Krivov Sergei V
Institute of Molecular and Cellular Biology, University of Leeds, Leeds, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Jul;84(1 Pt 1):011135. doi: 10.1103/PhysRevE.84.011135. Epub 2011 Jul 25.
Dimensionality reduction is ubiquitous in the analysis of complex dynamics. The conventional dimensionality reduction techniques, however, focus on reproducing the underlying configuration space, rather than the dynamics itself. The constructed low-dimensional space does not provide a complete and accurate description of the dynamics. Here I describe how to perform dimensionality reduction while preserving the essential properties of the dynamics. The approach is illustrated by analyzing the chess game--the archetype of complex dynamics. A variable that provides complete and accurate description of chess dynamics is constructed. The winning probability is predicted by describing the game as a random walk on the free-energy landscape associated with the variable. The approach suggests a possible way of obtaining a simple yet accurate description of many important complex phenomena. The analysis of the chess game shows that the approach can quantitatively describe the dynamics of processes where human decision-making plays a central role, e.g., financial and social dynamics.
在复杂动力学分析中，降维无处不在。然而，传统的降维技术侧重于再现潜在的构型空间，而非动力学本身。所构建的低维空间并不能对动力学提供完整且准确的描述。在此，我描述了如何在保留动力学基本特性的同时进行降维。通过分析国际象棋博弈——复杂动力学的典型例子，对该方法进行了说明。构建了一个能对国际象棋动力学提供完整且准确描述的变量。通过将博弈描述为与该变量相关的自由能景观上的随机游走，预测了获胜概率。该方法为获得对许多重要复杂现象的简单而准确的描述提供了一种可能途径。对国际象棋博弈的分析表明，该方法能够定量描述人类决策起核心作用的过程的动力学，例如金融和社会动力学。
