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Maps of the nervous system that identify individual cells along with their type, subcellular components, and connectivity have the potential to reveal fundamental organizational principles of neural circuits. Volumetric nanometer-resolution imaging of brain tissue provides the raw data needed to build such maps, but inferring all the relevant cellular and subcellular annotation layers is challenging. Here, we present Segmentation-Guided Contrastive Learning of Representations (“SegCLR”), a self-supervised machine learning technique that produces highly informative representations of cells directly from 3d electron microscope imagery and segmentations. When applied to volumes of human and mouse cerebral cortex, SegCLR enabled the classification of cellular subcompartments (axon, dendrite, soma, astrocytic process) with 4,000-fold less labeled data compared to fully supervised approaches. Surprisingly, SegCLR also enabled inference of cell types (neurons, glia, and subtypes of each) from fragments with lengths as small as 10 micrometers, a task that can be difficult for humans to perform and whose feasibility greatly enhances the utility of imaging portions of brains in which many neuron fragments terminate at a volume boundary. These predictions were further augmented via Gaussian process uncertainty estimation to enable analyses restricted to high confidence subsets of the data. Finally, SegCLR enabled detailed exploration of layer-5 pyramidal cell subtypes and automated large-scale statistical analysis of upstream and downstream synaptic partners in mouse visual cortex.

We acquired a rapidly preserved human surgical sample from the temporal lobe of the cerebral cortex. We stained a 1 mm3 volume with heavy metals, embedded it in resin, cut more than 5000 slices at ∼30 nm and imaged these sections using a high-speed multibeam scanning electron microscope. We used computational methods to render the three-dimensional structure containing 57,216 cells, hundreds of millions of neurites and 133.7 million synaptic connections. The 1.4 petabyte electron microscopy volume, the segmented cells, cell parts, blood vessels, myelin, inhibitory and excitatory synapses, and 104 manually proofread cells are available to peruse online. Many interesting and unusual features were evident in this dataset. Glia outnumbered neurons 2:1 and oligodendrocytes were the most common cell type in the volume. Excitatory spiny neurons comprised 69% of the neuronal population, and excitatory synapses also were in the majority (76%). The synaptic drive onto spiny neurons was biased more strongly toward excitation (70%) than was the case for inhibitory interneurons (48%). Despite incompleteness of the automated segmentation caused by split and merge errors, we could automatically generate (and then validate) connections between most of the excitatory and inhibitory neuron types both within and between layers. In studying these neurons we found that deep layer excitatory cell types can be classified into new subsets, based on structural and connectivity differences, and that chandelier interneurons not only innervate excitatory neuron initial segments as previously described, but also each other’s initial segments. Furthermore, among the thousands of weak connections established on each neuron, there exist rarer highly powerful axonal inputs that establish multi-synaptic contacts (up to ∼20 synapses) with target neurons. Our analysis indicates that these strong inputs are specific, and allow small numbers of axons to have an outsized role in the activity of some of their postsynaptic partners.

Reconstruction of neural circuitry at single-synapse resolution is a key target for improving understanding of the nervous system in health and disease. Serial section transmission electron microscopy (ssTEM) is among the most prolific imaging methods employed in pursuit of such reconstructions. We demonstrate how Flood-Filling Networks (FFNs) can be used to computationally segment a forty-teravoxel whole-brain Drosophila ssTEM volume. To compensate for data irregularities and imperfect global alignment, FFNs were combined with procedures that locally re-align serial sections as well as dynamically adjust and synthesize image content. The proposed approach produced a largely merger-free segmentation of the entire ssTEM Drosophila brain, which we make freely available. As compared to manual tracing using an efficient skeletonization strategy, the segmentation enabled circuit reconstruction and analysis workflows that were an order of magnitude faster.

