A connected graph $G$ is said to be $k$-connected if it has more than $k$ vertices and remains connected whenever fewer than $k$ vertices are deleted. In this paper, for a connected graph $G$ with sufficiently large order, we present a tight sufficie
nt condition for $G$ with fixed minimum degree to be $k$-connected based on the $Q$-index. Our result can be viewed as a spectral counterpart of the corresponding Dirac type condition.
In this report, we describe the Beijing ZKJ-NPU team submission to the VoxCeleb Speaker Recognition Challenge 2021 (VoxSRC-21). We participated in the fully supervised speaker verification track 1 and track 2. In the challenge, we explored various ki
nds of advanced neural network structures with different pooling layers and objective loss functions. In addition, we introduced the ResNet-DTCF, CoAtNet and PyConv networks to advance the performance of CNN-based speaker embedding model. Moreover, we applied embedding normalization and score normalization at the evaluation stage. By fusing 11 and 14 systems, our final best performances (minDCF/EER) on the evaluation trails are 0.1205/2.8160% and 0.1175/2.8400% respectively for track 1 and 2. With our submission, we came to the second place in the challenge for both tracks.
For $0leq alpha < 1$, the $mathcal{A}_{alpha}$-spectral radius of a $k$-uniform hypergraph $G$ is defined to be the spectral radius of the tensor $mathcal{A}_{alpha}(G):=alpha mathcal{D}(G)+(1-alpha) mathcal{A}(G)$, where $mathcal{D}(G)$ and $A(G)$ a
re diagonal and the adjacency tensors of $G$ respectively. This paper presents several lower bounds for the difference between the $mathcal{A}_{alpha}$-spectral radius and an average degree $frac{km}{n}$ for a connected $k$-uniform hypergraph with $n$ vertices and $m$ edges, which may be considered as the measures of irregularity of $G$. Moreover, two lower bounds on the $mathcal{A}_{alpha}$-spectral radius are obtained in terms of the maximum and minimum degrees of a hypergraph.
Joint modelling of longitudinal and time-to-event data is usually described by a random effect joint model which uses shared or correlated latent effects to capture associations between the two processes. Under this framework, the joint distribution
of the two processes can be derived straightforwardly by assuming conditional independence given the latent effects. Alternative approaches to induce interdependency into sub-models have also been considered in the literature and one such approach is using copulas, to introduce non-linear correlation between the marginal distributions of the longitudinal and time-to-event processes. A Gaussian copula joint model has been proposed in the literature to fit joint data by applying a Monte Carlo expectation-maximisation algorithm. Enlightening as it is, its original estimation procedure comes with some limitations. In the original approach, the log-likelihood function can not be derived analytically thus requires a Monte Carlo integration, which not only comes with intensive computation but also introduces extra variation/noise into the estimation. The combination with the EM algorithm slows down the computation further and convergence to the maximum likelihood estimators can not be always guaranteed. In addition, the assumption that the length of planned measurements is uniform and balanced across all subjects is not suitable when subjects have varying number of observations. In this paper, we relax this restriction and propose an exact likelihood estimation approach to replace the more computationally expensive Monte Carlo expectation-maximisation algorithm. We also provide a straightforward way to compute dynamic predictions of survival probabilities, showing that our proposed model is comparable in prediction performance to the shared random effects joint model.
In this paper, we conduct wireless channel measurements in indoor corridor scenarios at 2.4, 5 and 6 GHz bands with bandwidth of 320 MHz. The measurement results of channel characteristics at different frequency bands such as average power delay prof
ile (APDP), path loss (PL), delay spread (DS), and Ricean K factor (KF) are presented and analyzed. It is found that the PL exponent (PLE) and PL offset beta in the floating-intercept (FI) model tend to increase with the increase of frequency. The DS and KF values of the three frequency bands in line of sight (LOS) scenario are basically the same. These results are significant for the design of communication systems.
