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The integral-algebraic equation (IAE) is a mixed system of first-kind and second-kind Volterra integral equations (VIEs). This paper mainly focuses on the discontinuous Galerkin (DG) method to solve index-2 IAEs. First, the convergence theory of perturbed DG methods for first-kind VIEs is established, and then used to derive the optimal convergence properties of DG methods for index-2 IAEs. It is shown that an $(m-1)$-th degree DG approximation exhibits global convergence of order~$m$ when~$m$ is odd, and of order~$m-1$ when~$m$ is even, for the first component~$x_1$ of the exact solution, corresponding to the second-kind VIE, whereas the convergence order is reduced by two for the second component~$x_2$ of the exact solution, corresponding to the first-kind VIE. Each component also exhibits local superconvergence of one order higher when~$m$ is even. When~$m$ is odd, superconvergence occurs only if $x_1$ satisfies $x_1^{(m)}(0)=0$. Moreover, with this condition, we can extend the local superconvergence result for~$x_2$ to global superconvergence when~$m$ is odd. Note that in the DG method for an index-1 IAE, generally, the global superconvergence of the exact solution component corresponding to the second-kind VIE can only be obtained by iteration. However, we can get superconvergence for all components of the exact solution of the index-2 IAE directly. Some numerical experiments are given to illustrate the obtained theoretical results.

The emergence of massive ultra-reliable and low latency communications (mURLLC) as a category of time/reliability-sensitive service over 6G networks has received considerable research attention, which has presented unprecedented challenges. As one of the key enablers for 6G, satellite-terrestrial integrated networks (STIN) have been developed to offer more expansive connectivity and comprehensive 3D coverage in space-aerial-terrestrial domains for supporting 6G mission-critical mURLLC applications while fulfilling diverse and rigorous quality of service (QoS) requirements. In the context of these mURLLC-driven satellite services, data freshness assumes paramount importance, as outdated data may engender unpredictable or catastrophic outcomes. To effectively measure data freshness in satellite-terrestrial integrated communications, age of information (AoI) has recently surfaced as a new dimension of QoS metric to support time-sensitive applications. It is crucial to design new analytical models that ensure stringent and diverse QoS metrics bounded by different key parameters, including AoI, delay, and reliability, over 6G satellite-terrestrial integrated networks. However, due to the complicated and dynamic nature of satellite-terrestrial integrated network environments, the research on efficiently defining new statistical QoS schemes while taking into account varying degrees of freedom has still been in their infancy. To remedy these deficiencies, in this paper we develop statistical QoS provisioning schemes over 6G satellite-terrestrial integrated networks in the finite blocklength regime. Particularly, we firstly introduce and review key technologies for supporting mURLLC. Secondly, we formulate a number of novel fundamental statistical-QoS metrics in the finite blocklength regime. Finally, we conduct a set of simulations to evaluate our developed statistical QoS schemes.

Kinematics restrict the ability of rare charm decays to explore the charged Lepton Flavor Violation processes mediated by the quark-level $c\to u \ell \tau$ transition. To fill the gap, we propose exploring new physics (NP) through the quasielastic scattering process $e^-p\to \tau^-\Lambda_c$ and the polarization of the $\tau$ lepton. As analyzing modes for the $\tau$ polarization, we consider the decays $\tau^-\to \pi^-\nu_{\tau}$, $\tau^-\to \rho^-\nu_{\tau}$, and $\tau^- \to \ell^-\bar{\nu}_{\ell}\nu_{\tau}$, and show that the $\tau$ polarization components can be extracted from analyzing the kinematics of the $\tau$ visible decay products. In the framework of a general low-energy effective Lagrangian, we then perform a detailed analysis of the polarization components in various aspects and scrutinize possible NP signals. With one upcoming experimental setup, we finally demonstrate promising event rate can be expected for the cascade process and, even in the worst-case scenario -- no signals is observed at all -- it can still provide a competitive potential for constraining the NP, compared with those from the high-$p_T$ dilepton invariant mass tails at high-energy colliders., Comment: 20 pages, 4 figures, 5 tables

