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LU factorization for sparse matrices is an important computing step for many engineering and scientific problems such as circuit simulation. There have been many efforts toward parallelizing and scaling this algorithm, which include the recent efforts targeting the GPUs. However, it is still challenging to deploy a complete sparse LU factorization workflow on a GPU due to high memory requirements and data dependencies. In this paper, we propose the first complete GPU solution for sparse LU factorization. To achieve this goal, we propose an out-of-core implementation of the symbolic execution phase, thus removing the bottleneck due to large intermediate data structures. Next, we propose a dynamic parallelism implementation of Kahn's algorithm for topological sort on the GPUs. Finally, for the numeric factorization phase, we increase the parallelism degree by removing the memory limits for large matrices as compared to the existing implementation approaches. Experimental results show that compared with an implementation modified from GLU 3.0, our out-of-core version achieves speedups of 1.13--32.65X. Further, our out-of-core implementation achieves a speedup of 1.2--2.2 over an optimized unified memory implementation on the GPU. Finally, we show that the optimizations we introduce for numeric factorization turn out to be effective.more » « less
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Scope The action of brain disorders on peripheral metabolism is poorly understood. The impact of traumatic brain injury (TBI) on peripheral organ function and how TBI effects can be influenced by the metabolic perturbation elicited by fructose ingestion are studied.
Methods and Results It is found that TBI affects glucose metabolism and signaling proteins for insulin and growth hormone in the liver; these effects are exacerbated by fructose ingestion. Fructose, principally metabolized in the liver, potentiates the action of TBI on hepatic lipid droplet accumulation. Studies in isolated cultured hepatocytes identify GH and fructose as factors for the synthesis of lipids. The liver has a major role in the synthesis of lipids used for brain function and repair. TBI results in differentially expressed genes in the hypothalamus, primarily associated with lipid metabolism, providing cues to understand central control of peripheral alterations. Fructose‐fed TBI animals have elevated levels of markers of inflammation, lipid peroxidation, and cell energy metabolism, suggesting the pro‐inflammatory impact of TBI and fructose in the liver.
Conclusion Results reveal the impact of TBI on systemic metabolism and the aggravating action of fructose. The hypothalamic‐pituitary‐growth axis seems to play a major role in the regulation of the peripheral TBI pathology.