In this paper, we develop a robust fast method for mobile-immobile variable-order (VO) time-fractional diffusion equations (tFDEs), superiorly handling the cases of small or vanishing lower bound of the VO function. The valid fast approximation of th
e VO Caputo fractional derivative is obtained using integration by parts and the exponential-sum-approximation method. Compared with the general direct method, the proposed algorithm ($RF$-$L1$ formula) reduces the acting memory from $mathcal{O}(n)$ to $mathcal{O}(log^2 n)$ and computational cost from $mathcal{O}(n^2)$ to $mathcal{O}(n log^2 n)$, respectively, where $n$ is the number of time levels. Then $RF$-$L1$ formula is applied to construct the fast finite difference scheme for the VO tFDEs, which sharp decreases the memory requirement and computational complexity. The error estimate for the proposed scheme is studied only under some assumptions of the VO function, coefficients, and the source term, but without any regularity assumption of the true solutions. Numerical experiments are presented to verify the effectiveness of the proposed method.
Recognizing and localizing objects in the 3D space is a crucial ability for an AI agent to perceive its surrounding environment. While significant progress has been achieved with expensive LiDAR point clouds, it poses a great challenge for 3D object
detection given only a monocular image. While there exist different alternatives for tackling this problem, it is found that they are either equipped with heavy networks to fuse RGB and depth information or empirically ineffective to process millions of pseudo-LiDAR points. With in-depth examination, we realize that these limitations are rooted in inaccurate object localization. In this paper, we propose a novel and lightweight approach, dubbed {em Progressive Coordinate Transforms} (PCT) to facilitate learning coordinate representations. Specifically, a localization boosting mechanism with confidence-aware loss is introduced to progressively refine the localization prediction. In addition, semantic image representation is also exploited to compensate for the usage of patch proposals. Despite being lightweight and simple, our strategy leads to superior improvements on the KITTI and Waymo Open Dataset monocular 3D detection benchmarks. At the same time, our proposed PCT shows great generalization to most coordinate-based 3D detection frameworks. The code is available at: https://github.com/amazon-research/progressive-coordinate-transforms .
Unconventional Weyl points with topological charges higher than 1 can transform into various complex unconventional Weyl exceptional contours under non-Hermitian perturbations. However, theoretical studies of these exceptional contours have been limi
ted to tight-binding models. Here, we propose to realize unconventional Weyl exceptional contours in photonic continua -- non-Hermitian anisotropic chiral plasma, based on ab initio calculation by Maxwells equations. By perturbing in-plane permittivity, an unconventional Weyl point can transform into a quadratic Weyl exceptional circle, a Type-I Weyl exceptional chain with one chain point, a Type-II Weyl exceptional chain with two chain points, or other forms. Realistic metamaterials with effective constitutive parameters are proposed to implement these unconventional Weyl exceptional contours. Our work paves a way toward exploration of exotic physics of unconventional Weyl exceptional contours in non-Hermitian topological photonic continua.
Semantic segmentation is a challenging problem due to difficulties in modeling context in complex scenes and class confusions along boundaries. Most literature either focuses on context modeling or boundary refinement, which is less generalizable in
open-world scenarios. In this work, we advocate a unified framework(UN-EPT) to segment objects by considering both context information and boundary artifacts. We first adapt a sparse sampling strategy to incorporate the transformer-based attention mechanism for efficient context modeling. In addition, a separate spatial branch is introduced to capture image details for boundary refinement. The whole model can be trained in an end-to-end manner. We demonstrate promising performance on three popular benchmarks for semantic segmentation with low memory footprint. Code will be released soon.
Material surface may have a remarkable effect on the mechanical behavior of magneto-electro-elastic (or multiferroic) structures at nano-scale. In this paper, a surface magneto-electro-elasticity theory (or effective boundary condition formulation),
which governs the motion of the material surface of magneto-electro-elastic nano-plates, is established by employing the state-space formalism. The properties of anti-plane shear (SH) waves propagating in a transversely isotropic magneto-electro-elastic plate with nano-thickness are investigated by taking surface effects into account. The size-dependent dispersion relations of both antisymmetric and symmetric SH waves are presented. The thickness-shear frequencies and the asymptotic characteristics of the dispersion relations considering surface effects are determined analytically as well. Numerical results show that surface effects play a very pronounced role in elastic wave propagation in magneto-electro-elastic nano-plates, and the dispersion properties depend strongly on the chosen surface material parameters of magneto-electro-elastic nano-plates. As a consequence, it is possible to modulate the waves in magneto-electro-elastic nano-plates through surface engineering.
