Recent advances in neuroscience have enabled the exploration of brain structure at the level of individual synaptic connections. These connectomics datasets continue to grow in size and complexity; methods to search for and identify interesting graph patterns offer a promising approach to quickly reduce data dimensionality and enable discovery. These graphs are often too large to be analyzed manually, presenting significant barriers to searching for structure and testing hypotheses. We combine graph database and analysis libraries with an easy-to-use neuroscience grammar suitable for rapidly constructing queries and searching for subgraphs and patterns of interest. Our approach abstracts many of the computer science and graph theory challenges associated with nanoscale brain network analysis and allows scientists to quickly conduct research at scale. We demonstrate the utility of these tools by searching for motifs on simulated data and real public connectomics datasets, and we share simple and complex structures relevant to the neuroscience community. We contextualize our findings and provide case studies and software to motivate future neuroscience exploration.

Neuroscientists are actively pursuing high-precision maps, or graphs consisting of networks of neurons and connecting synapses in mammalian and non-mammalian brains. Such graphs, when coupled with physiological and behavioral data, are likely to facilitate greater understanding of how circuits in these networks give rise to complex information processing capabilities. Given that the automated or semi-automated methods required to achieve the acquisition of these graphs are still evolving, we developed a metric for measuring the performance of such methods by comparing their output with those generated by human annotators (“ground truth” data). Whereas classic metrics for comparing annotated neural tissue reconstructions generally do so at the voxel level, the metric proposed here measures the “integrity” of neurons based on the degree to which a collection of synaptic terminals belonging to a single neuron of the reconstruction can be matched to those of a single neuron in the ground truth data. The metric is largely insensitive to small errors in segmentation and more directly measures accuracy of the generated brain graph. It is our hope that use of the metric will facilitate the broader community's efforts to improve upon existing methods for acquiring brain graphs. Herein we describe the metric in detail, provide demonstrative examples of the intuitive scores it generates, and apply it to a synthesized neural network with simulated reconstruction errors. Demonstration code is available.

We introduce a pair of natural, equivalent models for random threshold graphs and use these models to deduce a variety of properties of random threshold graphs. Specifically, a random threshold graph $G$ is generated by choosing $n$ IID values $x_1,\ldots,x_n$ uniformly in $[0,1]$; distinct vertices $i,j$ of $G$ are adjacent exactly when $x_i + x_j \ge 1$. We examine various properties of random threshold graphs such as chromatic number, algebraic connectivity, and the existence of Hamiltonian cycles and perfect matchings.

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Emerging neuroimaging datasets (collected through modalities such as Electron Microscopy, Calcium Imaging, or X-ray Microtomography) describe the location and properties of neurons and their connections at unprecedented scale, promising new ways of understanding the brain. These modern imaging techniques used to interrogate the brain can quickly accumulate gigabytes to petabytes of structural brain imaging data. Unfortunately, many neuroscience laboratories lack the computational expertise or resources to work with datasets of this size: computer vision tools are often not portable or scalable, and there is considerable difficulty in reproducing results or extending methods. We developed an ecosystem of neuroimaging data analysis pipelines that utilize open source algorithms to create standardized modules and end-to-end optimized approaches. As exemplars we apply our tools to estimate synapse-level connectomes from electron microscopy data and cell distributions from X-ray microtomography data. To facilitate scientific discovery, we propose a generalized processing framework, that connects and extends existing open-source projects to provide large-scale data storage, reproducible algorithms, and workflow execution engines. Our accessible methods and pipelines demonstrate that approaches across multiple neuroimaging experiments can be standardized and applied to diverse datasets. The techniques developed are demonstrated on neuroimaging datasets, but may be applied to similar problems in other domains.

Collective motion in animal groups, such as swarms of insects, flocks of birds, and schools of fish, are some of the most visually striking examples of emergent behavior. Empirical analysis of these behaviors in experiment or computational simulation primarily involves the use of "swarm-averaged" metrics or order parameters such as velocity alignment and angular momentum. Recently, tools from computational topology have been applied to the analysis of swarms to further understand and automate the detection of fundamentally different swarm structures evolving in space and time. Here, we show how the field of graph signal processing can be used to fuse these two approaches by collectively analyzing swarm properties using graph Fourier harmonics that respect the topological structure of the swarm. This graph Fourier analysis reveals hidden structure in a number of common swarming states and forms the basis of a flexible analysis framework for collective motion.

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