Search

Recently, formal verification of deep neural networks (DNNs) has garnered considerable attention, and over-approximation based methods have become popular due to their effectiveness and efficiency. However, these strategies face challenges in addressing the "unknown dilemma" concerning whether the exact output region or the introduced approximation error violates the property in question. To address this, this paper introduces the UR4NNV verification framework, which utilizes under-approximation reachability analysis for DNN verification for the first time. UR4NNV focuses on DNNs with Rectified Linear Unit (ReLU) activations and employs a binary tree branch-based under-approximation algorithm. In each epoch, UR4NNV under-approximates a sub-polytope of the reachable set and verifies this polytope against the given property. Through a trial-and-error approach, UR4NNV effectively falsifies DNN properties while providing confidence levels when reaching verification epoch bounds and failing falsifying properties. Experimental comparisons with existing verification methods demonstrate the effectiveness and efficiency of UR4NNV, significantly reducing the impact of the "unknown dilemma"., Comment: 11 pages, 4 figures

Matrix factor model is drawing growing attention for simultaneous two-way dimension reduction of well-structured matrix-valued observations. This paper focuses on robust statistical inference for matrix factor model in the ``diverging dimension" regime. We derive the convergence rates of the robust estimators for loadings, factors and common components under finite second moment assumption of the idiosyncratic errors. In addition, the asymptotic distributions of the estimators are also derived under mild conditions. We propose a rank minimization and an eigenvalue-ratio method to estimate the pair of factor numbers consistently. Numerical studies confirm the iterative Huber regression algorithm is a practical and reliable approach for the estimation of matrix factor model, especially under the cases with heavy-tailed idiosyncratic errors . We illustrate the practical usefulness of the proposed methods by two real datasets, one on financial portfolios and one on the macroeconomic indices of China.

The matrix factor model has drawn growing attention for its advantage in achieving two-directional dimension reduction simultaneously for matrix-structured observations. In this paper, we propose a simple iterative least squares algorithm for matrix factor models, in contrast to the Principal Component Analysis (PCA)-based methods in the literature. In detail, we first propose to estimate the latent factor matrices by projecting the observations with two deterministic weight matrices, which are chosen to diversify away the idiosyncratic components. We show that the inferences on factors are still asymptotically valid even if we overestimate both the row/column factor numbers. We then estimate the row/column loading matrices by minimizing the squared loss function under certain identifiability conditions. The resultant estimators of the loading matrices are treated as the new weight/projection matrices and thus the above update procedure can be iteratively performed until convergence. Theoretically, given the true dimensions of the factor matrices, we derive the convergence rates of the estimators for loading matrices and common components at any $s$-th step iteration. Additionally, we propose an eigenvalue-ratio method to estimate the pair of factor numbers consistently. Thorough numerical simulations are conducted to investigate the finite-sample performance of the proposed methods and two real datasets associated with financial portfolios and multinational macroeconomic indices are used to illustrate our algorithm's practical usefulness.

A characteristic mode (CM) method that relies on a global multi-trace formulation (MTF) of surface integral equations is proposed to compute the modes and the resonance frequencies of microstrip patch antennas with finite dielectric substrates and ground planes. Compared to the coupled formulation of electric field and Poggio-Miller-Chang-Harrington-Wu-Tsai integral equations, global MTF allows for more direct implementation of a sub-structure CM method. This is achieved by representing the coupling of the electromagnetic fields on the substrate and ground plane in the form of a numerical Green function matrix, which yields a more compact generalized eigenvalue equation. The resulting sub-structure CM method avoids the cumbersome computation of the multilayered medium Green function (unlike the CM methods that rely on mixed-potential integral equations) and the volumetric discretization of the substrate (unlike the CM methods that rely on volume-surface integral equations), and numerical results show that it is a reliable and accurate approach to predicting the modal behavior of electromagnetic fields on practical microstrip antennas.

A coupled hybridizable discontinuous Galerkin (HDG) and boundary integral (BI) method is proposed to efficiently analyze electromagnetic scattering from inhomogeneous/composite objects. The coupling between the HDG and the BI equations is realized using the numerical flux operating on the equivalent current and the global unknown of the HDG. This approach yields sparse coupling matrices upon discretization. Inclusion of the BI equation ensures that the only error in enforcing the radiation conditions is the discretization. However, the discretization of this equation yields a dense matrix, which prohibits the use of a direct matrix solver on the overall coupled system as often done with traditional HDG schemes. To overcome this bottleneck, a "hybrid" method is developed. This method uses an iterative scheme to solve the overall coupled system but within the matrix-vector multiplication subroutine of the iterations, the inverse of the HDG matrix is efficiently accounted for using a sparse direct matrix solver. The same subroutine also uses the multilevel fast multipole algorithm to accelerate the multiplication of the guess vector with the dense BI matrix. The numerical results demonstrate the accuracy, the efficiency, and the applicability of the proposed HDG-BI solver.