Anomalous Hall effect (AHE), one of the most important electronic transport phenomena, generally appears in ferromagnetic materials but is rare in materials without magnetic elements. Here, we present a study of La$_3$MgBi$_5$, whose band structure carries multitype Dirac fermions. Although magnetic elements are absent in La$_3$MgBi$_5$, clear signals of AHE can be observed. In particular, the anomalous Hall conductivity is extremely large, reaching 42,356 $\Omega^{-1}$ cm$^{-1}$ with an anomalous Hall angle of 8.8 %, the largest one that has been observed in the current AHE systems. The AHE is suggested to originate from the combination of skew scattering and Berry curvature. Another unique property discovered in La$_3$MgBi$_5$ is the axial diamagnetism. The diamagnetism is significantly enhanced and dominates the magnetization in the axial directions, which is the result of restricted motion of the Dirac fermion at Fermi level. Our findings not only establish La$_3$MgBi$_5$ as a suitable platform to study AHE and quantum transport, but also indicate the great potential of 315-type Bi-based materials for exploring novel physical properties.

We report a study on low-temperature heat transport of Kitaev magnet Na$_2$Co$_2$TeO$_6$, with the heat current and magnetic fields along the honeycomb spin layer (the $ab$ plane). The zero-field thermal conductivity of $\kappa^a_{xx}$ and $\kappa^{a*}_{xx}$ display similar temperature dependence and small difference in their magnitudes; whereas, their magnetic field (parallel to the heat current) dependence are quite different and are related to the field-induced magnetic transitions. The $\kappa^a_{xx}(B)$ data for $B \parallel a$ at very low temperatures have an anomaly at 10.25--10.5 T, which reveals an unexplored magnetic transition. The planar thermal Hall conductivity $\kappa^a_{xy}$ and $\kappa^{a*}_{xy}$ show very weak signals at low fields and rather large values with sign change at high fields. This may point to a possible magnetic structure transition or the change of the magnon band topology that induces a radical change of magnon Berry curvature distribution before entering the spin polarized state. These results put clear constraints on the high-field phase and the theoretical models for Na$_2$Co$_2$TeO$_6$., Comment: 7 pages, 4 figures

Superconductivity becomes more interesting when it encounters dimensional constraint or topology, because it is of importance for exploring exotic quantum phenomena or developing superconducting electronics. Here we report the coexistence of naturally formed surface superconducting state and three-dimensional topological Dirac state in single crystals of BaMg$_2$Bi$_2$. The electronic structure obtained from the first-principles calculations demonstrates that BaMg$_2$Bi$_2$ is an ideal Dirac material, in which the Dirac point is very close to the Fermi level and no other energy band crosses the Fermi level. Superconductivity up to 4.77 K can be observed under ambient pressure in the measurements of resistivity. The angle dependent magnetoresistance reveals the two-dimensional characteristic of superconductivity, indicating that superconductivity occurs on the surface of the sample and is absent in the bulk state. Our study not only provides BaMg$_2$Bi$_2$ as a suitable platform to study the interplay between superconductivity and topological Dirac state, but also indicates that MgBi-based materials may be a promising system for exploring new superconductors.

Video Instance Segmentation (VIS) aims to simultaneously classify, segment, and track multiple object instances in videos. Recent clip-level VIS takes a short video clip as input each time showing stronger performance than frame-level VIS (tracking-by-segmentation), as more temporal context from multiple frames is utilized. Yet, most clip-level methods are neither end-to-end learnable nor real-time. These limitations are addressed by the recent VIS transformer (VisTR) which performs VIS end-to-end within a clip. However, VisTR suffers from long training time due to its frame-wise dense attention. In addition, VisTR is not fully end-to-end learnable in multiple video clips as it requires a hand-crafted data association to link instance tracklets between successive clips. This paper proposes EfficientVIS, a fully end-to-end framework with efficient training and inference. At the core are tracklet query and tracklet proposal that associate and segment regions-of-interest (RoIs) across space and time by an iterative query-video interaction. We further propose a correspondence learning that makes tracklets linking between clips end-to-end learnable. Compared to VisTR, EfficientVIS requires 15x fewer training epochs while achieving state-of-the-art accuracy on the YouTube-VIS benchmark. Meanwhile, our method enables whole video instance segmentation in a single end-to-end pass without data association at all., Comment: Accepted to CVPR 2022