The wiring diagram of the mouse brain has recently been mapped at a mesoscopic scale in the Allen Mouse Brain Connectivity Atlas. Axonal projections from brain regions were traced using green fluoresent proteins. The resulting data were registered to a common three-dimensional reference space. They yielded a matrix of connection strengths between 213 brain regions. Global features such as closed loops formed by connections of similar intensity can be inferred using tools from persistent homology. We map the wiring diagram of the mouse brain to a simplicial complex (filtered by connection strengths). We work out generators of the first homology group. Some regions, including nucleus accumbens, are connected to the entire brain by loops, whereas no region has non-zero connection strength to all brain regions. Thousands of loops go through the isocortex, the striatum and the thalamus. On the other hand, medulla is the only major brain compartment that contains more than 100 loops.
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