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.

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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.

Patients with pancreatic cancer (PC) show dismal prognosis and high mortality. The development of PC is associated with the overactivation of STAT3. Here, we have determined that the non-peptide small molecule Stattic inhibits PC development by targeting STAT3. In vitro, Stattic treatment time- and dose-dependently inhibited proliferation of pancreatic cancer cells (PCCs) by reducing c-Myc expression and enhancing p53 activity. Consequently, p-Rb, cyclin D1, Chk1, and p21 (cell cycle proteins) were downregulated, and PCCs were arrested at the G1 phase, which was also confirmed by decreased Ki67 expression and unaltered PCNA expression. In addition, Stattic-induced mitochondrial-dependent apoptosis by elevating cleaved caspase-3, and Bax, cytochrome C levels, while reducing expression of Bcl-2, which may be regulated by reduced survivin expression. Further studies showed that Stattic exerts its anti-tumor effect via inhibition of STAT3Y705 phosphorylation and nuclear localization in PCCs. In a nude mouse tumorigenesis model, Stattic inhibited PC growth by antagonizing STAT3Y705 phosphorylation. Interleukin-6 used as a molecule agonist to activate STAT3, as well as overexpression of STAT3, could partially reverse Stattic-mediated anti-proliferation and pro-apoptotic effects of PCCs. Thus, these findings indicate that inhibition of STAT3Y705 phosphorylation by Stattic suppresses PCC proliferation and promotes mitochondrial-mediated apoptosis.

Metabolic remodeling plays an essential role in the pathophysiology of heart failure (HF). Many studies have shown that the disruption of phosphoinositide-dependent protein kinase-1 (PDK1) caused severe and lethal HF; however, the metabolic pattern of PDK1 deletion remains ambiguous. 1H nuclear magnetic resonance-based metabolomics was applied to explore the altered metabolic pattern in Pdk1-deficient mice. Principle component analysis showed significant separation as early as 4 weeks of age, and dysfunction of metabolism precedes a morphological change in Pdk1-deficient mice. A time trajectory plot indicated that disturbed metabolic patterns were related to the pathological process of the HF in Pdk1-deficient mice, rather than the age of mice. Metabolic profiles demonstrated significantly increased levels of acetate, glutamate, glutamine, and O-phosphocholine in Pdk1 deletion mice. Levels of lactate, alanine, glycine, taurine, choline, fumarate, IMP, AMP, and ATP were significantly decreased compared with controls. Furthermore, PDK1 knockdown decreased the oxygen consumption rate in H9C2 cells as determined using a Seahorse XF96 Analyzer. These findings imply that the disruption of metabolism and impaired mitochondrial activity might be involved in the pathogenesis of HF with PDK1 deletion.

Unmanned aerial vehicles (UAVs) have attracted attentions due to their mobility and high possibility of the line of sight (LoS) channel. We can fully use these two properties by carefully optimizing the UAVs' trajectories and cooperating with some facilities. A UAV working as a mobile relay now attracts many interests due to its low cost and reliable performance. In this paper, we study a relaying system, where a UAV works as an aerial mobile relay to help some ground base stations send information to ground users periodically by using time division multiple access (TDMA). We aim to maximize the minimum average user rate through solving a non-convex and information causality constraints involved problem by jointly optimizing the UAV trajectory, nodes scheduling, and power allocation to ensure the fairness among all users. Finally, we propose an efficient iterative algorithm to solve a derived mixed-integer nonconvex optimization problem to achieve this target by using block coordinate descent (BCD) and successive convex approximation (SCA) methods and prove the convergence of our algorithm. Simulations show the effectiveness of our proposed algorithm, some useful trade-offs and insights about the structure of our optimized trajectory, and the influence of two widely used trajectory initialization methods.

For mechanical Hamiltonian systems on the torus, we study the dynamical properties of the generalized characteristics semiflows associated with certain Hamilton-Jacobi equations, and build the relation between the ω-limit set of this semiflow and the projected Aubry set.