A spectral projection method for transmission eigenvalues

In this paper, we consider a nonlinear integral eigenvalue problem, which is a reformulation of the transmission eigenvalue problem arising in the inverse scattering theory. The boundary element method is employed for discretization, which leads to a generalized matrix eigenvalue problem. We propose a novel method based on the spectral projection. The method probes a given region on the complex plane using contour integrals and decides if the region contains eigenvalue(s) or not. It is particularly suitable to test if zero is an eigenvalue of the generalized eigenvalue problem, which in turn implies that the associated wavenumber is a transmission eigenvalue. Effectiveness and efficiency of the new method are demonstrated by numerical examples.Comment: The paper has been accepted for publication in SCIENCE CHINA Mathematic

On the Depth of Deep Neural Networks: A Theoretical View

People believe that depth plays an important role in success of deep neural networks (DNN). However, this belief lacks solid theoretical justifications as far as we know. We investigate role of depth from perspective of margin bound. In margin bound, expected error is upper bounded by empirical margin error plus Rademacher Average (RA) based capacity term. First, we derive an upper bound for RA of DNN, and show that it increases with increasing depth. This indicates negative impact of depth on test performance. Second, we show that deeper networks tend to have larger representation power (measured by Betti numbers based complexity) than shallower networks in multi-class setting, and thus can lead to smaller empirical margin error. This implies positive impact of depth. The combination of these two results shows that for DNN with restricted number of hidden units, increasing depth is not always good since there is a tradeoff between positive and negative impacts. These results inspire us to seek alternative ways to achieve positive impact of depth, e.g., imposing margin-based penalty terms to cross entropy loss so as to reduce empirical margin error without increasing depth. Our experiments show that in this way, we achieve significantly better test performance.Comment: AAAI 201

Novel complete ensemble EMD with adaptive noise-based hybrid filtering for rolling bearing fault diagnosis

A feature extraction of fault bearing has attracted considerable attention in recent years. However, weak fault feature is difficult to extract under heavy background noise. To solve this problem, a novel multi-layer filtering method is proposed to filter out noise and extract weak fault feature. The first layer introduces a metric based on de-trended fluctuation analysis (DFA) to identify intrinsic mode function (IMF) that reflect period impulsive information for vibration signal adaptively. The second layer uses non-local mean (NLM) method as a pre-filter of the third layer to realize extraction of singular value decomposition (SVD) which reflect the most information of IMFs. The last layer introduces a relative energy difference criterion of a singular value to extract important feature of Hankel matrix of IMFs. The filtered signal is obtained by re-constructed signal from identified singular value of SVD. Experiment results on simulation and real vibration signals indicate that the hybrid filtering method removes heavy noise successfully and extract weak fault feature of rolling bearing effectively

Do coupling exciton and oscillation of electron-hole pair exist in neutral and charged pi-dimeric quinquethiophenes?

Optical physical properties of neutral and charged quinquethiophene monomer, and neutral and cationic pi-dimeric quinquethiophenes were investigated with density functional theory as well as the two dimensional (2D) site (transition density matrix) and three dimensional (3D) cube (transition density and charge difference density) representations, stimulated by the recent experimental report [T. Sakai , J. Am. Chem. Soc. 127, 8082 (2005)]. Transition density shows the orientation and strength of the transition dipole moment of neutral and charged quinquethiophene monomer, and charge difference density reveals the orientation and result of the charge transfer in neutral and charged quinquethiophene monomer. To study if coupling exciton and oscillation of electron-hole pair exist in neutral and cationic pi-dimeric quinquethiophenes, the coupling constants J (coupling exciton of electron-hole pair) and K (coupling oscillation of electron-hole pair) were introduced to the exciton coordinate and momentum operators, respectively, and the 2D and 3D analysis methods were further developed by extending our previous theoretical methods [M. T. Sun, J. Chem. Phys. 124, 054903 (2006)]. With the new developed 2D and 3D analysis methods, we investigated the excited state properties of neutral and cationic pi-dimeric quinquethiophenes, especially on the coupling exciton and oscillation of electron-hole pair between monomers. The 2D results show that there is neither coupling exciton (J=0) nor oscillation (K=0) of electron-hole pair in neutral pi-dimeric quinquethiophenes. For some excited states of cationic pi-dimeric quinquethiophenes, there is no coupling exciton (J=0), but there is coupling oscillation (K not equal 0); while for some excited states, there are both coupling exciton and coupling oscillator simultaneously (J not equal 0 and K not equal 0). The strength of transition dipole moments of pi-dimeric quinquethiophenes were interpreted with 3D transition density, which reveals the orientations of their two subtransition dipole moments. The 3D charge transition density reveals the orientation and result of intermonomer and/or intramonomer charge transfer. The calculated results reveal that excited state properties of neutral pi-dimeric quinquethiophene are significantly different from those of the cationic pi-dimeric quinquethiophenes

