This paper studies an optimization problem on the sum of traces of matrix quadratic forms in m semiorthogonal matrices, which can be considered as a generalization of the synchronization of rotations. While the problem is nonconvex, this paper shows that its semidefinite programming relaxation solves the original nonconvex problems exactly with high probability under an additive noise model with small noise in the order of O(m^1/4). In addition, it shows that, with high probability, the sufficient condition for global optimality considered in Won, Zhou, and Lange [SIAM J. Matrix Anal. Appl., 2 (2021), pp. 859-882] is also necessary under a similar small noise condition. These results can be considered as a generalization of existing results on phase synchronization.

Crystalline polymers have attracted significant interest in recent years due to their enhanced mechanical and thermal properties. As one type of organic-inorganic hybrid polymer crystals, polysilsesquioxane can be synthesized by large-scale and inexpensive so-gel processes with two precursors. In this paper, both octylene-bridged and hexylene-bridged PSQ crystals are characterized with infrared spectroscopy and X-ray crystallography to reveal their super high crystallinity. To study the thermal transport in these unique polymer crystals, we use a suspended micro thermal device to examine their thermal properties from 20 K to 320 K, and demonstrate their tunable thermal conductivity by varying the length of alkyl chains. We also conduct non-equilibrium molecular dynamics simulations to study the phonon behaviors across the hydrogen bond interface. The simulation results demonstrate good agreement with the experimental results regarding both the value and trend of the PSQ thermal conductivity. Furthermore, from the simulation, we find that the anharmonic phonon scattering and interfacial anharmnic coupling effects across the hydrogen bond interface may explain the experimentally observed thermal properties.

Multilayered hard coatings with a CrN matrix and an Al₂O₃, TiO₂, or nanolaminate-Al₂O₃/TiO₂ sealing layer were designed by a hybrid deposition process combined with physical vapor deposition (PVD) and atomic layer deposition (ALD). The strategy was to utilize ALD thin films as pinhole-free barriers to seal the intrinsic defects to protect the CrN matrix. The influences of the different sealing layers added in the coatings on the microstructure, surface roughness, and corrosion behaviors were investigated. The results indicated that the sealing layer added by ALD significantly decreased the average grain size and improved the corrosion resistance of the CrN coatings. The insertion of the nanolaminate-Al₂O₃/TiO₂ sealing layers resulted in a further increase in corrosion resistance, which was attributed to the synergistic effect of Al₂O₃ and TiO₂, both acting as excellent passivation barriers to the diffusion of corrosive substances.

Regulatory T (Treg) cells are potent suppressors that maintain immune homeostasis. Accumulation of Treg can inhibit effective immune responses in cancer patients, leading to tumor development and progression. Despite direct cytotoxicity, several chemotherapeutic drugs have been reported to deplete Treg cells for better prognosis for cancer patients. Treg cells are a heterogenous population with at least three different subsets, nonsuppressive, resting, and activated Treg cells. However, the characteristics of Treg cell subsets in lung cancer patients and how chemotherapy affects Treg cells remain elusive. In this study, we first analyzed Treg cell subsets in peripheral blood samples from 40 nonsmall cell lung cancer (NSCLC) patients and 20 healthy donors. Treg cells, specifically activated Treg cell subset, significantly increased in patients with NSCLC. Compared to nonsuppressive Treg cells, activated Treg cells expressed higher level of CD39 and predominantly produced inhibitory cytokines. In vitro assay showed that docetaxel reduced all three subsets of Treg cells. More importantly, we found docetaxel-based chemotherapy significantly decreased all three Treg subsets after 4 cycles of treatment in 17 NSCLC patients. Taken together, this study revealed dynamic changes of various Treg cell subsets in NSCLC patients before and after chemotherapy, providing activated Treg cells as a potential target for chemotherapy.

Graphene has demonstrated great potential in new-generation electronic applications due to its unique electronic properties such as large carrier Fermi velocity, ultrahigh carrier mobility, and high material stability. Interestingly, the electronic structures can be further engineered in multilayer graphene by the introduction of a twist angle between different layers to create van Hove singularities (vHSs) at adjustable binding energy. In this work, using angle-resolved photoemission spectroscopy with sub-micrometer spatial resolution, the band structures and their evolution are systematically studied with twist angle in bilayer and trilayer graphene sheets. A doping effect is directly observed in graphene multilayer system as well as vHSs in bilayer graphene over a wide range of twist angles (from 5° to 31°) with wide tunable energy range over 2 eV. In addition, the formation of multiple vHSs (at different binding energies) is also observed in trilayer graphene. The large tuning range of vHS binding energy in twisted multilayer graphene provides a promising material base for optoelectrical applications with broadband wavelength selectivity from the infrared to the ultraviolet regime, as demonstrated by an example application of wavelength selective photodetector.