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

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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.