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Edge computing provides computing capability at close-user proximity to reduce service latency for end users. To improve the efficiency of edge computing infrastructures, geographically-distributed edge datacenters can co-work with each other and with cloud datacenters, forming a new paradigm referred to as cooperative edge-cloud computing. In this context, applications typically run on a virtual machine (VM) that can be replicated at multiple sites, and thus user traffic can be served at all the sites where corresponding VMs reside. For the performance of many applications, latency is a critical parameter. In this work, taking applications latencies as the primary constraint, we model the problem of VM placement and workload assignment as a mixed integer linear program and develop heuristic algorithms accordingly. The goal is to minimize the consumption of information technology (IT) infrastructures for placing VMs in cooperative edge-cloud computing, while meeting the heterogeneous latency demands of different applications. Some preliminary results indicate that edge datacenters resource efficiency can be optimized by proper cross-site VM placement and workload re-direction.

Objective. This study is aimed at investigating the correlation between lumbar spinal stenosis (LSS) severity, ligamentum flavum hypertrophy, and the upregulation of inflammatory markers. Methods. From March 2019 and May 2022, eighty-five inpatients with LSS were enlisted as the study’s research group, while sixty-five patients hospitalized for lumbar intervertebral disc herniation over the same time period served as the study’s control group. Moreover, mild, moderate, and severe subgroups of patients were created within the research population based on their LSS severity. The ligamentum flavum thickness and the positive expression rates of TNF-α, TGF-β1, and IL-1α were compared between the study group and the control group. The levels of TNF-α, TGF-β1, and IL-1α that were found to be positively expressed were compared between the mild, moderate, and severe groups. Patients with LSS had their ligamentum flavum thickness and their positive expression rates of TNF-α, TGF-β1, and IL-1α analyzed using Spearman correlation analysis. We evaluated the diagnostic utility of the positive expression rates of IL-α1, TGF-β1, and TNF-α and ligamentum flavum thickness in distinguishing the severity of LSS using a receiver operating characteristic (ROC) curve. Results. The rates of both lower limb pain (40.00%) and intermittent claudication (80.00%) in the LSS group were higher than those in the lumbar disc herniation group (15.38%, 12.31%), with statistical significance ( P < 0.05 ). However, no substantial disparity was observed in left lower limb pain, right lower limb pain, low back pain, lower limb sensation, muscle strength, and reflex abnormalities between the two groups ( P > 0.05 ). Positive expressions of TGF-β1, TNF-α, and IL-1α and thicker ligamentum flavum were more prevalent in the LSS group than in the lumbar intervertebral disc herniation group. All indexes were significantly ( P < 0.05 ) higher in the moderate stenosis group than in the severe stenosis group. Additionally, the thickness of the ligamentum flavum and the positive expression rates of TNF-α, TGF-β1, and IL-1α were higher in the mild and moderate stenosis groups than in the severe stenosis group. The expression levels of TNF-α, TGF-β1, and IL-1α were favorably linked with ligamentum flavum thickness ( P < 0.05 ). ROC curve analysis showed that the thickness of ligamentum flavum, the expression of IL-1α, the expression of TGF-β1, and the expression of TNF-α could effectively diagnose mild, moderate, and severe LSS ( P < 0.05 ). Conclusion. Ligamentum flavum hypertrophy and positive expression rates of IL-1α, TGF-β1, and TNF-α are closely linked to LSS, which can effectively identify mild, moderate, and severe LSS.