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We assembled a semi-automated reconstruction of L2/3 mouse primary visual cortex from ~250×140×90 μm(3) of electron microscopic images, including pyramidal and non-pyramidal neurons, astrocytes, microglia, oligodendrocytes and precursors, pericytes, vasculature, nuclei, mitochondria, and synapses. Visual responses of a subset of pyramidal cells are included. The data are publicly available, along with tools for programmatic and three-dimensional interactive access. Brief vignettes illustrate the breadth of potential applications relating structure to function in cortical circuits and neuronal cell biology. Mitochondria and synapse organization are characterized as a function of path length from the soma. Pyramidal connectivity motif frequencies are predicted accurately using a configuration model of random graphs. Pyramidal cells receiving more connections from nearby cells exhibit stronger and more reliable visual responses. Sample code shows data access and analysis.

We consider the following iterative construction of a random planar triangulation. Start with a triangle embedded in the plane. In each step, choose a bounded face uniformly at random, add a vertex inside that face and join it to the vertices of the face. After n − 3 steps, we obtain a random triangulated plane graph with n vertices, which is called a Random Apollonian Network (RAN). We show that asymptotically almost surely (a.a.s.) every path in a RAN has length o ( n ) , refuting a conjecture of Frieze and Tsourakakis. We also show that a RAN always has a path of length ( 2 n − 5 ) log 2 / log 3 , and that the expected length of its longest path is Ω ( n 0.88 ) . Finally, we prove that a.a.s. the diameter of a RAN is asymptotic to c log n , where c ≈ 1.668 is the solution of an explicit equation.