Abstract

The formal quantum systems under study demonstrate significant capabilities for solving classification problems in studying dynamical behavior of stochastic systems. Among their features are entanglement by measuring, quantitative estimating the fit for a closed qubit system and observations to identify qubit representation parameters, the specialized discretized spectral metric for comparing patterns of system behaviors, with the multidimensional scaling, cluster analysis and discriminant analysis being applied to the matrices of mutual distances calculated using the presented discretized spectral metric. Hidden evolution periodicities during the observation time period are determined by means of the quantum systems spectral analysis to clarify the system behavior structure. These systems can be also used for representing the Markovian processes with the aid of qubit representations of staying in the corresponding states. An illustrative example revealed diagnostic benefits of the new technique as compared with one based on the Markovian representation.

中文翻译：

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随机系统的动力学行为建模：量子位表示与互马尔可夫模型似然估计的谱分析

摘要

所研究的形式量子系统在研究随机系统的动态行为中表现出解决分类问题的重要能力。它们的特征包括通过测量纠缠、定量估计封闭量子位系统的拟合和观察以识别量子位表示参数、用于比较系统行为模式的专门离散化光谱度量，以及多维缩放、聚类分析和判别分析应用于使用所提供的离散光谱度量计算的相互距离矩阵。通过量子系统光谱分析确定观测时间段内隐藏的演化周期，以阐明系统行为结构。这些系统还可用于借助停留在相应状态的量子位表示来表示马尔可夫过程。一个说明性示例揭示了与基于马尔可夫表示的新技术相比，新技术的诊断优势。