Within ab initio Quantum Monte Carlo simulations, the leading numerical cost for large systems is the computation of the values of the Slater determinants in the trial wavefunction. Each Monte Carlo step requires finding the determinant of a dense matrix. This is most commonly iteratively evaluated using a rank-1 Sherman-Morrison updating scheme to avoid repeated explicit calculation of the inverse. The overall computational cost is therefore formally cubic in the number of electrons or matrix size. To improve the numerical efficiency of this procedure, we propose a novel multiple rank delayed update scheme. This strategy enables probability evaluation with application of accepted moves to the matrices delayed until after a predetermined number of moves, K. The accepted events are then applied to the matrices en bloc with enhanced arithmetic intensity and computational efficiency via matrix-matrix operations instead of matrix-vector operations. This procedure does not change the underlying Monte Carlo sampling or its statistical efficiency. For calculations on large systems and algorithms such as diffusion Monte Carlo where the acceptance ratio is high, order of magnitude improvements in the update time can be obtained on both multicore CPUs and GPUs.
providers like Spotify [21], Cloudflare [23] and Google [11] have highlighted the global impact of this problem. Existing tools designed to curtail leaks, like the many Internet Routing Registries (IRRs), are challenging to deploy or limited in scope. IRRs are databases where ASes can publish their routing policies. Other ASes can then convert IRR-stored policies into filters to validate received routes. IRRbased filtering is limited by its requirement for broad AS participation, however, as the motivations and sophistication of network operators varies greatly between ASes [22]. Other BGP security extensions, like the Resource Public Key Infrastructure (RPKI), only enable filtering for a subset of leaks (e.g. re-origination leaks for RPKI). The Peerlock [44], [18] leak defense system was presented in 2016 to address the need for a deployable solution. Each Peerlock deployment occurs between two neighboring ASes, the protector AS and protected AS. The protector AS agrees to filter routes that transit the protected AS unless they arrive directly from the protected AS or one of its designated upstreams. The filter prevents the protector AS from propagating or steering its traffic onto any leaked route that transits the protected AS, regardless of origin AS/destination prefix. Peerlock is designed to leverage the rich web of relationships that exist between transit networks in the Internet's core, and functions without coordination with other ASes on potential leak paths. This makes Peerlock especially viable in the peering clique formed by the 19 Tier 1 ASes that sit atop the inter-domain routing hierarchy. A related technique, Peerlocklite, enables networks to spot likely leaks without prior outof-band communication. ASes deploying Peerlock-lite drop routes arriving from customers that contain a Tier 1 AS; it is highly improbable that customers are providing transit for large global networks. Our first contribution is a measurement of Peerlock/Peerlock-lite deployment on the control plane. In Section IV we design, execute, and evaluate active Internet measurements to search for evidence of filtering consistent with these systems. Our experiments use BGP poisoning, a technique used in prior work for traffic engineering [42] and path discovery [1], to mimic route leaks that transit some target AS. We then listen for which networks propagateor filter-these "leaks" relative to control advertisements. This information feeds several inference techniques designed to uncover which ASes are Peerlocking for (protecting) the target AS.
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