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3D genomics methods such as Hi-C and Micro-C have uncovered chromatin loops across the genome and linked these loops to gene regulation. However, these methods only measure 3D interaction probabilities on a relative scale. Here, we overcome this limitation by using live imaging data to calibrate Micro-C in mouse embryonic stem cells, thus obtaining absolute looping probabilities for 36,804 chromatin loops across the genome. We find that the looped state is generally rare, with a mean probability of 2.3% and a maximum of 26% across the quantified loops. On average, CTCF-CTCF loops are stronger than loops between cis-regulatory elements (3.2% vs. 1.1%). Our findings can be extended to human stem cells and differentiated cells under certain assumptions. Overall, we establish an approach for genome-wide absolute loop quantification and report that loops generally occur with low probabilities, generalizing recent live imaging results to the whole genome. 

Discrete subfactors include a particular class of infinite index subfactors and all finite index ones. A discrete subfactor is called local when it is braided and it fulfills a commutativity condition motivated by the study of inclusion of Quantum Field Theories in the algebraic Haag–Kastler setting. In Bischoff et al. (J Funct Anal 281(1):109004, 2021), we proved that every irreducible local discrete subfactor arises as the fixed point subfactor under the action of a canonical compact hypergroup. In this work, we prove a Galois correspondence between intermediate von Neumann algebras and closed subhypergroups, and we study the subfactor theoretical Fourier transform in this context. Along the way, we extend the main results concerning 𝛼-induction and 𝜎-restriction for braided subfactors previously known in the finite index case.