To understand how the neocortex underlies our ability to perceive, think, and act, it is important to study the relationship between circuit connectivity and function. Previous research has shown that excitatory neurons in layer 2/3 of the primary visual cortex of mice with similar response properties are more likely to form connections. However, technical challenges of combining synaptic connectivity and functional measurements have limited these studies to few, highly local connections. Utilizing the millimeter scale and nanometer resolution of the MICrONS dataset, we studied the connectivity-function relationship in excitatory neurons of the mouse visual cortex across interlaminar and interarea projections, assessing connection selectivity at the coarse axon trajectory and fine synaptic formation levels. A digital twin model of this mouse, that accurately predicted responses to arbitrary video stimuli, enabled a comprehensive characterization of the function of neurons. We found that neurons with highly correlated responses to natural videos tended to be connected with each other, not only within the same cortical area but also across multiple layers and visual areas, including feedforward and feedback connections, whereas we did not find that orientation preference predicted connectivity. The digital twin model separated each neuron's tuning into a feature component (what the neuron responds to) and a spatial component (where the neuron's receptive field is located). We show that the feature, but not the spatial component, predicted which neurons were connected at the fine synaptic scale. Together, our results demonstrate the "like-to-like" connectivity rule generalizes to multiple connection types, and the rich MICrONS dataset is suitable to further refine a mechanistic understanding of circuit structure and function.

We are now in the era of millimeter-scale electron microscopy (EM) volumes collected at nanometer resolution. Dense reconstruction of cellular compartments in these EM volumes has been enabled by recent advances in Machine Learning (ML). Automated segmentation methods can now yield exceptionally accurate reconstructions of cells, but despite this accuracy, laborious post-hoc proofreading is still required to generate large connectomes free of merge and split errors. The elaborate 3-D meshes of neurons produced by these segmentations contain detailed morphological information, from the diameter, shape, and branching patterns of axons and dendrites, down to the fine-scale structure of dendritic spines. However, extracting information about these features can require substantial effort to piece together existing tools into custom workflows. Building on existing open-source software for mesh manipulation, here we present "NEURD", a software package that decomposes each meshed neuron into a compact and extensively-annotated graph representation. With these feature-rich graphs, we implement workflows for state-of-the art automated post-hoc proofreading of merge errors, cell classification, spine detection, axon-dendritic proximities, and other features that can enable many downstream analyses of neural morphology and connectivity. NEURD can make these new massive and complex datasets more accessible to neuroscience researchers focused on a variety of scientific questions.

Hyperplane codes are a class of convex codes that arise as the output of a one layer feed-forward neural network. Here we establish several natural properties of stable hyperplane codes in terms of the polar complex of the code, a simplicial complex associated to any combinatorial code. We prove that the polar complex of a stable hyperplane code is shellable and show that most currently known properties of hyperplane codes follow from the shellability of the appropriate polar complex.