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Quantum metrology explores quantum effects to improve the measurement accuracy of some physical quantities beyond the classical limit. However, due to the interaction between the system and the environment, the decoherence can significantly reduce the accuracy of the measurement. Many methods have been proposed to restore the accuracy of the measurement in the long-time limit. Recently, it has been found that the bound state can assist the error-free measurement and recover the $t^{-1}$ scaling [K. Bai, Z. Peng, H. G. Luo, and J. H. An, Phys. Rev. Lett. 123, 040402 (2019)]. Here, by using $N$-qubits, we propose a method to simulate the open quantum dynamics of the hybrid system including one atom and coupled resonators. We find that the error of the measurement can vanish as the time increases due to the existence of the bound state. By both analytical and numerical simulations, we prove the $t^{-1}$ scaling of the measurement error can be recovered when there is a bound state in the hybrid system. Interestingly, we observe that there are perfect oscillations which can be used for the evaluation of the atomic transition frequency. For a finite-$N$, the duration of the perfect oscillations doubles as one more qubit is involved., Comment: 9 pages,9 figures

We investigate theoretically the enhancement of mechanical squeezing in a multimode optomechanical system by introducing a coherent phonon-photon interaction via the backward stimulated Brillouin scattering (BSBS) process. The coherent photon-phonon interaction where two optical modes couple to a Brillouin acoustic mode with a large decay rate provides an extra channel for the cooling of a Duffing mechanical oscillator. The squeezing degree and the robustness to the thermal noises of the Duffing mechanical mode can be enhanced greatly. When the Duffing nonlinearity is weak, the squeezing degree of the mechanical mode in the presence of BSBS can be improved more than one order of magnitude compared with the absence of BSBS. Our scheme may be extended to other quantum systems to study novel quantum effects.

In this paper, we consider a class of structured fractional programs, where the numerator part is the sum of a block-separable (possibly nonsmooth nonconvex) function and a locally Lipschitz differentiable (possibly nonconvex) function, while the denominator is a convex (possibly nonsmooth) function. We first present a novel reformulation for the original problem and show the relationship between optimal solutions, critical points and KL exponents of these two problems. Inspired by the reformulation, we propose a flexible framework of multi-proximity gradient algorithms (MPGA), which computes the proximity operator with respect to the Fenchel conjugate associated with the convex denominator of the original problem rather than evaluating its subgradient as in the existing methods. Also, MPGA employs a nonmonotone linear-search scheme in its gradient descent step, since the smooth part in the numerator of the original problem is not globally Lipschitz differentiable. Based on the framework of MPGA, we develop two specific algorithms, namely, cyclic MPGA and randomized MPGA, and establish their subsequential convergence under mild conditions. Moreover, the sequential convergence of cyclic MPGA with the monotone line-search (CMPGA_ML) is guaranteed if the extended objective associated with the reformulated problem satisfies the Kurdyka-{\L}ojasiewicz (KL) property and some other mild assumptions. In particular, we prove that the corresponding KL exponents are 1/2 for several special cases of the fractional programs, and so, CMPGA_ML exhibits a linear convergence rate. Finally, some preliminary numerical experiments are performed to demonstrate the efficiency of our proposed algorithms.

Data augmentation has been proven effective for training high-accuracy convolutional neural network classifiers by preventing overfitting. However, building deep neural networks in real-world scenarios requires not only high accuracy on clean data but also robustness when data distributions shift. While prior methods have proposed that there is a trade-off between accuracy and robustness, we propose IPMix, a simple data augmentation approach to improve robustness without hurting clean accuracy. IPMix integrates three levels of data augmentation (image-level, patch-level, and pixel-level) into a coherent and label-preserving technique to increase the diversity of training data with limited computational overhead. To further improve the robustness, IPMix introduces structural complexity at different levels to generate more diverse images and adopts the random mixing method for multi-scale information fusion. Experiments demonstrate that IPMix outperforms state-of-the-art corruption robustness on CIFAR-C and ImageNet-C. In addition, we show that IPMix also significantly improves the other safety measures, including robustness to adversarial perturbations, calibration, prediction consistency, and anomaly detection, achieving state-of-the-art or comparable results on several benchmarks, including ImageNet-R, ImageNet-A, and ImageNet-O., Comment: NeurIPS 2023

