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

复杂网络上的随机搜索过程、Levy 飞行和随机游走

• 批准号: 316131235
• 负责人: Professor Dr. Ralf Metzler
• 金额: --
• 依托单位: Institut für Physik und Astronomie
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2017-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/316131235?language=en
• 关键词: Random; search; processes; Levy; fllights

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.

通过对随机搜索过程进行分析和数值研究，该项目旨在通过分析首次到达时间、搜索可靠性和随机搜索过程的效率来理解随机游走者的搜索策略。该项目阐明了搜索优化中不对称 Levy 航班背后的机制。这将通过一方面在不存在和存在外部偏置的情况下研究带有 delta-sink 项的 Fokker-Planck 方程，另一方面应用 Langevin 方程方法来实现。该项目还涉及复杂网络和图（包括空间随机图和有向图）上有偏和无偏随机游走的研究。将开发的方法和工具预计将适用于物理、化学和生物学中出现的各种现象，以及本质上采用随机工作过程来执行所需任务的各种算法。尽管我们的主要关注点是搜索算法，特别是 Page Rank 及其变体，但基于随机游走的其他著名算法，例如 BLAST（用于蛋白质和 DNA 对齐）、推荐引擎和链接预测算法也可以从我们的分析中受益。

项目成果

The role of multiplex network structure in cooperation through generalized reciprocity

• DOI: 10.1016/j.physa.2019.121805
• 发表时间: 2018-05
• 期刊: Physica A: Statistical Mechanics and its Applications
• 作者: Viktor Stojkoski;Zoran Utkovski;E. André;L. Kocarev

Random diffusivity from stochastic equations: comparison of two models for Brownian yet non-Gaussian diffusion

• DOI: 10.1088/1367-2630/aab696
• 发表时间: 2018-04
• 期刊: New Journal of Physics
• 影响因子: 3.3
• 作者: V. Sposini;A. Chechkin;F. Seno;G. Pagnini;R. Metzler

Promoting cooperation by preventing exploitation: The role of network structure.

通过防止剥削促进合作：网络结构的作用

• DOI: 10.1103/physreve.96.022315
• 发表时间: 2017
• 期刊: Physical review. E
• 作者: Z. Utkovski;V. Stojkoski;L. Basnarkov;L. Kocarev
• 通讯作者: L. Kocarev

Brownian yet Non-Gaussian Diffusion: From Superstatistics to Subordination of Diffusing Diffusivities

• DOI: 10.1103/physrevx.7.021002
• 发表时间: 2017-04-05
• 期刊: PHYSICAL REVIEW X
• 影响因子: 12.5
• 作者: Chechkin, Aleksei V.;Seno, Flavio;Sokolov, Igor M.
• 通讯作者: Sokolov, Igor M.

From continuous time random walks to the generalized diffusion equation

• DOI: 10.1515/fca-2018-0002
• 发表时间: 2018-02
• 期刊: Fractional Calculus and Applied Analysis
• 影响因子: 3
• 作者: Trifce Sandev;R. Metzler;A. Chechkin