Distributed storage systems provide reliable access to data through redundancy spread in network system. A key goal is to minimize bandwidth overhead to maintain the redundancy. This paper studies the flexible recovery from multiple node failures in distributed storage systems. Via a cut-based analysis of information flow graph, we obtain a lower bound of maintenance bandwidth for multi-loss flexible recovery (MFR). We also design a coding scheme based on MFR with maintenance bandwidth matching the lower bound. So the lower bound of maintenance bandwidth for multi-loss recovery is tight and the proposed recovery scheme is optimal.

In this paper, we propose a novel patient-specific method of modelling pulmonary airflow using graphics processing unit (GPU) computation that can be applied in medical practice. To overcome the barriers imposed by computation speed, installation price and footprint to the application of computational fluid dynamics, we focused on GPU computation and the lattice Boltzmann method (LBM). The GPU computation and LBM are compatible due to the characteristics of the GPU. As the optimisation of data access is essential for the performance of the GPU computation, we developed an adaptive meshing method, in which an airway model is covered by isotropic subdomains consisting of a uniform Cartesian mesh. We found that 4(3) size subdomains gave the best performance. The code was also tested on a small GPU cluster to confirm its performance and applicability, as the price and footprint are reasonable for medical applications.