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The augmented Bergman complex of a matroid is a simplicial complex introduced recently in work of Braden, Huh, Matherne, Proudfoot and Wang.  It may be viewed as a hybrid of two well-studied pure shellable simplicial complexes associated to matroids: the independent set complex and Bergman complex. It is shown here that the augmented Bergman complex is also shellable, via two different families of shelling orders.  Furthermore, comparing the description of its homotopy type induced from the two shellings re-interprets a known convolution formula counting bases of the matroid. The representation of the automorphism group of the matroid on the homology of the augmented Bergman complex turns out to have a surprisingly simple description. This last fact is generalized to closures beyond those coming from a matroid. 

The past decade has witnessed the rapid development of real-time wireless technologies and their wide adoption in various industrial Internet-of-Things (IIoT) applications. Among those wireless technologies, 6TiSCH is a promising candidate as the de facto standard due to its nice feature of gluing a real-time link-layer standard (802.15.4e, for offering deterministic communication performance) together with an IP-enabled upper-layer stack (for seamlessly supporting Internet services). 6TiSCH's built-in random slot selection scheduling algorithm, however, often leads to large and unbounded transmission latency, thus can hardly meet the real-time requirements of IIoT applications. This paper proposes an adaptive partition based scheduling framework, APaS, for 6TiSCH networks. APaS introduces the concept of resource partitioning into 6TiSCH network management. Instead of allocating network resources to individual devices, APaS partitions and assigns network resources to different groups of devices based on their layers in the network so as to guarantee that the transmission latency of any end-toend flow is within one slotframe length. APaS also employs a novel online partition adjustment method to further improve its adaptability to dynamic network topology changes. The effectiveness of APaS is validated through both simulation and testbed experiments on a 122-node multi-hop 6TiSCH network. 

Materials with giant spin splitting are desired for spintronic applications. The fabrications of spintronic devices from half metals with one spin direction are often hampered, however, by stray magnetic fields, domain walls, short spin coherence times, scattering on magnetic atoms or magnetically active interfaces, and other characteristics that come along with the magnetism. The surfaces of topological insulators, or Dirac/Weyl semimetals, could be an alternative, but production of high‐quality thin films without the presence of the bulk states at the Fermi energy remains very challenging. Here, by utilizing angle‐resolved photoemission spectroscopy, a record‐high Dresselhaus spin–orbit splitting of the bulk state in the nonmagnetic IrBiSe is found. The band structure calculations indicate that the splitting band is fully spin‐polarized with 3D chiral spin texture. As a source of spin‐polarized electrons, lightly doped IrBiSe is expected to generate electric‐field‐controlled spin‐polarized currents, free from back scattering, and could host triplet and Fulde–Ferrel–Larkin–Ovchinnikov (FFLO) superconductivity.