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Research Notes: Gradient sensing in Bayesian chemotaxis

Bayesian chemotaxis is an information-based target search problem inspired by biological chemotaxis. It is defined by a decision strategy coupled to the dynamic estimation of target position from detections of signaling molecules. We extend the case of a point-like agent previously introduced in [Vergassola et al., Nature 2007], which establishes concentration sensing as the dominant contribution to information processing, to the case of a circular agent of small finite size. We identify gradient sensing and a Laplacian correction to concentration sensing as the two leading-order expansion terms in the expected entropy variation. Numerically, we find that the impact of gradient sensing is most relevant because it provides direct directional information to break symmetry in likelihood distributions, which are generally circle-shaped by concentration sensing.