The neural circuits responsible for animal behavior remain largely unknown. We summarize new methods and present the circuitry of a large fraction of the brain of the fruit fly Drosophila melanogaster. Improved methods include new procedures to prepare, image, align, segment, find synapses in, and proofread such large data sets. We define cell types, refine computational compartments, and provide an exhaustive atlas of cell examples and types, many of them novel. We provide detailed circuits consisting of neurons and their chemical synapses for most of the central brain. We make the data public and simplify access, reducing the effort needed to answer circuit questions, and provide procedures linking the neurons defined by our analysis with genetic reagents. Biologically, we examine distributions of connection strengths, neural motifs on different scales, electrical consequences of compartmentalization, and evidence that maximizing packing density is an important criterion in the evolution of the fly’s brain.

The neural circuits responsible for behavior remain largely unknown. Previous efforts have reconstructed the complete circuits of small animals, with hundreds of neurons, and selected circuits for larger animals. Here we (the FlyEM project at Janelia and collaborators at Google) summarize new methods and present the complete circuitry of a large fraction of the brain of a much more complex animal, the fruit fly Drosophila melanogaster. Improved methods include new procedures to prepare, image, align, segment, find synapses, and proofread such large data sets; new methods that define cell types based on connectivity in addition to morphology; and new methods to simplify access to a large and evolving data set. From the resulting data we derive a better definition of computational compartments and their connections; an exhaustive atlas of cell examples and types, many of them novel; detailed circuits for most of the central brain; and exploration of the statistics and structure of different brain compartments, and the brain as a whole. We make the data public, with a web site and resources specifically designed to make it easy to explore, for all levels of expertise from the expert to the merely curious. The public availability of these data, and the simplified means to access it, dramatically reduces the effort needed to answer typical circuit questions, such as the identity of upstream and downstream neural partners, the circuitry of brain regions, and to link the neurons defined by our analysis with genetic reagents that can be used to study their functions.Note: In the next few weeks, we will release a series of papers with more involved discussions. One paper will detail the hemibrain reconstruction with more extensive analysis and interpretation made possible by this dense connectome. Another paper will explore the central complex, a brain region involved in navigation, motor control, and sleep. A final paper will present insights from the mushroom body, a center of multimodal associative learning in the fly brain.

Recent advances in automatic image segmentation and synapse prediction in electron microscopy (EM) datasets of the brain enable more efficient reconstruction of neural connectivity. In these datasets, a single neuron can span thousands of images containing complex tree-like arbors with thousands of synapses. While image segmentation algorithms excel within narrow fields of views, the algorithms sometimes struggle to correctly segment large neurons, which require large context given their size and complexity. Conversely, humans are comparatively good at reasoning with large objects. In this paper, we introduce several semi-automated strategies that combine 3D visualization and machine guidance to accelerate connectome reconstruction. In particular, we introduce a strategy to quickly correct a segmentation through merging and cleaving, or splitting a segment along supervoxel boundaries, with both operations driven by affinity scores in the underlying segmentation. We deploy these algorithms as streamlined workflows in a tool called Neu3 and demonstrate superior performance compared to prior work, thus enabling efficient reconstruction of much larger datasets. The insights into proofreading from our work clarify the trade-offs to consider when tuning the parameters of image segmentation algorithms.

Reconstruction of neural circuitry at single-synapse resolution is a key target for improving understanding of the nervous system in health and disease. Serial section transmission electron microscopy (ssTEM) is among the most prolific imaging methods employed in pursuit of such reconstructions. We demonstrate how Flood-Filling Networks (FFNs) can be used to computationally segment a forty-teravoxel whole-brain Drosophila ssTEM volume. To compensate for data irregularities and imperfect global alignment, FFNs were combined with procedures that locally re-align serial sections as well as dynamically adjust and synthesize image content. The proposed approach produced a largely merger-free segmentation of the entire ssTEM Drosophila brain, which we make freely available. As compared to manual tracing using an efficient skeletonization strategy, the segmentation enabled circuit reconstruction and analysis workflows that were an order of magnitude faster.

