Random search processes, Levy fllights, and random walks on complex networks

本计画借由提供随机搜寻过程的分析与数值研究，借由分析随机步行者的首次抵达时间、搜寻可靠度与随机搜寻过程的效率，来了解其搜寻策略。该项目澄清了搜索优化中不对称Levy航班背后的机制。这将使通过调查的福克-普朗克方程与δ-汇项的存在和不存在的外部偏压，一方面，并应用朗之万方程的方法在其他。该项目还涉及复杂网络和图上的有偏和无偏随机游动的研究，包括空间随机图和有向图。预计将开发的方法和工具将适用于物理，化学和生物学中出现的各种现象以及基本上采用随机工作过程来执行所需任务的各种算法。虽然我们主要关注的是搜索算法，特别是Page Rank及其变体，但其他基于随机游走的知名算法，如BLAST（用于蛋白质和DNA比对），推荐引擎和链接预测算法也可以从我们的分析中受益。

By providing analytical and numerical investigations of random search processes, this project aims at understanding the search strategy of a random walker by analyzing the first arrival time, search reliability, and the efficiency of the random search process. The project clarifies the mechanism behind asymmetric Levy flights in the search optimization. This will be enabled by investigating the Fokker-Planck equation with delta-sink term in absence and presence of external bias, at one hand and applying the Langevin equation approach on the other. The project also relates to investigation of biased and unbiased random walks on complex networks and graphs, including spatial random graphs and directed graphs. The methods and tools which will be developed are expected to be applicable for various phenomena arising in physics, chemistry, and biology as well as for various algorithms that essentially employ random work processes for performing a desired task. Although our primary focus is on search algorithms, in particular Page Rank and its variants, the other well-known algorithms based on random walks such as BLAST (for protein and DNA alignment), recommendation engines, and link predictions algorithms could also benefit from our analysis.