Due to the rapid increase of air cargo and postal transport volume, an efficient automated multi-dimensional warehouse with elevating transfer vehicles (ETVs) should be established and an effective scheduling strategy should be designed for improving the cargo handling efficiency. In this paper, artificial bee colony algorithm, which possesses strong global optimization ability and fewer parameters, is firstly introduced to simultaneously optimize the route of ETV and the assignment of entrances and exits. Moreover, for further improve the optimization performance of ABC, novel full-dimensional search strategy with parallelization, and random multi-dimensional search strategy are incorporated in the framework of ABC to improve the diversity of the population and the convergence speed respectively. Our proposed algorithms are evaluated on several benchmark functions, and then applied to solve the combinatorial optimization problem with multitask, multiple entrances and exits in air cargo terminal. The simulations show that the proposed algorithms can achieve much more desired performance than the traditional artificial bee colony algorithm at balancing the exploitation and exploration abilities.

Simulations support the conjecture that the dimension of the trace of Brownian earthworm is strictly greater than 3/2.

Automatic detection of polyps is challenging because different polyps vary greatly, while the changes between polyps and their analogues are small. The state-of-the-art methods are based on convolutional neural networks (CNNs). However, they may fail due to lack of training data, resulting in high rates of missed detection and false positives (FPs). In order to solve these problems, our method combines the two-dimensional (2-D) CNN-based real-time object detector network with spatiotemporal information. Firstly, we use a 2-D detector network to detect static images and frames, and based on the detector network, we propose two feature enhancement modules-the FP Relearning Module (FPRM) to make the detector network learning more about the features of FPs for higher precision, and the Image Style Transfer Module (ISTM) to enhance the features of polyps for sensitivity improvement. In video detection, we integrate spatiotemporal information, which uses Structural Similarity (SSIM) to measure the similarity between video frames. Finally, we propose the Inter-frame Similarity Correlation Unit (ISCU) to combine the results obtained by the detector network and frame similarity to make the final decision. We verify our method on both private databases and publicly available databases. Experimental results show that these modules and units provide a performance improvement compared with the baseline method. Comparison with the state-of-the-art methods shows that the proposed method outperforms the existing ones which can meet real-time constraints. It's demonstrated that our method provides a performance improvement in sensitivity, precision and specificity, and has great potential to be applied in clinical colonoscopy., Comment: This paper has been accepted by Biomedical Signal Processing and Control. Please cite the paper as Xu, J., Zhao, R., Yu, Y., Zhang, Q., Bian, X., Wang, J., Ge, Z., Qian, D., 2021. Real-time automatic polyp detection in colonoscopy using feature enhancement module and spatiotemporal similarity correlation unit. Biomedical Signal Processing and Control 66, 102503

Conventional surface integral equation (SIE)-based characteristic mode formulation for the patch antenna structure with a finite substrate is susceptible to the spurious (nonphysical) modes due to the dielectric part. To avoid the contamination of spurious modes, we propose a novel generalized eigenvalue formulation based on the electric field integral equation coupled Poggio-Miller-Chang-Harrington-Wu-Tsai (EFIE-PMCHWT) equation. In this formulation, the real and imaginary parts of the exterior integral operators are chosen to construct the finalized weighting matrices, to connect radiated power of the characteristic current. Compared with other SIE-based methods, this equation doesn't need additional post-processing since it can effectively avoid spurious modes. Numerical results compared with the volume-surface integral equation (VSIE) are investigated to validate the accuracy.

Magnetic programming soft machines has great development prospects in the fields of minimally invasive medicine, wearable device and soft robot. However, unrepeatable magnetization and low modulus limits their applications. So far, there are few techniques that can make magnetic soft robots have adjustable functions, mechanical and electrical properties. This paper presented a magnetic functional elastomer based on liquid metal-NdFeB-Silicone composite materials. This magnetoelastomer uses the phase transition characteristics of liquid-metal and magnetic guided rotation of micro ferromagnetic particles to realize reprogrammable magnetization and modulus. The elastomer's fabrication method was given and the basic programmable properties were tested. Some robot prototypes have also been manufactured to show how to respond to different mission requirements by programming magnetization and modulus. Our research provides a new path for the design and large-scale manufacturing of magnetic soft robot., Comment: 9 pages, 5 figures