英文翻译!急求!谢谢啦!
AbstractInalineofrecentdevelopment,probabilisticconstructionsofuniversal,homogeneouso...
Abstract In a line of recent development, probabilistic constructions of universal, homogeneous objects have been provided in various categories of ordered structures, such as causal
sets[12], bifinite domains[13], and countable partial orders[10]. These constructions have been shown to produce objects with the desired properties with probability 1 in an appropriately
defined measure space. A common strategy for these constructions is successive point-wise extension of an existing finite structure, with decisions on the relationships between the newly added point and the existing structure made according to well-specified probabilistic choices. This strategy is a departure from (and understandably so due to the increased complexity) the original one for random graphs[16] where a universal homogeneous countable
graph is constructed with probability 1 in a single step (i.e., a single round of countably many probabilistic choices made independently). It would be interesting to see which of the
categories studied more recently may admit such "one-step" constructions. The main focus of this paper is a new strategy, consisting of a single round of countably many probabilistic
choices made independently, for the construction of a universal, homogeneous prime event structure. The intuition that the one-round construction is desirable has a similar flavor to a more general setting in e.g. Calculus/Real Analysis. When taking limits, iterative step-by-step processes are usually given, but a set of machineries was invented to determine the limit, i.e., achieving a "one-round" direct and explicit description of the limit. 展开
sets[12], bifinite domains[13], and countable partial orders[10]. These constructions have been shown to produce objects with the desired properties with probability 1 in an appropriately
defined measure space. A common strategy for these constructions is successive point-wise extension of an existing finite structure, with decisions on the relationships between the newly added point and the existing structure made according to well-specified probabilistic choices. This strategy is a departure from (and understandably so due to the increased complexity) the original one for random graphs[16] where a universal homogeneous countable
graph is constructed with probability 1 in a single step (i.e., a single round of countably many probabilistic choices made independently). It would be interesting to see which of the
categories studied more recently may admit such "one-step" constructions. The main focus of this paper is a new strategy, consisting of a single round of countably many probabilistic
choices made independently, for the construction of a universal, homogeneous prime event structure. The intuition that the one-round construction is desirable has a similar flavor to a more general setting in e.g. Calculus/Real Analysis. When taking limits, iterative step-by-step processes are usually given, but a set of machineries was invented to determine the limit, i.e., achieving a "one-round" direct and explicit description of the limit. 展开
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摘要在行最近的发展,概率建筑普遍,均匀物体时所提供的各种类别的有序结构,如因果
集[ 12 ] , bifinite域[ 13 ] ,以及数部分订单[ 10 ] 。这些建筑已显示出物体的产生所期望的性能与概率1在一个适当的
定义测度空间。一项共同战略,这些建筑是历届点明智延长现有的有限的结构,决定之间的关系,新增加的点和现有的结构以及按照指定的概率选择。这一战略是背离(和理解的原因是越来越复杂)原来的随机图[ 16 ]在一个普遍的同质数
图1构造的概率在一个步骤(即单轮数许多概率选择独立) 。这将是有趣的,看看哪
各类研究最近可能会承认这种“一步”的构架。重点本文是一个新的战略,由一个单一的轮数许多概率
选择独立,为建设一个普遍的,均匀总理的事件结构。的直觉,一个全面建设是可取的也有类似的味道更宽泛的环境中如演算/实时分析。当采取的限制,迭代步过程通常,但一套机制,以确定发明的限制,即实现“一个全面”直接和明确的说明限制。
有些地方不太明确,您自己理下就行,希望能帮上你,祝学习生活愉快。
集[ 12 ] , bifinite域[ 13 ] ,以及数部分订单[ 10 ] 。这些建筑已显示出物体的产生所期望的性能与概率1在一个适当的
定义测度空间。一项共同战略,这些建筑是历届点明智延长现有的有限的结构,决定之间的关系,新增加的点和现有的结构以及按照指定的概率选择。这一战略是背离(和理解的原因是越来越复杂)原来的随机图[ 16 ]在一个普遍的同质数
图1构造的概率在一个步骤(即单轮数许多概率选择独立) 。这将是有趣的,看看哪
各类研究最近可能会承认这种“一步”的构架。重点本文是一个新的战略,由一个单一的轮数许多概率
选择独立,为建设一个普遍的,均匀总理的事件结构。的直觉,一个全面建设是可取的也有类似的味道更宽泛的环境中如演算/实时分析。当采取的限制,迭代步过程通常,但一套机制,以确定发明的限制,即实现“一个全面”直接和明确的说明限制。
有些地方不太明确,您自己理下就行,希望能帮上你,祝学习生活愉快。
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