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We improve a result in Kim and Lee [Ann. Appl. Math. 37 (2021), pp. 111–130], showing that if the coefficients of an elliptic operator in non-divergence form are of Dini mean oscillation, then its Green’s function has the same asymptotic behavior near the pole x 0 x_0 as that of the corresponding Green’s function for the elliptic equation with constant coefficients frozen at x 0 x_0 . 

Analytic workloads on terabyte data-sets are often run in the cloud, where application and storage servers are separate and connected via network. In order to saturate the storage bandwidth and to hide the long storage latency, such a solution requires an expensive server cluster with sufficient aggregate DRAM capacity and hardware threads. An alternative solution is to push the query computation into storage servers. In this paper we present an in-storage Analytics QUery Offloading MAchiNe (AQUOMAN) to “offload” most SQL operators, including multi-way joins, to SSDs. AQUOMAN executes Table Tasks, which apply a static dataflow graph of SQL operators to relational tables to produce an output table. Table Tasks use a streaming computation model, which allows AQUOMAN to process queries with a reasonable amount of DRAM for intermediate results. AQUOMAN is a general analytic query processor, which can be integrated in the database software stack transparently. We have built a prototype of AQUOMAN in FPGAs, and using TPC-H benchmarks on 1TB data sets, shown that a single instance of 1TB AQUOMAN disk, on average, can free up 70% CPU cycles and reduce DRAM usage by 60%. One way to visualize this saving is to think that if we run queries sequentially and ignore inter-query page cache reuse, MonetDB running on a 4-core, 16GB-DRAM machine with AQUOMAN augmented SSDs performs, on average, as well as a MonetDB running on a 32-core, 128GB-DRAM machine with standard SSDs. 

Key-value store based on a log-structured merge-tree (LSMtree) is preferable to hash-based KV store because an LSMtree can support a wider variety of operations and show better performance, especially for writes. However, LSM-tree is difficult to implement in the resource constrained environment of a key-value SSD (KV-SSD) and consequently, KV-SSDs typically use hash-based schemes. We present PinK, a design and implementation of an LSM-tree-based KV-SSD, which compared to a hash-based KV-SSD, reduces 99th percentile tail latency by 73%, improves average read latency by 42% nd shows 37% higher throughput. The key idea in improving the performance of an LSM-tree in a resource constrained environment is to avoid the use of Bloom filters and instead, use a small amount of DRAM to keep/pin the top levels of the LSM-tree. 

Ransomware is a malware that encrypts victim's data, where the decryption key is released after a ransom is paid by the data owner to the attacker. Many ransomware attacks were reported recently, making anti-ransomware a crucial need in security operation, and an issue for the security community to tackle. In this paper, we propose a new approach to defending against ransomware inside NAND flash-based SSDs. To realize the idea of defense-inside-SSDs, both a lightweight detection technique and a perfect recovery algorithm to be used as a part of SSDs firmware should be developed. To this end, we propose a new set of lightweight behavioral features on ran-somware's overwriting pattern, which are invariant across various ransomwares. Our features rely on observing the block I/O request headers only, and not the payload. For perfect and instant recovery, we also propose using the delayed deletion feature of SSDs, which is intrinsic to NAND flash. To demonstrate their feasibility, we implement our algorithms atop an open-channel SSD as a working prototype called SSD-Insider. In experiments using eight real-world and two in-house ransomwares with various background applications running, SSD-Insider achieved a detection accuracy 0% FRR/FAR in most scenarios, and only 5% FAR when heavy overwriting resembling ransomware's data wiping occurs. SSD-Insider detects ransomware activity within 10s, and recovers instantly an infected SSD within 1s with 0% data loss. The additional software overheads incurred by the SSD-Insider is just 147 ns and 254 ns for 4-KB reads and writes, respectively, which is negligible considering NAND chip latency (50-1000 μs).