摘要翻译：
我们定义了一个活动相关的分支比率，它允许比较不同的时间序列$x_{t}$。分支比率$b_x$定义为$b_x=e[\xi_x/x]$。随机变量$\xi_x$是下一个信号的值，假定前一个信号等于$x$，所以$\xi_x=\{X_{t+1}x_t=x\}$。如果$b_x>1$，当信号等于$x$时，该过程平均为超临界，而如果$b_x<1$，则为次临界。对于股票价格，我们发现在统计不确定性范围内$b_x=1$，对于所有$x$，符合“有效市场假说”。对于库存量、太阳X射线通量强度和Bak-Tang-Wiesenfeld(BTW)沙堆模型，$B_x$对于小的活动值是超临界的，对于最大的活动值是亚临界的，表明有回到典型值的趋势。对于股票交易量，这种趋势具有近似幂律的行为。对于太阳X射线通量和BTW模型，在$B_X\SIMEQ1$处存在一个广泛的活动范围，我们将其解释为临界行为的指示。尽管$x_t$和$\xi_x$的潜在概率分布不同，但这是正确的。对于BTW模型，$\xi_x$的分布为高斯分布，当$x$大于1时，其方差随$x$线性增长。因此，当对过去的历史进行抽样时，BTW模型中的活动服从一个中心极限定理。在BTW模型中引入体积耗散后，$B_x$接近于1的活动范围就消失了--支持了我们的假设，即它是临界性的一个指标。
---
英文标题：
《Activity Dependent Branching Ratios in Stocks, Solar X-ray Flux, and the
  Bak-Tang-Wiesenfeld Sandpile Model》
---
作者：
Elliot Martin, Amer Shreim, and Maya Paczuski
---
最新提交年份：
2009
---
分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
--
一级分类：Physics        物理学
二级分类：Disordered Systems and Neural Networks        无序系统与神经网络
分类描述：Glasses and spin glasses; properties of random, aperiodic and quasiperiodic systems; transport in disordered media; localization; phenomena mediated by defects and disorder; neural networks
眼镜和旋转眼镜；随机、非周期和准周期系统的性质；无序介质中的传输；本地化；由缺陷和无序介导的现象；神经网络
--
一级分类：Physics        物理学
二级分类：Physics and Society        物理学与社会
分类描述：Structure, dynamics and collective behavior of societies and groups (human or otherwise). Quantitative analysis of social networks and other complex networks. Physics and engineering of infrastructure and systems of broad societal impact (e.g., energy grids, transportation networks).
社会和团体（人类或其他）的结构、动态和集体行为。社会网络和其他复杂网络的定量分析。具有广泛社会影响的基础设施和系统（如能源网、运输网络）的物理和工程。
--
一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
--

---
英文摘要：
  We define an activity dependent branching ratio that allows comparison of different time series $X_{t}$. The branching ratio $b_x$ is defined as $b_x= E[\xi_x/x]$. The random variable $\xi_x$ is the value of the next signal given that the previous one is equal to $x$, so $\xi_x=\{X_{t+1}|X_t=x\}$. If $b_x>1$, the process is on average supercritical when the signal is equal to $x$, while if $b_x<1$, it is subcritical. For stock prices we find $b_x=1$ within statistical uncertainty, for all $x$, consistent with an ``efficient market hypothesis''. For stock volumes, solar X-ray flux intensities, and the Bak-Tang-Wiesenfeld (BTW) sandpile model, $b_x$ is supercritical for small values of activity and subcritical for the largest ones, indicating a tendency to return to a typical value. For stock volumes this tendency has an approximate power law behavior. For solar X-ray flux and the BTW model, there is a broad regime of activity where $b_x \simeq 1$, which we interpret as an indicator of critical behavior. This is true despite different underlying probability distributions for $X_t$, and for $\xi_x$. For the BTW model the distribution of $\xi_x$ is Gaussian, for $x$ sufficiently larger than one, and its variance grows linearly with $x$. Hence, the activity in the BTW model obeys a central limit theorem when sampling over past histories. The broad region of activity where $b_x$ is close to one disappears once bulk dissipation is introduced in the BTW model -- supporting our hypothesis that it is an indicator of criticality.
---
PDF链接：
https://arxiv.org/pdf/0910.2447