for different Reynolds and Schmidt numbers with a fast multiscale technique applied to very high-resolution simulation data. The scales always take values across the whole Batchelor range and beyond. Furthermore, their distribution is traced back to the distribution of the contractive short-time Lyapunov exponent of the flow.