求解单分子：过滤由光子和其他类型的可观测量组成的噪声离散数据
Solving single molecules: filtering noisy discrete data made of photons and other type of observables
摘要：
在生物物理学和相关领域的许多系统中，科学家（用非常聪明的方法）测量单个分子（例如生物聚合物（蛋白质，DNA，RNA等），纳米晶体，离子通道），旨在从数据中找到模型。但是，在不太少的情况下，噪声没有得到准确的解决，这可能会导致误导性的模型。在这里，我们解决了噪音。我们考虑任意开-关动力学模型（KS）中的两态光子轨迹：当过程处于开态时，它以速率γon发射光子;当过程处于关态时，它以速率γoff发射光子。我们开发了一个过滤器，去除噪声，从而在干净的数据，也在合并失败的情况下。滤波器是一种具有各种新的统计处理的数值算法。它是基于一个新的一般似然函数在这里开发的，可观察的依赖形式。滤波器可以解决噪声，在速率空间的可检测区域：也就是说，我们还找到了数据“太”噪声的区域。一致性测试将从数据中找到区域的类型。如果数据被判定为“太嘈杂”，则分箱显然失败，并且应该对原始数据应用更简单的方法，并意识到提取的信息是部分的。我们表明，不应用过滤器，而清洁的结果在错误率。该滤波器（通过微小的调整）可以解决任何离散状态轨迹中的噪声，但在“处理”来自其他数据（例如连续数据和FRET数据）的噪声时需要扩展。这里开发的过滤器与我们以前在这个领域的项目是互补的，在这个领域中，我们已经通过开发降维形式（RDFs）解决了干净的两个状态数据：只有组合程序才能从单个分子的噪声轨迹中构建最准确的模型。
英文摘要：
In numerous systems in biophysics and related fields, scientists measure (with very smart methods) individual molecules (e.g. biopolymers (proteins, DNA, RNA, etc), nano - crystals, ion channels), aiming at finding a model from the data. But the noise is not solved accurately in not so few cases and this may lead to misleading models. Here, we solve the noise. We consider two state photon trajectories from any on off kinetic scheme (KS): the process emitting photons with a rate γon when it is in the on state, and emitting with a rate γoff when it is in the off state. We develop a filter that removes the noise resulting in clean data also in cases where binning fails. The filter is a numerical algorithm with various new statistical treatments. It is based on a new general likelihood function developed here, with observable dependent form. The filter can solve the noise, in the detectable region of the rate space: that is, we also find a region where the data is "too" noisy. Consistency tests will find the region's type from the data. If the data is ruled "too noisy", binning obviously fails, and one should apply simpler methods on the raw data and realizing that the extracted information is partial. We show that not applying the filter while cleaning results in erroneous rates. This filter (with minor adjustments) can solve the noise in any discrete state trajectories, yet extensions are needed in "tackling" the noise from other data, e.g. continuous data and FRET data. The filter developed here is complementary with our previous projects in this field, where we have solved clean two state data with the development of reduced dimensions forms (RDFs): only the combined procedures enabling building the most accurate model from noisy trajectories from single molecules
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