Linear-quadratic Mean Field Control with Non-convex Data

In this manuscript, we study a class of linear-quadratic (LQ) mean field control problems with a common noise and their corresponding $N$-particle systems. The mean field control problems considered are not standard LQ mean field control problems in the sense that their dependence on the mean field terms can be non-linear and non-convex. Therefore, all the existing methods to deal with LQ mean field control problems fail. The key idea to solve our LQ mean field control problem is to utilize the common noise. We first prove the global well-posedness of the corresponding Hamilton-Jacobi equations via the non-degeneracy of the common noise. In contrast to the LQ mean field games master equations, the Hamilton-Jacobi equations for the LQ mean field control problems can not be reduced to finite-dimensional PDEs. We then globally solve the Hamilton-Jacobi equations for $N$-particle systems. As byproducts, we derive the optimal quantitative convergence results from the $N$-particle systems to the mean field control problem and the propagation of chaos property for the related optimal trajectories. This paper extends the results in [{\sc M. Li, C. Mou, Z. Wu and C. Zhou}, \emph{Trans. Amer. Math. Soc.}, 376(06) (2023), pp.~4105--4143] to the LQ mean field control problems.Comment: 35 page

Pressure induced superconductivity bordering a charge-density-wave state in NbTe4 with strong spinorbit coupling

Transition-metal chalcogenides host various phases of matter, such as charge-density wave (CDW), superconductors, and topological insulators or semimetals. Superconductivity and its competition with CDW in low-dimensional compounds have attracted much interest and stimulated considerable research. Here we report pressure induced superconductivity in a strong spin-orbit (SO) coupled quasi-one-dimensional (1D) transition-metal chalcogenide NbTe$_4$, which is a CDW material under ambient pressure. With increasing pressure, the CDW transition temperature is gradually suppressed, and superconducting transition, which is fingerprinted by a steep resistivity drop, emerges at pressures above 12.4 GPa. Under pressure $p$ = 69 GPa, zero resistance is detected with a transition temperature $T_c$ = 2.2 K and an upper critical field $H_{c2}$= 2 T. We also find large magnetoresistance (MR) up to 102\% at low temperatures, which is a distinct feature differentiating NbTe$_4$ from other conventional CDW materials.Comment: https://rdcu.be/LX8

Observation of Bulk Fermi Arc and Polarization Half Charge from Paired Exceptional Points

The ideas of topology have found tremendous success in Hermitian physical systems, but even richer properties exist in the more general non-Hermitian framework. Here, we theoretically propose and experimentally demonstrate a new topologically-protected bulk Fermi arc which---unlike the well-known surface Fermi arcs arising from Weyl points in Hermitian systems---develops from non-Hermitian radiative losses in photonic crystal slabs. Moreover, we discover half-integer topological charges in the polarization of far-field radiation around the Fermi arc. We show that both phenomena are direct consequences of the non-Hermitian topological properties of exceptional points, where resonances coincide in their frequencies and linewidths. Our work connects the fields of topological photonics, non-Hermitian physics and singular optics, and paves the way for future exploration of non-Hermitian topological systems.Comment: 7 pages, 4 figure

Two-sample smooth tests for the equality of distributions

This paper considers the problem of testing the equality of two unspecified distributions. The classical omnibus tests such as the Kolmogorov–Smirnov and Cramér–von Mises are known to suffer from low power against essentially all but location-scale alternatives. We propose a new two-sample test that modifies the Neyman’s smooth test and extend it to the multivariate case based on the idea of projection pursue. The asymptotic null property of the test and its power against local alternatives are studied. The multiplier bootstrap method is employed to compute the critical value of the multivariate test. We establish validity of the bootstrap approximation in the case where the dimension is allowed to grow with the sample size. Numerical studies show that the new testing procedures perform well even for small sample sizes and are powerful in detecting local features or high-frequency components

Dietary supplementation of exopolysaccharides from Lactobacillus rhamnosus GCC-3 improved the resistance of zebrafish against spring viremia of carp virus infection

Spring viremia of carp virus (SVCV) can cause high mortality of fish. The aim of this study was to investigate the effects of Lactobacillus rhamnosus GCC-3 exopolysaccharides (GCC-3 EPS) on zebrafish (Danio rerio) infected with SVCV and elucidate the underlying mechanisms. Zebrafish were fed with a control diet or diet supplemented with 0.5% and 1% of GCC-3 EPS for 2 weeks. The results showed that supplementation of GCC-3 EPS significantly improved the survival rate of zebrafish compared with the control group. In addition, dietary 0.5% and 1% GCC-3 EPS significantly up-regulated the expression of genes related to type I interferon (IFN) antiviral immunity. Consistent with in vivo results, GCC-3 EPS significantly inhibited SVCV replication in zebrafish embryonic fibroblast (ZF4) cells while significantly increased the expression of type I IFN signaling pathway related genes. Furthermore, knocking down TANK-binding kinase 1 significantly blocked the antiviral effect of GCC-3 EPS. Dietary GCC-3 EPS improved gut microbiota, and the culture supernatant of GCC-3 EPS-associated microbiota significantly inhibited SVCV replication in ZF4 cells compared with the control-microbiota counterpart. In conclusion, our results indicate that dietary GCC-3 EPS can improve the resistance of zebrafish against SVCV infection, and the mechanism may involve enhanced type I interferon signaling. KEYW

