This study concentrates on the differential private distributed optimization problem with an event-triggered mechanism, whose goals include preserving the privacy of agents’ initial states and local cost functions and improving communication efficiency. A distributed event-triggered mechanism is integrated into the differentially private subgradient-push distributed optimization algorithm and then a new algorithm named as DP-ETSP is designed, where the real-time information propagation among agents is avoided. Additionally, under the proposed event-triggered mechanism, an analysis of mean-square consensus and optimality over time-varying directed networks is made when the added Laplace noises meet some specific decaying conditions. Convergence rate results are further established under a specific stepsize, which are equal to the rate of stochastic gradient-push algorithm without event-triggered communication. Moreover, the differential privacy preservation performance is analyzed and the rule for selecting privacy level is discussed. Finally, the feasibility and effectiveness of DP-ETSP are verified in two simulation cases.

Osteosarcoma (OS) is the most prevalent type of primary malignant bone cancer and currently lacks effective targeted treatments. Increasing evidence indicates that SOX2 overexpression is a primary driver of OS. By screening a small-molecule kinase inhibitor library, we identified AKT as a kinase essential for robust SOX2 expression in OS cells. AKT was found to be frequently overexpressed in OS and positively correlated with SOX2 protein levels. We demonstrated that AKT has no effect on SOX2 transcription but promotes SOX2 protein stability. Mechanistically, AKT binds to and phosphorylates SOX2 at T116, preventing SOX2 ubiquitination and proteasome-dependent degradation by ubiquitin E3 ligases UBR5 and STUB1. Moreover, we found that AKT-SOX2 axis is a significant modulator of cancer stemness and chemoresistance and that the combination of AKT inhibitor MK2206 and cisplatin resulted in a synergistic and potent inhibition of OS tumor growth in the PDX model. In conclusion, we identified a critical role for AKT in promoting SOX2 overexpression, tumor stemness, and chemoresistance in OS, and provided evidence that targeting AKT combined with chemotherapy may hold promise for treating refractory OS.