This paper is devoted to study the vanishing contact structure problem which is a generalization of the vanishing discount problem. Let H λ (x, p, u) be a family of Hamiltonians of contact type with parameter λ > 0 and converges to G(x, p). For the contact type Hamilton-Jacobi equation with respect to H λ , we prove that, under mild assumptions, the associated viscosity solution u λ converges to a specific viscosity solution u 0 of the vanished contact equation. As applications, we give some convergence results for the nonlinear vanishing discount problem.
The deregulation of S100A2 has been implicated in the pathogenesis of several types of cancers. However, the molecular mechanisms underlying the protumorigenic capacities of S100A2 have not been fully elucidated. Here, we demonstrated the molecular mechanisms underlying the roles of S100A2 in glycolysis reprogramming and proliferation of colorectal cancer (CRC) cells. The results indicated that S100A2 overexpression raises glucose metabolism and proliferation. Mechanistically, S100A2 activated the PI3K/AKT signaling pathway, upregulated GLUT1 expression, induced glycolytic reprogramming, and consequently increased proliferation. Clinical data showed significantly increased S100A2 levels in CRC tissues and the Oncomine database. In addition, analysis revealed a positive correlation between S100A2 and GLUT1 mRNA expression in CRC tissues. Together, these results demonstrate that the S100A2/GLUT1 axis can promote the progression of CRC by modulating glycolytic reprogramming. Our results further suggest that targeting S100A2 could present a promising therapeutic avenue for the prevention of colorectal cancer progression.
Unmanned aerial vehicles (UAVs) can enhance the overall performance of terrestrial communication systems due to their high possibility of the line of sight (LoS) links and on-demand deployments. The advantages of the UAV position optimization now attract attentions from researchers to study the cooperation among static UAV relays. In this paper, we study a relaying system, where multiple UAVs establish a cooperative UAV relay network to help some transmitters (Txs) communicate with their corresponding receivers (Rxs) by employing orthogonal frequency division multiple access (OFDMA). We maximize the paired Tx-Rxs' minimum rate through solving a non-convex, information causality constraints involved problem by optimizing the UAV relays' locations, nodes' powers, and bandwidth allocations together. An iterative algorithm is proposed by using block coordinate descent (BCD) and successive convex approximation (SCA) methods. Moreover, we also propose a new position initialization method, discuss some special cases of our problem to show some insights for future works, and prove the convergence of our algorithm. Simulations show the effectiveness of our proposed algorithm, some interesting trade-offs about the optimized UAVs' locations, and the influence of available resources.
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