A mapping α:V(G)→V(H) from the vertex set of one graph G to another graph H is an isometric embedding if the shortest path distance between any two vertices in G equals the distance between their images in H. Here, we consider isometric embeddings of a weighted graph G into unweighted Hamming graphs, called Hamming embeddings, when G satisfies the property that every edge is a shortest path between its endpoints. Using a Cartesian product decomposition of G called its canonical isometric representation, we show that every Hamming embedding of G may be partitioned into a canonical partition, whose parts provide Hamming embeddings for each factor of the canonical isometric representation of G. This implies that G permits a Hamming embedding if and only if each factor of its canonical isometric representation is Hamming embeddable. This result extends prior work on unweighted graphs that showed that an unweighted graph permits a Hamming embedding if and only if each factor is a complete graph. When a graph G has nontrivial isometric representation, determining whether G has a Hamming embedding can be simplified to checking embeddability of two or more smaller graphs.

MOTIVATION: The study of T cell receptor (TCR) repertoires has generated new insights into immune system recognition. However, the ability to robustly characterize these populations has been limited by technical barriers and an inability to reliably infer heterodimeric chain pairings for TCRs. RESULTS: Here, we describe a novel analytical approach to an emerging immune repertoire sequencing method, improving the resolving power of this low-cost technology. This method relies upon the distribution of a T cell population across a 96-well plate, followed by barcoding and sequencing of the relevant transcripts from each T cell. Multicell Analytical Deconvolution for High Yield Paired-chain Evaluation (MAD-HYPE) uses Bayesian inference to more accurately extract TCR information, improving our ability to study and characterize T cell populations for immunology and immunotherapy applications. AVAILABILITY AND IMPLEMENTATION: The MAD-HYPE algorithm is released as an open-source project under the Apache License and is available from https://github.com/birnbaumlab/MAD-HYPE. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Neuronal synapses transmit electrochemical signals between cells through the coordinated action of presynaptic vesicles, ion channels, scaffolding and adapter proteins, and membrane receptors. In situ structural characterization of numerous synaptic proteins simultaneously through multiplexed imaging facilitates a bottom-up approach to synapse classification and phenotypic description. Objective automation of efficient and reliable synapse detection within these datasets is essential for the high-throughput investigation of synaptic features. Convolutional neural networks can solve this generalized problem of synapse detection, however, these architectures require large numbers of training examples to optimize their thousands of parameters. We propose DoGNet, a neural network architecture that closes the gap between classical computer vision blob detectors, such as Difference of Gaussians (DoG) filters, and modern convolutional networks. DoGNet is optimized to analyze highly multiplexed microscopy data. Its small number of training parameters allows DoGNet to be trained with few examples, which facilitates its application to new datasets without overfitting. We evaluate the method on multiplexed fluorescence imaging data from both primary mouse neuronal cultures and mouse cortex tissue slices. We show that DoGNet outperforms convolutional networks with a low-to-moderate number of training examples, and DoGNet is efficiently transferred between datasets collected from separate research groups. DoGNet synapse localizations can then be used to guide the segmentation of individual synaptic protein locations and spatial extents, revealing their spatial organization and relative abundances within individual synapses. The source code is publicly available: https://github.com/kulikovv/dognet.