The purpose of the GraphBLAS Forum is to stan- dardize linear-algebraic building blocks for graph computations. An important part of this standardization effort is to translate the mathematical specification into an actual Application Programming Interface (API) that (i) is faithful to the mathematics and (ii) enables efficient implementations on modern hardware. This paper documents the approach taken by the C language specification subcommittee and presents the main concepts, constructs, and objects within the GraphBLAS API. Use of the API is illustrated by showing an implementation of the betweenness centrality algorithm.

The GraphBLAS C specification provisional release 1.0 is complete. To manage the scope of the project, we had to defer important functionality to a future version of the specification.  For example, we are well aware that many algorithms benefit from an inspector-executor execution strategy.  We also know that users would benefit from a number of standard predefined semirings as well as more general user-defined types. These and other features are described in this paper in the context of a future release of the GraphBLAS C API.

Sparse times dense matrix multiplication (SpMM) finds its applications in well-established fields such as computational linear algebra as well as emerging fields such as graph neural networks. In this study, we evaluate the performance of various techniques for performing SpMM as a distributed computation across many nodes by focusing on GPU accelerators. We examine how the actual local computational performance of state-of-the-art SpMM implementations affect computational efficiency as dimensions change when we scale to large numbers of nodes, which proves to be an unexpectedly important bottleneck. We consider various distribution strategies, including A-Stationary, B-Stationary, and C-Stationary algorithms, 1.5D and 2D algorithms, and RDMA-based and bulk synchronous methods of data transfer. Our results show that the best choice of algorithm and implementation technique depends not only on the cost of communication for particular matrix sizes and dimensions, but also on the performance of local SpMM operations. Our evaluations reveal that with the involvement of GPU accelerators, the best design choices for SpMM differ from the conventional algorithms that are known to perform well for dense matrix-matrix or sparse matrix-sparse matrix multiplies.

The GraphBLAS standard (GraphBlas.org) is being developed to bring the potential of matrix-based graph algorithms to the broadest possible audience. Mathematically, the GraphBLAS defines a core set of matrix-based graph operations that can be used to implement a wide class of graph algorithms in a wide range of programming environments. This paper provides an introduction to the mathematics of the GraphBLAS. Graphs represent connections between vertices with edges. Matrices can represent a wide range of graphs using adjacency matrices or incidence matrices. Adjacency matrices are often easier to analyze while incidence matrices are often better for representing data. Fortunately, the two are easily connected by matrix multiplication. A key feature of matrix mathematics is that a very small number of matrix operations can be used to manipulate a very wide range of graphs. This composability of a small number of operations is the foundation of the GraphBLAS. A standard such as the GraphBLAS can only be effective if it has low performance overhead. Performance measurements of prototype GraphBLAS implementations indicate that the overhead is low.

The epilepsies are commonly accompanied by widespread abnormalities in cerebral white matter. ENIGMA-Epilepsy is a large quantitative brain imaging consortium, aggregating data to investigate patterns of neuroimaging abnormalities in common epilepsy syndromes, including temporal lobe epilepsy, extratemporal epilepsy, and genetic generalized epilepsy. Our goal was to rank the most robust white matter microstructural differences across and within syndromes in a multicentre sample of adult epilepsy patients. Diffusion-weighted MRI data were analysed from 1069 healthy controls and 1249 patients: temporal lobe epilepsy with hippocampal sclerosis (n = 599), temporal lobe epilepsy with normal MRI (n = 275), genetic generalized epilepsy (n = 182) and non-lesional extratemporal epilepsy (n = 193). A harmonized protocol using tract-based spatial statistics was used to derive skeletonized maps of fractional anisotropy and mean diffusivity for each participant, and fibre tracts were segmented using a diffusion MRI atlas. Data were harmonized to correct for scanner-specific variations in diffusion measures using a batch-effect correction tool (ComBat). Analyses of covariance, adjusting for age and sex, examined differences between each epilepsy syndrome and controls for each white matter tract (Bonferroni corrected at P < 0.001). Across 'all epilepsies' lower fractional anisotropy was observed in most fibre tracts with small to medium effect sizes, especially in the corpus callosum, cingulum and external capsule. There were also less robust increases in mean diffusivity. Syndrome-specific fractional anisotropy and mean diffusivity differences were most pronounced in patients with hippocampal sclerosis in the ipsilateral parahippocampal cingulum and external capsule, with smaller effects across most other tracts. Individuals with temporal lobe epilepsy and normal MRI showed a similar pattern of greater ipsilateral than contralateral abnormalities, but less marked than those in patients with hippocampal sclerosis. Patients with generalized and extratemporal epilepsies had pronounced reductions in fractional anisotropy in the corpus callosum, corona radiata and external capsule, and increased mean diffusivity of the anterior corona radiata. Earlier age of seizure onset and longer disease duration were associated with a greater extent of diffusion abnormalities in patients with hippocampal sclerosis. We demonstrate microstructural abnormalities across major association, commissural, and projection fibres in a large multicentre study of epilepsy. Overall, patients with epilepsy showed white matter abnormalities in the corpus callosum, cingulum and external capsule, with differing severity across epilepsy syndromes. These data further define the spectrum of white matter abnormalities in common epilepsy syndromes, yielding more detailed insights into pathological substrates that may explain cognitive and psychiatric co-morbidities and be used to guide biomarker studies of treatment outcomes and/or genetic research.

