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The occurrence and formation of genomic structural variants (SVs) is known to be influenced by the 3D chromatin architecture, but the extent and magnitude have been challenging to study. Here, we apply Hi-C to study chromatin organization before and after induction of chromothripsis in human cells. We use Hi-C to manually assemble the derivative chromosomes following the occurrence of massive complex rearrangements, which allows us to study the sources of SV formation and their consequences on gene regulation. We observe an action–reaction interplay whereby the 3D chromatin architecture directly impacts the location and formation of SVs. In turn, the SVs reshape the chromatin organization to alter the local topologies, replication timing, and gene regulation in cis . We show that SVs have a strong tendency to occur between similar chromatin compartments and replication timing regions. Moreover, we find that SVs frequently occur at 3D loop anchors, that SVs can cause a switch in chromatin compartments and replication timing, and that this is a major source of SV-mediated effects on nearby gene expression changes. Finally, we provide evidence for a general mechanistic bias of the 3D chromatin on SV occurrence using data from more than 2700 patient-derived cancer genomes. 

In various applications within signal processing, system identification, pattern recognition, and scientific computing, the canonical polyadic decomposition (CPD) of a higher-order tensor is only known via general linear measurements. In this paper, we show that the computation of such a CPD can be reformulated as a sum of CPDs with linearly constrained factor matrices by assuming that the measurement matrix can be approximated by a sum of a (small) number of Kronecker products. By properly exploiting the hypothesized structure, we can derive an efficient non-linear least squares algorithm, allowing us to tackle large-scale problems.