反应扩散过程中反应间时间的结构及其对计数统计的影响

Benjamin Garcia de Figueiredo, Justin M. Calabrese, William F. Fagan, Ricardo Martinez-Garcia
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引用次数: 0

摘要

从晶格中准粒子的湮灭,到景观中捕食者与猎物的相遇,再到神经网络中的尖峰,许多自然现象都是通过对可观测事件的计数来量化的。当底层动力系统在其相空间中占据一组反应状态时,这些事件就会以随机间隔触发。我们推导出了此类计数过程中事件间隔时间分布的一般表达式,假设底层触发动力学是一个收敛于静态分布的随机过程。我们的结果有助于解决反应-扩散过程研究中长期存在的二分法问题,表明反应间点过程介于反应限制和扩散限制机制之间。在低反应速率下,反应间过程是泊松过程,其速率取决于事件触发随机过程的静态特性。在高反应速率下,反应间时间主要由到达反应状态的时间决定。为了进一步说明这种方法的威力,我们应用我们的框架来获取在多个生物物理场景中出现的两个计数过程的计数统计量。首先,我们研究了通过动物穿越探测器的频率来估计其活动水平的常见情况,结果表明穿越事件的平均次数会随着命中率的下降而单调减少,这一看似 "矛盾 "的结果可能会导致对实验计数数据的误解。其次,我们推导出了许多粒子检测的集合统计,恢复并推广了化学感受生物物理学中的已知结果。总之,我们建立了一个统一的理论框架来量化反应扩散系统中的事件间时间分布,澄清了现有文献中的争论,并提供了应用于现实世界场景的实例。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The structure of inter-reaction times in reaction-diffusion processes and consequences for counting statistics
Many natural phenomena are quantified by counts of observable events, from the annihilation of quasiparticles in a lattice to predator-prey encounters on a landscape to spikes in a neural network. These events are triggered at random intervals when an underlying dynamical system occupies a set of reactive states in its phase space. We derive a general expression for the distribution of times between events in such counting processes assuming the underlying triggering dynamics is a stochastic process that converges to a stationary distribution. Our results contribute to resolving a long-standing dichotomy in the study of reaction-diffusion processes, showing the inter-reaction point process interpolates between a reaction- and a diffusion-limited regime. At low reaction rates, the inter-reaction process is Poisson with a rate depending on stationary properties of the event-triggering stochastic process. At high reaction rates, inter-reaction times are dominated by the hitting times to the reactive states. To further illustrate the power of this approach we apply our framework to obtain the counting statistics of two counting processes appearing in several biophysical scenarios. First, we study the common situation of estimating an animal's activity level by how often it crosses a detector, showing that the mean number of crossing events can decrease monotonically with the hitting rate, a seemingly 'paradoxical' result that could possibly lead to misinterpretation of experimental count data. Second, we derive the ensemble statistics for the detection of many particles, recovering and generalizing known results in the biophysics of chemosensation. Overall, we develop a unifying theoretical framework to quantify inter-event time distributions in reaction-diffusion systems that clarifies existing debates in the literature and provide examples of application to real-world scenarios.
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