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 kn...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.展开更多
Sums of convergent series for any desired number of terms, which may be infinite, are estimated very accurately by establishing definite rational polynomials. For infinite number of terms the sum infinite is obtained ...Sums of convergent series for any desired number of terms, which may be infinite, are estimated very accurately by establishing definite rational polynomials. For infinite number of terms the sum infinite is obtained by taking the asymptotic limit of the rational polynomial. A rational function with second-degree polynomials both in the numerator and denominator is found to produce excellent results. Sums of series with different characteristics such as alternating signs are considered for testing the performance of the proposed approach.展开更多
In this paper, we investigate local properties in the system of completely 1-summing mapping spaces. We introduce notions of injectivity, local reflexivity, exactness, nuclearity and finite-representability in the sys...In this paper, we investigate local properties in the system of completely 1-summing mapping spaces. We introduce notions of injectivity, local reflexivity, exactness, nuclearity and finite-representability in the system of completely 1-summing mapping spaces. First we obtain that if V has WEP, V is locally reflexive in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)) if and only if it is locally reflexive in the system (Ⅰ(⋅,⋅), t(⋅)). Furthermore we prove that an operator space V ⊆ B(H) is exact in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)) if and only if V is finitely representable in {M<sub>n</sub>}<sub>n∈N</sub> in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)). At last, we show that an operator space V is finitely representable in {M<sub>n</sub>}<sub>n∈N</sub> in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)) if and only if V = C.展开更多
目的应用平均幅度差函数之和(the sum of average magnitude difference function,SAMDF)处理室颤的心电信号,通过与常用预测除颤时间方法振幅谱面积(amplitude spectrum area,AMSA)进行对比找到预测除颤时间更优的方法。方法应用56头重...目的应用平均幅度差函数之和(the sum of average magnitude difference function,SAMDF)处理室颤的心电信号,通过与常用预测除颤时间方法振幅谱面积(amplitude spectrum area,AMSA)进行对比找到预测除颤时间更优的方法。方法应用56头重(40±5)kg雄性家猪,诱导室颤后进行10 min未处理的室颤、6 min的心肺复苏和除颤。在室颤和心肺复苏过程当中会记录每1 min SAMDF和AMSA的数据并记录下来。进而计算受试者工作特征(receiver operating characteristic,ROC)曲线,应用单向方差分析(one-way analyses of variance,one-way ANOVA)以及正负样本散点图的比较,以此说明两者均能优化最佳除颤时间。比较除颤成功组(Group R)和除颤失败组(Group N)的SAMDF和AMSA的数值以说明两者预测除颤成功的能力。结果散点图显示SAMDF和AMSA均能够区分阳性和负样本(P<0.001)。ROC曲线显示SAMDF(AUC=0.801,P<0.001)和AMSA(AUC=0.777,P<0.001)一样有着相同的能力预测最佳除颤时间。两组SAMDF和AMSA数值比较,Group R的SAMDF和AMSA数值明显高于Group N(P<0.001)。结论SAMDF在优化预测除颤时机方面具有很高的潜力,并且可以作为AMSA等现有有效预测除颤时机特征的补充。展开更多
文摘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.
文摘Sums of convergent series for any desired number of terms, which may be infinite, are estimated very accurately by establishing definite rational polynomials. For infinite number of terms the sum infinite is obtained by taking the asymptotic limit of the rational polynomial. A rational function with second-degree polynomials both in the numerator and denominator is found to produce excellent results. Sums of series with different characteristics such as alternating signs are considered for testing the performance of the proposed approach.
文摘In this paper, we investigate local properties in the system of completely 1-summing mapping spaces. We introduce notions of injectivity, local reflexivity, exactness, nuclearity and finite-representability in the system of completely 1-summing mapping spaces. First we obtain that if V has WEP, V is locally reflexive in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)) if and only if it is locally reflexive in the system (Ⅰ(⋅,⋅), t(⋅)). Furthermore we prove that an operator space V ⊆ B(H) is exact in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)) if and only if V is finitely representable in {M<sub>n</sub>}<sub>n∈N</sub> in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)). At last, we show that an operator space V is finitely representable in {M<sub>n</sub>}<sub>n∈N</sub> in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)) if and only if V = C.
文摘目的应用平均幅度差函数之和(the sum of average magnitude difference function,SAMDF)处理室颤的心电信号,通过与常用预测除颤时间方法振幅谱面积(amplitude spectrum area,AMSA)进行对比找到预测除颤时间更优的方法。方法应用56头重(40±5)kg雄性家猪,诱导室颤后进行10 min未处理的室颤、6 min的心肺复苏和除颤。在室颤和心肺复苏过程当中会记录每1 min SAMDF和AMSA的数据并记录下来。进而计算受试者工作特征(receiver operating characteristic,ROC)曲线,应用单向方差分析(one-way analyses of variance,one-way ANOVA)以及正负样本散点图的比较,以此说明两者均能优化最佳除颤时间。比较除颤成功组(Group R)和除颤失败组(Group N)的SAMDF和AMSA的数值以说明两者预测除颤成功的能力。结果散点图显示SAMDF和AMSA均能够区分阳性和负样本(P<0.001)。ROC曲线显示SAMDF(AUC=0.801,P<0.001)和AMSA(AUC=0.777,P<0.001)一样有着相同的能力预测最佳除颤时间。两组SAMDF和AMSA数值比较,Group R的SAMDF和AMSA数值明显高于Group N(P<0.001)。结论SAMDF在优化预测除颤时机方面具有很高的潜力,并且可以作为AMSA等现有有效预测除颤时机特征的补充。
