A simple optimization strategy for the computation of 3D finite-differencing kernels on many-cores architectures is proposed. The 3D finite-differencing computation is split direction-by-direction and exploits two level of parallelism: in-core vectorization and multi-threads shared-memory parallelization. The main application of this method is to accelerate the high-order stencil computations in numerical relativity codes.

Investigating the network response to node removal and the efficacy of the node removal strategies are related and fundamental questions in network science. Research studies proposed many node centralities based on the network structure ranking node to remove. The random walk (RW) on networks describes a stochastic process in which a walker travels among nodes. RW can be a model of transport, diffusion, and search on networks, and an essential tool for studying the importance of network nodes. In this manuscript, we propose four new measures of node centrality based on RW. Then, we compare the efficacy of the new RW node removal strategies to network dismantle with effective node removal strategies from the literature, such as betweenness and closeness node removal over synthetic and real-world networks. We evaluate the network dismantle along node removal using the size of the largest connected component (LCC). We find that, hence the betweenness nodes attack is the best strategy overall, the new node removal strategies based on RW show the highest efficacy in peculiar network topology. Specifically, RW strategies based on covering times emerge as the most effective strategy on a synthetic lattice network and two real-world road networks. Our results may be useful in selecting the best node attack strategies in a specific class of networks and in building more robust network structures.

Weight thresholding (WT) is a method intended to decrease the number of links within weighted networks that may otherwise be excessively dense for network science applications. WT aims to remove links to simplify the networks by holding most of the features of the original network. Here, we test the robustness and the efficacy of the node attack strategies on real-world networks subjected to WT that remove links of higher weight (strong links). We measure the network robustness along node removal with the largest connected component (LCC). We find that the real-world networks under study are generally stable in terms of robustness when subjected to WT. Nonetheless, WT by strong link removal changes the efficacy of the attack strategies and the rank of node centralities. Also, WT by strong link removal may trigger a greater change in node centrality rank than WT by removing weak links. Network science research finding important/influential nodes in the network has to consider that simplifying the network with WT methodologies may change the node centrality.