Real-space Formalism for the Euler Class and Fragile Topology in Quasicrystals and Amorphous Lattices

We propose a real-space formalism of the topological Euler class, which characterizes the fragile topology of two-dimensional systems with real wave functions. This real-space description is characterized by local Euler markers whose macroscopic average coincides with the Euler number, and it applies equally well to periodic and open boundary conditions for both crystals and noncrystalline systems. We validate this by diagnosing topological phase transitions in clean and disordered crystalline systems with the reality endowed by the space-time inversion symmetry $\mathcal{I}_{ST}$. Furthermore, we demonstrated the topological Euler phases in quasicrystals and even in amorphous lattices lacking any spatial symmetries. Our work not only provides a local characterization of the fragile topology but also significantly extends its territory beyond $\mathcal{I}_{ST}$-symmetric crystalline materials.Comment: 41 pages,8 figure

Metamaterial Broadband Angular Selectivity

We demonstrate how broadband angular selectivity can be achieved with stacks of one-dimensionally periodic photonic crystals, each consisting of alternating isotropic layers and effective anisotropic layers, where each effective anisotropic layer is constructed from a multilayered metamaterial. We show that by simply changing the structure of the metamaterials, the selective angle can be tuned to a broad range of angles; and, by increasing the number of stacks, the angular transmission window can be made as narrow as desired. As a proof of principle, we realize the idea experimentally in the microwave regime. The angular selectivity and tunability we report here can have various applications such as in directional control of electromagnetic emitters and detectors.Comment: 5 pages, 5 figure

EVMP: enhancing machine learning models for synthetic promoter strength prediction by Extended Vision Mutant Priority framework

IntroductionIn metabolic engineering and synthetic biology applications, promoters with appropriate strengths are critical. However, it is time-consuming and laborious to annotate promoter strength by experiments. Nowadays, constructing mutation-based synthetic promoter libraries that span multiple orders of magnitude of promoter strength is receiving increasing attention. A number of machine learning (ML) methods are applied to synthetic promoter strength prediction, but existing models are limited by the excessive proximity between synthetic promoters.MethodsIn order to enhance ML models to better predict the synthetic promoter strength, we propose EVMP(Extended Vision Mutant Priority), a universal framework which utilize mutation information more effectively. In EVMP, synthetic promoters are equivalently transformed into base promoter and corresponding k-mer mutations, which are input into BaseEncoder and VarEncoder, respectively. EVMP also provides optional data augmentation, which generates multiple copies of the data by selecting different base promoters for the same synthetic promoter.ResultsIn Trc synthetic promoter library, EVMP was applied to multiple ML models and the model effect was enhanced to varying extents, up to 61.30% (MAE), while the SOTA(state-of-the-art) record was improved by 15.25% (MAE) and 4.03% (R2). Data augmentation based on multiple base promoters further improved the model performance by 17.95% (MAE) and 7.25% (R2) compared with non-EVMP SOTA record.DiscussionIn further study, extended vision (or k-mer) is shown to be essential for EVMP. We also found that EVMP can alleviate the over-smoothing phenomenon, which may contributes to its effectiveness. Our work suggests that EVMP can highlight the mutation information of synthetic promoters and significantly improve the prediction accuracy of strength. The source code is publicly available on GitHub: https://github.com/Tiny-Snow/EVMP