Epilepsy is a common and serious neurological disorder, with many different constituent conditions characterized by their electro clinical, imaging, and genetic features. MRI has been fundamental in advancing our understanding of brain processes in the epilepsies. Smaller-scale studies have identified many interesting imaging phenomena, with implications both for understanding pathophysiology and improving clinical care. Through the infrastructure and concepts now well-established by the ENIGMA Consortium, ENIGMA-Epilepsy was established to strengthen epilepsy neuroscience by greatly increasing sample sizes, leveraging ideas and methods established in other ENIGMA projects, and generating a body of collaborating scientists and clinicians to drive forward robust research. Here we review published, current, and future projects, that include structural MRI, diffusion tensor imaging (DTI), and resting state functional MRI (rsfMRI), and that employ advanced methods including structural covariance, and event-based modeling analysis. We explore age of onset- and duration-related features, as well as phenomena-specific work focusing on particular epilepsy syndromes or phenotypes, multimodal analyses focused on understanding the biology of disease progression, and deep learning approaches. We encourage groups who may be interested in participating to make contact to further grow and develop ENIGMA-Epilepsy.

The problem of poor reproducibility of scientific findings has received much attention over recent years, in a variety of fields including psychology and neuroscience. The problem has been partly attributed to publication bias and unwanted practices such as p-hacking. Low statistical power in individual studies is also understood to be an important factor. In a recent multisite collaborative study, we mapped brain anatomical left-right asymmetries for regional measures of surface area and cortical thickness, in 99 MRI datasets from around the world, for a total of over 17,000 participants. In the present study, we revisited these hemispheric effects from the perspective of reproducibility. Within each dataset, we considered that an effect had been reproduced when it matched the meta-analytic effect from the 98 other datasets, in terms of effect direction and significance threshold. In this sense, the results within each dataset were viewed as coming from separate studies in an "ideal publishing environment," that is, free from selective reporting and p hacking. We found an average reproducibility rate of 63.2% (SD = 22.9%, min = 22.2%, max = 97.0%). As expected, reproducibility was higher for larger effects and in larger datasets. Reproducibility was not obviously related to the age of participants, scanner field strength, FreeSurfer software version, cortical regional measurement reliability, or regional size. These findings constitute an empirical illustration of reproducibility in the absence of publication bias or p hacking, when assessing realistic biological effects in heterogeneous neuroscience data, and given typically-used sample sizes.

Hemispheric asymmetry is a cardinal feature of human brain organization. Altered brain asymmetry has also been linked to some cognitive and neuropsychiatric disorders. Here, the ENIGMA (Enhancing NeuroImaging Genetics through Meta-Analysis) Consortium presents the largest-ever analysis of cerebral cortical asymmetry and its variability across individuals. Cortical thickness and surface area were assessed in MRI scans of 17,141 healthy individuals from 99 datasets worldwide. Results revealed widespread asymmetries at both hemispheric and regional levels, with a generally thicker cortex but smaller surface area in the left hemisphere relative to the right. Regionally, asymmetries of cortical thickness and/or surface area were found in the inferior frontal gyrus, transverse temporal gyrus, parahippocampal gyrus, and entorhinal cortex. These regions are involved in lateralized functions, including language and visuospatial processing. In addition to population-level asymmetries, variability in brain asymmetry was related to sex, age, and intracranial volume. Interestingly, we did not find significant associations between asymmetries and handedness. Finally, with two independent pedigree datasets (n = 1,443 and 1,113, respectively), we found several asymmetries showing significant, replicable heritability. The structural asymmetries identified and their variabilities and heritability provide a reference resource for future studies on the genetic basis of brain asymmetry and altered laterality in cognitive, neurological, and psychiatric disorders.

The cerebral cortex underlies our complex cognitive capabilities, yet little is known about the specific genetic loci that influence human cortical structure. To identify genetic variants that affect cortical structure, we conducted a genome-wide association meta-analysis of brain magnetic resonance imaging data from 51,665 individuals. We analyzed the surface area and average thickness of the whole cortex and 34 regions with known functional specializations. We identified 199 significant loci and found significant enrichment for loci influencing total surface area within regulatory elements that are active during prenatal cortical development, supporting the radial unit hypothesis. Loci that affect regional surface area cluster near genes in Wnt signaling pathways, which influence progenitor expansion and areal identity. Variation in cortical structure is genetically correlated with cognitive function, Parkinson's disease, insomnia, depression, neuroticism, and attention deficit hyperactivity disorder.