It is well established that Nash equilibrium exists within the framework of mixed strategies in strategic-form non-cooperative games. However, finding the Nash equilibrium generally belongs to the class of problems known as PPAD (Polynomial Parity Argument on Directed graphs), for which no polynomial-time solution methods are known, even for two-player games. This paper demonstrates that in fixed-sum two-player games (including zero-sum games), the Nash equilibrium forms a convex set, and has a unique expected payoff. Furthermore, these equilibria are Pareto optimal. Additionally, it is shown that the Nash equilibrium of fixed-sum two-player games can theoretically be found in polynomial time using the principal-dual interior point method, a solution method of linear programming.
Ever since the first discovery of chemical modifications of RNA in 1951,researchers have been captivated by the diverse types of modifications,their associated enzymes and proteins(writers,erasers,or readers),and their downstream functional implications(Song and Yi,2017).Among the over 170 distinct types of RNA modifications identified thus far,N^(6)-methyladenosine(m6A)stands out as the most prevalent internal modification on mammalian messenger RNA(mRNA)(Song and Yi,2017).
We study n-player games of portfolio choice in general common Ito-diffusion markets under relative performance criteria and time monotone forward utilities.We,also,consider their continuum limit which gives rise to a forward mean field game with unbounded controls in both the drift and volatility terms.Furthermore,we allow for general(time monotone)preferences,thus departing from the homothetic case,the only case so far analyzed.We produce explicit solutions for the optimal policies,the optimal wealth processes and the game values,and also provide representative examples for both the finite and the mean field game.
A differential game guidance scheme with obstacle avoidance,based on the formulation of a combined linear quadratic and norm-bounded differential game,is designed for a three-player engagement scenario,which includes a pursuer,an interceptor,and an evader.The confrontation between the players is divided into four phases(P1-P4)by introducing the switching time,and proposing different guidance strategies according to the phase where the static obstacle is located:the linear quadratic game method is employed to devise the guidance scheme for the energy optimization when the obstacle is located in the P1 and P3 stages;the norm-bounded differential game guidance strategy is presented to satisfy the acceleration constraint under the circumstance that the obstacle is located in the P2 and P4 phases.Furthermore,the radii of the static obstacle and the interceptor are taken as the design parameters to derive the combined guidance strategy through the dead-zone function,which guarantees that the pursuer avoids the static obstacle,and the interceptor,and attacks the evader.Finally,the nonlinear numerical simulations verify the performance of the game guidance strategy.
While extensive studies have illuminated the impact of Alzheimer's disease(AD) on neuronal survival,there is growing evidence that abnormal postnatal neurogenesis in early AD brains contributes to disease progression.Postnatal neurogenesis serves as a mechanism to replace dead or damaged neurons.New neurons generated from neural stem cells(NSCs) in the subgranular zone(SGZ) of the dentate gyrus integrate into the existing hippocampal circuit.
miR-135 is a highly conserved miRNA in mammals and includes miR-135a and miR-135b.Recent studies have shown that miR-135b is a key regulatory factor in cardio-cerebrovascular diseases.It is involved in regulating the pathological process of myocardial infarction,myocardial ischemia/reperfusion injury,cardiac hypertrophy,atrial fibrillation,diabetic cardiomyopathy,atherosclerosis,pulmonary hyperten-sion,cerebral ischemia/reperfusion injury,Parkinson's disease,and Alzheimer's disease.Obviously,miR-135b is an emerging player in cardio-cerebrovascular diseases and is expected to be an important target for the treatment of cardio-cerebrovascular diseases.However,the crucial role of miR-135b in cardio-cerebrovascular diseases and its underlying mechanism of action has not been reviewed.Therefore,in this review,we aimed to comprehensively summarize the role of miR-135b and the signaling pathway mediated by miR-135b in cardio-cerebrovascular diseases.Drugs targeting miR-135b for the treatment of diseases and related patents,highlighting the importance of this target and its utility as a therapeutic target for cardio-cerebrovascular diseases,have been discussed.
