Topology-dependent density optima for efficient simultaneous network exploration

9 Jul 2018, 12:10
New Law School/--022 (University of Sydney)

New Law School/--022

University of Sydney

Oral Presentation Other Mathematical Biology Biochemistry, signalling & mathematical techniques


Daniel Wilson (The University of Oxford)


From the foraging strategies of large organisms, to T-cells hunting pathogens, to proteins examining strands of DNA, carefully optimised search processes are a phenomenon that pervades throughout nature at many scales. Often these search processes do not proceed in isolation, but instead many instances proceed in parallel, competing for space and resources. In this talk I shall discuss optimisation of search processes on networked topologies where the searchers interact with each other through competition for space. Taking the simple exclusion process as the fundamental model for spatial interactions, I consider search strategies that seek to minimise the average cover time for individuals that search in parallel. We will see that the optimal strategy is to implement parallel searching at an optimal density of searchers that depends heavily on the given network topology, and that the optimal density can be well predicted by the spectral gap of the network. These results are verified over a broad class of networks, as well as real-world transport networks such as the London tube network. I will conclude by considering an asymmetric search process that reveals unexpected changes in efficiency between classes of networks.

Primary authors

Prof. Ruth Baker (University of Oxford) Daniel Wilson (The University of Oxford) Dr Francis Woodhouse (The University of Cambridge)

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