Field inversion in $$\mathbb {F}_{2^{m}}$$F2m dominates the cost of modern software implementations of certain elliptic curve cryptographic operations, such as point encoding/hashing into elliptic curves (Brown et al. in: Submission to NIST, 2008; Brown in: IACR Cryptology ePrint Archive 2008:12, 2008; Aranha et al. in: Cryptology ePrint Archive, Report 2014/486, 2014) Itoh---Tsujii inversion using a polynomial basis and precomputed table-based multi-squaring has been demonstrated to be highly effective for software implementations (Taverne et al. in: CHES 2011, 2011; Oliveira et al. in: J Cryptogr Eng 4(1):3---17, 2014; Aranha et al. in: Cryptology ePrint Archive, Report 2014/486, 2014), but the performance and memory use depend critically on the choice of addition chain and multi-squaring tables, which in prior work have been determined only by suboptimal ad-hoc methods and manual selection. We thoroughly investigated the performance/memory tradeoff for table-based linear transforms used for efficient multi-squaring. Based upon the results of that investigation, we devised a comprehensive cost model for Itoh---Tsujii inversion and a corresponding optimization procedure that is empirically fast and provably finds globally-optimal solutions. We tested this method on eight binary fields commonly used for elliptic curve cryptography; our method found lower-cost solutions than the ad-hoc methods used previously, and for the first time enables a principled exploration of the time/memory tradeoff of inversion implementations.

Reconstruction of neural circuits from volume electron microscopy data requires the tracing of cells in their entirety, including all their neurites. Automated approaches have been developed for tracing, but their error rates are too high to generate reliable circuit diagrams without extensive human proofreading. We present flood-filling networks, a method for automated segmentation that, similar to most previous efforts, uses convolutional neural networks, but contains in addition a recurrent pathway that allows the iterative optimization and extension of individual neuronal processes. We used flood-filling networks to trace neurons in a dataset obtained by serial block-face electron microscopy of a zebra finch brain. Using our method, we achieved a mean error-free neurite path length of 1.1 mm, and we observed only four mergers in a test set with a path length of 97 mm. The performance of flood-filling networks was an order of magnitude better than that of previous approaches applied to this dataset, although with substantially increased computational costs.

A homomorphic, or incremental, multiset hash function, associates a hash value to arbitrary collections of objects (with possible repetitions) in such a way that the hash of the union of two collections is easy to compute from the hashes of the two collections themselves: it is simply their sum under a suitable group operation. In particular, hash values of large collections can be computed incrementally and/or in parallel. Homomorphic hashing is thus a very useful primitive with applications ranging from database integrity verification to streaming set/multiset comparison and network coding. Unfortunately, constructions of homomorphic hash functions in the literature are hampered by two main drawbacks: they tend to be much longer than usual hash functions at the same security level (e.g. to achieve a collision resistance of 2^128, they are several thousand bits long, as opposed to 256 bits for usual hash functions), and they are also quite slow. In this paper, we introduce the Elliptic Curve Multiset Hash (ECMH), which combines a usual bit string-valued hash function like BLAKE2 with an efficient encoding into binary elliptic curves to overcome both difficulties. On the one hand, the size of ECMH digests is essentially optimal: 2m-bit hash values provide O(2^m) collision resistance. On the other hand, we demonstrate a highly-efficient software implementation of ECMH, which our thorough empirical evaluation shows to be capable of processing over 3 million set elements per second on a 4 GHz Intel Haswell machine at the 128-bit security level---many times faster than previous practical methods., Implementation available on https://github.com/jbms/ecmh

Investigations of biological ultrastructure, such as comprehensive mapping of connections within a nervous system, increasingly rely on large, high-resolution electron microscopy (EM) image volumes. However, discontinuities between the registered section images from which these volumes are assembled, due to variations in imaging conditions and section thickness, among other artifacts, impede truly 3-D analysis of these volumes. We propose an optimization procedure, called EMISAC (EM Image Stack Artifact Correction), to correct these discontinuities. EMISAC optimizes the parameters of spatially varying linear transformations of the data in order to minimize the squared norm of the gradient along the section axis, subject to detail-preserving regularization.