In this paper, the steady inviscid flows with radial symmetry for the isothermal Euler system are studied in an annulus. We present a complete classification of transonic radially symmetric flow patterns in term of physical boundary conditions at the inner and outer circle. By solving the one side boundary problem, we obtain that there exist accelerating or decelerating smooth transonic flows in an annulus. Moreover, the structural stability of these smooth symmetric transonic flows with nonzero angular velocity are further investigated. Furthermore, we examine the transonic solutions with shocks as well via prescribing suitable boundary conditions on the inner and outer circle., Comment: arXiv admin note: substantial text overlap with arXiv:2101.00452, arXiv:2101.00450 by other authors

The Sparse Generalized Eigenvalue Problem (sGEP), a pervasive challenge in statistical learning methods including sparse principal component analysis, sparse Fisher's discriminant analysis, and sparse canonical correlation analysis, presents significant computational complexity due to its NP-hardness. The primary aim of sGEP is to derive a sparse vector approximation of the largest generalized eigenvector, effectively posing this as a sparse optimization problem. Conventional algorithms for sGEP, however, often succumb to local optima and exhibit significant dependency on initial points. This predicament necessitates a more refined approach to avoid local optima and achieve an improved solution in terms of sGEP's objective value, which we address in this paper through a novel successive two-stage method. The first stage of this method incorporates an algorithm for sGEP capable of yielding a stationary point from any initial point. The subsequent stage refines this stationary point by adjusting its support, resulting in a point with an enhanced objective value relative to the original stationary point. This support adjustment is achieved through a novel procedure we have named support alteration. The final point derived from the second stage then serves as the initial point for the algorithm in the first stage, creating a cyclical process that continues until a predetermined stopping criterion is satisfied. We also provide a comprehensive convergence analysis of this process. Through extensive experimentation under various settings, our method has demonstrated significant improvements in the objective value of sGEP compared to existing methodologies, underscoring its potential as a valuable tool in statistical learning and optimization.

In this paper, both smooth subsonic and transonic flows to steady Euler-Poisson system in a concentric cylinder are studied. We first establish the existence of cylindrically symmetric smooth subsonic and transonic flows to steady Euler-Poisson system in a concentric cylinder. On one hand, we investigate the structural stability of smooth cylindrically symmetric subsonic flows under three-dimensional perturbations on the inner and outer cylinders. On the other hand, the structural stability of smooth transonic flows under the axi-symmetric perturbations are examined. There is no any restrictions on the background subsonic and transonic solutions. A deformation-curl-Poisson decomposition to the steady Euler-Poisson system is utilized in our work to deal with the hyperbolic-elliptic mixed structure in subsonic region. It should be emphasized that there is a special structure of the steady Euler-Poisson system which yields a priori estimates and uniqueness of a second order elliptic system for the velocity potential and the electrostatic potential.

This paper unveils CG-Eval, the first-ever comprehensive and automated evaluation framework designed for assessing the generative capabilities of large Chinese language models across a spectrum of academic disciplines. CG-Eval stands out for its automated process, which critically assesses models based on their proficiency in generating precise and contextually relevant responses to a diverse array of questions within six key domains: Science and Engineering, Humanities and Social Sciences, Mathematical Calculations, Medical Practitioner Qualification Examination, Judicial Examination, and Certified Public Accountant Examination. Alongside this, we introduce Gscore, an innovative composite index developed from a weighted sum of multiple metrics. Gscore uniquely automates the quality measurement of a model's text generation against reference standards, providing a detailed and nuanced assessment of model performance. This automation not only enhances the efficiency and scalability of the evaluation process but also ensures objective and consistent assessment across various models. The detailed test data and results, highlighting the robust capabilities and comparative performance of the evaluated models, are accessible at http://cgeval.besteasy.com/.

