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Previous evolutionary models of duplicate gene evolution have overlooked the pivotal role of genome architecture. Here, we show that proximity-based regulatory recruitment by distally duplicated genes is an efficient mechanism for modulating tissue-specific production of preexisting proteins. By leveraging genomic asymmetries, we performed a coexpression analysis onDrosophila melanogastertissue data to show the generality of enhancer capture-divergence (ECD) as a significant evolutionary driver of asymmetric, distally duplicated genes. We use the recently evolved geneHP6/Umbreaas an example of the ECD process. By assaying genome-wide chromosomal conformations in multipleDrosophilaspecies, we show thatHP6/Umbreawas inserted near a preexisting, long-distance three-dimensional genomic interaction. We then use this data to identify a newly found enhancer (FLEE1), buried within the coding region of the highly conserved, essential geneMFS18, that likely neofunctionalizedHP6/Umbrea. Last, we demonstrate ancestral transcriptional coregulation ofHP6/Umbrea’s future insertion site, illustrating how enhancer capture provides a highly evolvable, one-step solution to Ohno’s dilemma. 

Abstract We investigate the symmetries of the so-called generalized extended Cantero–Moral–Velázquez (CMV) matrices. It is well-documented that problems involving reflection symmetries of standard extended CMV matrices can be subtle. We show how to deal with this in an elegant fashion by passing to the class of generalized extended CMV matrices via explicit diagonal unitaries in the spirit of Cantero–Grünbaum–Moral–Velázquez. As an application of these ideas, we construct an explicit family of almost-periodic CMV matrices, which we call the mosaic unitary almost-Mathieu operator, and prove the occurrence of exact mobility edges. That is, we show the existence of energies that separate spectral regions with absolutely continuous and pure point spectrum and exactly calculate them. 

We show that reactive molecules with a unit probability of reaction naturally provide a simulator of some intriguing black hole physics. The unit reaction at the short distance acts as an event horizon and delivers a one-way traffic for matter waves passing through the potential barrier when two molecules interact by high partial-wave scatterings or dipole-dipole interactions. In particular, the scattering rate as a function of the incident energy exhibits a thermal-like distribution near the maximum of the interaction energy in the same manner as a scalar field scatters with the potential barrier outside the event horizon of a black hole. Such a thermal-like scattering can be extracted from the temperature-dependent two-body loss rate measured in experiments on KRb and other molecules. 

We consider standard and extended CMV matrices with small quasi-periodic Verblunsky coefficients and show that on their essential spectrum, all spectral measures are purely absolutely continuous. This answers a question of Barry Simon from 2005.