Search and broadcast in stochastic environments, a biological perspective.

Abstract : This thesis is built around two series of works, each motivated by experiments on ants. We derive and analyse new models, that use computer science concepts and methodology, despite their biological roots and motivation. The first model studied in this thesis takes its inspiration in collaborative transport of food in the P. Longicornis species. We find that some key aspects of the process are well described by a graph search problem with noisy advice. The advice corresponds to characteristic short scent marks laid in front of the load in order to facilitate its navigation. In this thesis, we provide detailed analysis of the model on trees, which are relevant graph structures from a computer science standpoint. In particular our model may be viewed as a noisy extension of binary search to trees. Tight results in expectation and high probability are derived with matching upper and lower bounds. Interestingly, there is a sharp phase transition phenomenon for the expected runtime, but not when the algorithms are only required to succeed with high probability. The second model we work with was initially designed to capture information broadcast amongst desert ants. The model uses a stochastic meeting pattern and noise in the interactions, in a way that matches experimental data. Within this theoretical model, we present in this document a strong lower bound on the number of interactions required before information can be spread reliably. Experimentally, we see that the time required for the recruitment process of even few ants increases sharply with the group size, in accordance with our result. A theoretical consequence of the lower bound is a separation between the uniform noisy PUSH and PULL models of interaction. We also study a close variant of broadcast, without noise this time but under more strict convergence requirements and show that in this case, the problem can be solved efficiently, even with very limited exchange of information on each interaction.
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Lucas Boczkowski. Search and broadcast in stochastic environments, a biological perspective.. Computer Science [cs]. Université Paris 7, 2018. English. ⟨tel-01963290⟩

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