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Motivated by the study of the growth rate of the number of geodesics in flat surfaces with bounded lengths, we study generalizations of such problems for K3 surfaces. In one gener- alization, we give a result regarding the upper bound on the asymptotics of the number of classes of irreducible special Lagrangians in K3 surfaces with bounded period integrals. In another generalization, we give the exact leading term in the asymptotics of the number of Mukai vectors of semistable coherent sheaves on algebraic K3 surfaces with bounded central charges, with respect to generic Bridgeland stability conditions. 

Building on the base of the existing telescopes of the Event Horizon Telescope (EHT) and ALMA, the next-generation EHT (ngEHT) aspires to deploy ∼10 more stations. The ngEHT targets an angular resolution of ∼15 microarcseconds. This resolution is achieved using Very Long Baseline Interferometry (VLBI) at the shortest radio wavelengths ∼1 mm. The Submillimeter Array (SMA) is both a standalone radio interferometer and a station of the EHT and will conduct observations together with the new ngEHT stations. The future EHT + ngEHT array requires a dedicated correlator to process massive amounts of data. The current correlator-beamformer (CBF) of the SMA would also benefit from an upgrade, to expand the SMA’s bandwidth and also match the EHT + ngEHT observations. The two correlators share the same basic architecture, so that the development time can be reduced using common technology for both applications. This paper explores the prospects of using Tensor Core Graphics Processing Units (TC GPU) as the primary digital signal processing (DSP) engine. This paper describes the architecture, aspects of the detailed design, and approaches to performance optimization of a CBF using the “FX” approach. We describe some of the benefits and challenges of the TC GPU approach. 

Supramolecular nanocages with inner cavities have attracted increasing attention due to their fascinating molecular aesthetics and vast number of potential applications. Even though a wide array of discrete supramolecular cages with precisely designed sizes and shapes have been established, the controlled assembly of higher-order supramolecular frameworks from discrete molecular entities still represents a formidable challenge. In this work, a novel metallo-organic cage [Zn12L4] was assembled based on a triphenylene-cored hexapod terpyridine ligand. Synchotron X-ray analysis revealed a pair of enantiomeric cages in the crystal with flexible ligands twisted clockwise or anticlockwise due to steric hindrance in the structure. Interestingly, due to the strong π–π intermolecular interaction between triphenylene units, a controlled hierarchical packing of sphere-like cages in the crystal was established having a sparse packing mode with huge channels of around 3.6 nm diameter. This research sheds light on the design of strong π–π interactions in supramolecular hierarchical packing and materials science.