SummaryAnimal behavior arises from computations in neuronal circuits, but our understanding of these computations has been frustrated by the lack of detailed synaptic connection maps, or connectomes. For example, despite intensive investigations over half a century, the neuronal implementation of local motion detection in the insect visual system remains elusive. Here, we developed a semi-automated pipeline using electron microscopy to reconstruct a connectome, containing 379 neurons and 8,637 chemical synaptic contacts, within the Drosophila optic medulla. By matching reconstructed neurons to examples from light microscopy, we assigned neurons to cell types and assembled a connectome of the medulla's repeating module. Within this module, we identified cell types constituting a motion detection circuit and showed that the connections onto individual motion-sensitive neurons in this circuit were consistent with their direction selectivity. Our results identify cellular targets for future functional investigations, and demonstrate that connectomes can provide key insights into neuronal computations.

Introduction 7 1 -1tends to zero as r^-1 for every 0=|=Omod27r, and P (r,9) clearly satisfies condition (ii) above.Secondly, if condition (ii) above is weakened by replacing 'o' by '0', the conclusion of the above theorem does not hold. For dP{r,6)ld6 = -£ nr n sinn6 7 1 = 1 tends to zero as r-> 1 for every 6. On the other hand, as r -> 1.Thirdly, if condition (ii) above is weakened by replacing ||/(r, 0)|| by \\f(r, 6) WJJ,, where \\f(r, 6) \\JJ, is the L p -norm on concentric circles of radius r, l^pl. (For further comments concerning the Z>-norm on concentric circles of radius r, see the concluding section of the paper.) f This research was supported by the Air Force Office of Scientific Research. Proc. London Math. Soc. (3) 13 (1963) 639-52 640 V. L. SHAPIRO We shall designate limsup/(r, 0) by f*{6) and liminf/(r,0) by r-»1 r-*lThe principal result.that we shall prove in this paper is the following: f(r, 0) be a function harmonic in the interior of the unit disk and let E be a countable set contained in the interval [0,27r). Suppose that (i) \\f(r t 0)\\ = o[(l-r)-*]a8r-»l, (ii) /*(0) andf*{9) are finite for 9 in [0,2TT)\E, (iii) /*(#) andf*{d) are both in L 1 on [0,2rr), (iv) (l-r)/(r,0)-*O as r->l for 6 in E. Thenf*{9) =/*(0) almost everywhere in [0, 2TT) and

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ABSTRACT. The notion for (u, p)