Good outcomes of elbow arthroscopy-assisted absorbable screw fixation for capitellum fracture of the humerus in children: a case series

BackgroundCapitellum fractures are rare coronal fractures of the distal humerus which accounts for 6% of all distal humeral fractures and only 1% of all elbow fractures. The purpose of this study was to investigate the efficacy and complications of arthroscopically assisted reduction and fixation with absorbable screws for capitellar fracture of the humerus in children.MethodsThis was a retrospective case series study, which considered four patients (4 elbows), ranging from 10 to 15 years old, who were treated by arthroscopic-assisted percutaneous absorbable screw between 2018 and 2020. The elbow flexion-extension and forearm supination-pronation ranges of motion (ROM) were measured at the preoperative examination and last follow-up examination. Finally, the clinical and radiological results were assessed.ResultsThe result of operations is satisfactory. The mean follow-up was 3.0 years (range 2–3.8 years). Average range of motion significantly improved from pre- to postoperation, with forearm supination from 60°(50°−60°) to 90°(90°) and pronation improved from 75°(70°−80°) to 90°(90°). The postoperative elbow flexion-extension range of motion was significantly higher compared with range of motion before surgery (P < 0.001; r = 0.949). At the final follow-up examination, the Mayo Elbow Performance Score was excellent. Satisfactory clinical results were achieved in all patients, and no postoperative complications were observed.ConclusionsIt is an effective and safe surgical option to use arthroscopic-assisted percutaneous absorbable screw fixation for treating capitellum fracture of the humerus without any complications in children.Level of evidenceLevel IV; case series

Band Structure Engineering of Interfacial Semiconductors Based on Atomically Thin Lead Iodide Crystals

To explore new constituents in two-dimensional materials and to combine their best in van der Waals heterostructures, are in great demand as being unique platform to discover new physical phenomena and to design novel functionalities in interface-based devices. Herein, PbI2 crystals as thin as few-layers are first synthesized, particularly through a facile low-temperature solution approach with the crystals of large size, regular shape, different thicknesses and high-yields. As a prototypical demonstration of flexible band engineering of PbI2-based interfacial semiconductors, these PbI2 crystals are subsequently assembled with several transition metal dichalcogenide monolayers. The photoluminescence of MoS2 is strongly enhanced in MoS2/PbI2 stacks, while a dramatic photoluminescence quenching of WS2 and WSe2 is revealed in WS2/PbI2 and WSe2/PbI2 stacks. This is attributed to the effective heterojunction formation between PbI2 and these monolayers, but type I band alignment in MoS2/PbI2 stacks where fast-transferred charge carriers accumulate in MoS2 with high emission efficiency, and type II in WS2/PbI2 and WSe2/PbI2 stacks with separated electrons and holes suitable for light harvesting. Our results demonstrate that MoS2, WS2, WSe2 monolayers with very similar electronic structures themselves, show completely distinct light-matter interactions when interfacing with PbI2, providing unprecedent capabilities to engineer the device performance of two-dimensional heterostructures.Comment: 36 pages, 5 figure

A novel ZRS variant causes preaxial polydactyly type I by increased sonic hedgehog expression in the developing limb bud.

PurposePreaxial polydactyly (PPD) is a common congenital hand malformation classified into four subtypes (PPD I-IV). Variants in the zone of polarizing activity regulatory sequence (ZRS) within intron 5 of the LMBR1 gene are linked to most PPD types. However, the genes responsible for PPD I and the underlying mechanisms are unknown.MethodsA rare large four-generation family with isolated PPD I was subjected to genome-wide genotyping and sequence analysis. In vitro and in vivo functional studies were performed in Caco-2 cells, 293T cells, and a knockin transgenic mouse model.ResultsA novel g.101779T>A (reference sequence: NG_009240.2; position 446 of the ZRS) variant segregates with all PPD I-affected individuals. The knockin mouse with this ZRS variant exhibited PPD I phenotype accompanying ectopic and excess expression of Shh. We confirmed that HnRNP K can bind the ZRS and SHH promoters. The ZRS mutant enhanced the binding affinity for HnRNP K and upregulated SHH expression.ConclusionOur results identify the first PPD I disease-causing variant. The variant leading to PPD I may be associated with enhancing SHH expression mediated by HnRNP K. This study adds to the ZRS-associated syndromes classification system for PPD and clarifies the underlying molecular mechanisms