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Traditional workload analysis uses discrete times measured by data accesses. An example is the classic independent reference model (IRM). Effective solutions have been developed to model workloads with stochastic access patterns, but they incur a high cost for Zipfian workloads, which may contain millions of items each accessed with a different frequency. This paper first presents a continuous-time model of locality for workloads with stochastic access patterns. It shows that two previous techniques by Dan and Towsley and by Denning and Schwartz can be interpreted as a single model using different discrete times. Using continuous time, it derives a closed-form solution for an item and a general solution that is a differentiable function. In addition, the paper presents an approximation technique by grouping items into partitions. When evaluated using Zipfian workloads, it shows that a workload with millions of items can be approximated using a small number of partitions, and the continuous-time model has greater accuracy and is faster to compute numerically. For the largest data size verifiable using trace generation and simulation, the new techniques reduce the time of locality analysis by 6 orders of magnitude. 

Glycosyltransferase OGT catalyzes the conjugation of O-linked β-D-N-acetylglucosamine (O-GlcNAc) to Ser and Thr residues of the cellular proteins and regulates many key processes in the cell. Here, we report the identification of OGT as a ubiquitination target of HECT-type E3 ubiquitin (UB) ligase E6AP, whose overexpression in HEK293 cells would induce the degradation of OGT. We also found that the expression of E6AP in HeLa cells with the endogenous expression of the E6 protein of the human papillomavirus (HPV) would accelerate OGT degradation by the proteasome and suppress O-GlcNAc modification of OGT substrates in the cell. Overall, our study establishes a new mechanism of OGT regulation by the ubiquitin–proteasome system (UPS) that mediates the crosstalk between protein ubiquitination and O-GlcNAcylation pathways underlying diverse cellular processes.