Input symmetry invariance, and applications to biological systems

This paper studies invariance with respect to symmetries in sensory fields, a particular case of which, scale-invariance, has recently been found in certain eukaryotic as well as bacterial cell signaling systems. We describe a necessary and sufficient characterization of symmetry invariance in terms of equivariant transformations, show how this characterization helps find all possible symmetries in standard models of biological adaptation, and discuss symmetry-invariant searches.