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A b-matching is a subset of edges M such that at most b(v) edges in M are incident on each vertex v, where b(v) is specified. We present a distributed-memory parallel algorithm, \bsuitor, that computes a b-matching with more than half the maximum weight in a graph with weights on the edges. The approximation algorithm is designed to have high concurrency and low time complexity. We organize the implementation of the algorithm in terms of asynchronous super-steps that combine computation and communication, and balance the computational work and frequency of communication to obtain high performance. Since the performance of the b-suitor algorithm is strongly influenced by communication, we present several strategies to reduce the communication volume. We implement the algorithm using a hybrid strategy where inter-node communication uses MPI and intra-node computation is done with OpenMP threads. We demonstrate strong and weak scaling of b-suitor up to 16,000 processors on two supercomputers at NERSC. We compute a b-matching in a graph with 2 billion edges in under 4 seconds using 16,000 processors. 

Functional magnetic resonance imaging (fMRI) offers a rich source of data for studying the neural basis of cognition. Here, we describe the Brain Imaging Analysis Kit (BrainIAK), an open-source, free Python package that provides computationally optimized solutions to key problems in advanced fMRI analysis. A variety of techniques are presently included in BrainIAK: intersubject correlation (ISC) and intersubject functional connectivity (ISFC), functional alignment via the shared response model (SRM), full correlation matrix analysis (FCMA), a Bayesian version of representational similarity analysis (BRSA), event segmentation using hidden Markov models, topographic factor analysis (TFA), inverted encoding models (IEMs), an fMRI data simulator that uses noise characteristics from real data (fmrisim), and some emerging methods. These techniques have been optimized to leverage the efficiencies of high-performance compute (HPC) clusters, and the same code can be seamlessly transferred from a laptop to a cluster. For each of the aforementioned techniques, we describe the data analysis problem that the technique is meant to solve and how it solves that problem; we also include an example Jupyter notebook for each technique and an annotated bibliography of papers that have used and/or described that technique. In addition to the sections describing various analysis techniques in BrainIAK, we have included sections describing the future applications of BrainIAK to real-time fMRI, tutorials that we have developed and shared online to facilitate learning the techniques in BrainIAK, computational innovations in BrainIAK, and how to contribute to BrainIAK. We hope that this manuscript helps readers to understand how BrainIAK might be useful in their research.