Optimal Transport-Guided Conditional Score-Based Diffusion Models

Conditional score-based diffusion model (SBDM) is for conditional generation of target data with paired data as condition, and has achieved great success in image translation. However, it requires the paired data as condition, and there would be insufficient paired data provided in real-world applications. To tackle the applications with partially paired or even unpaired dataset, we propose a novel Optimal Transport-guided Conditional Score-based diffusion model (OTCS) in this paper. We build the coupling relationship for the unpaired or partially paired dataset based on $L_2$-regularized unsupervised or semi-supervised optimal transport, respectively. Based on the coupling relationship, we develop the objective for training the conditional score-based model for unpaired or partially paired settings, which is based on a reformulation and generalization of the conditional SBDM for paired setting. With the estimated coupling relationship, we effectively train the conditional score-based model by designing a ``resampling-by-compatibility'' strategy to choose the sampled data with high compatibility as guidance. Extensive experiments on unpaired super-resolution and semi-paired image-to-image translation demonstrated the effectiveness of the proposed OTCS model. From the viewpoint of optimal transport, OTCS provides an approach to transport data across distributions, which is a challenge for OT on large-scale datasets. We theoretically prove that OTCS realizes the data transport in OT with a theoretical bound. Code is available at \url{https://github.com/XJTU-XGU/OTCS}.Comment: Accepted in NeurIPS 202

Modeling and Simulation of Working Characteristics of Lithium Titanate Batteries for Emergency Power Transmission

This paper presents a battery model applied to dynamic simulation software. The simulation model uses only the battery State-Of-Charge (SOC) as a state variable in order to avoid the algebraic loop problem. It is shown that this model, composed of a controlled voltage source in series with a resistance, can accurately describe the lithium titanate battery discharge process. The model’s parameters can be easily extracted from the manufacturer’s discharge curve. In this paper, it is actually applied to the self-starting system after the emergency stop of the EMU, the simulation model of the system is established by MATLAB/Simulink, and the ground test platform is used to simulate the actual working condition of EMU to complete the experimental verification. The results of both simulation and experiment proved that the scheme of battery self-shifting driven system is feasible and correct

A model-data asymptotic-preserving neural network method based on micro-macro decomposition for gray radiative transfer equations

We propose a model-data asymptotic-preserving neural network(MD-APNN) method to solve the nonlinear gray radiative transfer equations(GRTEs). The system is challenging to be simulated with both the traditional numerical schemes and the vanilla physics-informed neural networks(PINNs) due to the multiscale characteristics. Under the framework of PINNs, we employ a micro-macro decomposition technique to construct a new asymptotic-preserving(AP) loss function, which includes the residual of the governing equations in the micro-macro coupled form, the initial and boundary conditions with additional diffusion limit information, the conservation laws, and a few labeled data. A convergence analysis is performed for the proposed method, and a number of numerical examples are presented to illustrate the efficiency of MD-APNNs, and particularly, the importance of the AP property in the neural networks for the diffusion dominating problems. The numerical results indicate that MD-APNNs lead to a better performance than APNNs or pure data-driven networks in the simulation of the nonlinear non-stationary GRTEs