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Acknowledgements We thank M. Krumin for assistance with the two-photon
microscopes, C. Reddy for surgeries, and K. Falconer, A. Gretton and M. Benna
for discussions of mathematics. This research was funded by Wellcome Trust
Investigator grants (108726, 205093 and 204915) and by a grant from the
Simons Foundation (SCGB 325512). C.S. was funded by a four-year Gatsby
Foundation PhD studentship. M.C. holds the GlaxoSmithKline/Fight for Sight
Chair in Visual Neuroscience. K.D.H. was funded by the European Research
Council (694401). N.S. was supported by postdoctoral fellowships from the
Human Frontier Sciences Program and the Marie Curie Action of the EU
(656528). C.S. and M.P. are now funded by HHMI Janelia.Reviewer information Nature thanks Jakob Macke, Ken Miller and Byron Yu for
their contribution to the peer review of this work.Author contributions C.S., M.P., N.S., M.C. and K.D.H. conceptualized the study;
C.S., M.P., N.S. and K.D.H. devised the methodology; C.S. and M.P. designed the
software; C.S., M.P. and N.S. performed experiments; C.S. and M.P. analysed the
data; K.D.H. proved mathematical theorems; C.S., M.P., N.S., M.C. and K.D.H.
wrote the paper; and M.C. and K.D.H. provided resources and acquired funding.Competing interests The authors declare no competing interests.Additional information
Extended data is available for this paper at https://doi.org/10.1038/s41586-
019-1346-5.
Supplementary information is available for this paper at https://doi.org/
10.1038/s41586-019-1346-5.
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