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From FORTRAN to NumPy, tensors have revolutionized how we express computation. However, tensors in these, and almost all prominent systems, can only handle dense rectilinear integer grids. Real world tensors often contain underlying structure, such as sparsity, runs of repeated values, or symmetry. Support for structured data is fragmented and incomplete. Existing frameworks limit the tensor structures and program control flow they support to better simplify the problem. In this work, we propose a new programming language, Finch, which supports both flexible control flow and diverse data structures. Finch facilitates a programming model which resolves the challenges of computing over structured tensors by combining control flow and data structures into a common representation where they can be co-optimized. Finch automatically specializes control flow to data so that performance engineers can focus on experimenting with many algorithms. Finch supports a familiar programming language of loops, statements, ifs, breaks, etc., over a wide variety of tensor structures, such as sparsity, run-length-encoding, symmetry, triangles, padding, or blocks. Finch reliably utilizes the key properties of structure, such as structural zeros, repeated values, or clustered non-zeros. We show that this leads to dramatic speedups in operations such as SpMV and SpGEMM, image processing, and graph analytics. 

Abstract Paneth cells (PCs), a specialized secretory cell type in the small intestine, are increasingly recognized as having an essential role in host responses to microbiome and environmental stresses. Whether and how commensal and pathogenic microbes modify PC composition to modulate inflammation remain unclear. Using newly developed PC‐reporter mice under conventional and gnotobiotic conditions, we determined PC transcriptomic heterogeneity in response to commensal and invasive microbes at single cell level. Infection expands the pool of CD74⁺PCs, whose number correlates with auto or allogeneic inflammatory disease progressions in mice. Similar correlation was found in human inflammatory disease tissues. Infection‐stimulated cytokines increase production of reactive oxygen species (ROS) and expression of a PC‐specific mucosal pentraxin (Mptx2) in activated PCs. A PC‐specific ablation ofMyD88reduced CD74⁺PC population, thus ameliorating pathogen‐induced systemic disease. A similar phenotype was also observed in mice lacking Mptx2. Thus, infection stimulates expansion of a PC subset that influences disease progression.