Unconstrained face recognition is an active research area among computer vision and biometric researchers for many years now. Still the problem of face recognition in low quality photos has not been well-studied so far. In this paper, we explore the face recognition performance on low quality photos, and we try to improve the accuracy in dealing with low quality face images. We assemble a large database with low quality photos, and examine the performance of face recognition algorithms for three different quality sets. Using state-of-the-art facial image enhancement approaches, we explore the face recognition performance for the enhanced face images. To perform this without experimental bias, we have developed a new protocol for recognition with low quality face photos and validate the performance experimentally. Our designed protocol for face recognition with low quality face images can be useful to other researchers. Moreover, experiment results show some of the challenging aspects of this problem., Comment: 8 pages, 11 figures

MOBIO is a bi-modal database that was captured almost exclusively on mobile phones. It aims to improve research into deploying biometric techniques to mobile devices. Research has been shown that face and speaker recognition can be performed in a mobile environment. Facial landmark localization aims at finding the coordinates of a set of pre-defined key points for 2D face images. A facial landmark usually has specific semantic meaning, e.g. nose tip or eye centre, which provides rich geometric information for other face analysis tasks such as face recognition, emotion estimation and 3D face reconstruction. Pretty much facial landmark detection methods adopt still face databases, such as 300W, AFW, AFLW, or COFW, for evaluation, but seldomly use mobile data. Our work is first to perform facial landmark detection evaluation on the mobile still data, i.e., face images from MOBIO database. About 20,600 face images have been extracted from this audio-visual database and manually labeled with 22 landmarks as the groundtruth. Several state-of-the-art facial landmark detection methods are adopted to evaluate their performance on these data. The result shows that the data from MOBIO database is pretty challenging. This database can be a new challenging one for facial landmark detection evaluation., Comment: 13 pages, 10 figures

Deep learning has received increasing interests in face recognition recently. Large quantities of deep learning methods have been proposed to handle various problems appeared in face recognition. Quite a lot deep methods claimed that they have gained or even surpassed human-level face verification performance in certain databases. As we know, face image quality poses a great challenge to traditional face recognition methods, e.g. model-driven methods with hand-crafted features. However, a little research focus on the impact of face image quality on deep learning methods, and even human performance. Therefore, we raise a question: Is face image quality still one of the challenges for deep learning based face recognition, especially in unconstrained condition. Based on this, we further investigate this problem on human level. In this paper, we partition face images into three different quality sets to evaluate the performance of deep learning methods on cross-quality face images in the wild, and then design a human face verification experiment on these cross-quality data. The result indicates that quality issue still needs to be studied thoroughly in deep learning, human own better capability in building the relations between different face images with large quality gaps, and saying deep learning method surpasses human-level is too optimistic., Comment: 11 pages, 11 figures

The ratio of L1 and L2 norms (L1/L2), serving as a sparse promoting function, receives considerable attentions recently due to its effectiveness for sparse signal recovery. In this paper, we propose an L1/L2 based penalty model for recovering sparse signals from noiseless or noisy observations. It is proven that stationary points of the proposed problem tend to those of the elliptically constrained L1/L2 minimization problem as the smoothing parameter goes to zero. Moreover, inspired by the parametric approach for the fractional programming, we design a parameterized proximal-gradient algorithm (PPGA) as well as its line search counterpart (PPGA_L) for solving the proposed model. The closed-form solution of the involved proximity operator is derived, which enable the efficiency of the proposed algorithms. We establish the global convergence of the entire sequences generated by PPGA and PPGA_L with monotone objective values by taking advantage of the fact that the objective of the proposed model is a KL function. Numerical experiments show the efficiency of the proposed algorithms over the state-of-the-art methods in both noiseless and noisy sparse signal recovery problems.