论文标题
最佳的固定标记
Optimal stationary markings
论文作者
论文摘要
从理论概率到统计物理的应用，组合优化和通信的许多特定问题可以作为对大型相互作用粒子系统中局部参数的最佳调整。使用欧几里得空间中固定点过程的框架，我们将其作为最佳静止标记的问题，是给定的固定点过程的最佳固定标记。给定标记的质量是根据所提出的标记配置功能的所有点以协变量计算的分数评估的。在没有分数配置的总顺序的情况下，我们将强度 - 优先级和局部最优性确定为定义最佳固定标记的两种自然方法。我们得出了存在强度 - 最佳标记的紧密度和整合性条件，并进一步稳定条件，使其等同于本地最佳的标记。我们提出了激励提议的一般框架的例子。最后，我们讨论了导致独特结果的各种可能的方法。
Many specific problems ranging from theoretical probability to applications in statistical physics, combinatorial optimization and communications can be formulated as an optimal tuning of local parameters in large systems of interacting particles. Using the framework of stationary point processes in the Euclidean space, we pose it as a problem of an optimal stationary marking of a given stationary point process. The quality of a given marking is evaluated in terms of scores calculated in a covariant manner for all points in function of the proposed marked configuration. In the absence of total order of the configurations of scores, we identify intensity-optimality and local optimality as two natural ways for defining optimal stationary marking. We derive tightness and integrability conditions under which intensity-optimal markings exist and further stabilization conditions making them equivalent to locally optimal ones. We present examples motivating the proposed, general framework. Finally, we discuss various possible approaches leading to uniqueness results.
