In this paper, we are mainly concerned with oscillatory behaviour of solutions for a class of second order nonlinear neutral difference equations with continuous variable. Using an integral transformation, the Riccati transformation and iteration, some oscillation criteria are obtained.
In this paper, the influence of data imbalance on neural networks is discussed, and an improved learning algorithm to solve this problem is proposed. The experimental results show that in the case of imbalanced data, the training error of neural network converges slowly and the generalization ability is poor. Our theoretical analysis shows that in the process of training, the gradient descent direction of the weights is dominated by the major-classes, which accounts for the slow convergence of the training error. Based on these results, we propose the Equilibration Mini-batch Stochastic Gradient Descent (EMSGD) method to ensure the equilibrium of the data in the mini-batch. The advantage of this technique is that it makes full use of the existing random sampling step of MSGD without increasing the computational complexity. In addition, by over-sampling of minor-classes in the mini-batch, duplicated instances would be greatly reduced, thus preventing the model from overfitting. The experimental results show that under the condition of the imbalanced training data, EMSGD can make the neural network training error converge rapidly. INDEX TERMS Data imbalance, back propagation algorithm, stochastic gradient descent.
Federated Learning (FL) is a promising paradigm, where the local users collaboratively learn models by repeatedly sharing information while the data is kept distributing on these users. FL has been considered in multiple access channels (FL-MAC), which is a hot issue. Even though FL-MAC has many advantages, it is still possible to leak privacy to a third party during the whole training process. To avoid privacy leakage, we propose to add Rényi differential privacy (RDP) into FL-MAC. At the same time, to maximize the convergent rate of users under the constraints of transmission rate and privacy, the quantization stochastic gradient descent (QSGD) is performed by users. We also illustrate our results on MNIST, and the illustration demonstrate that our scheme can improve the model accuracy with a little loss of communication efficiency.
Abstract-In recent years, there is a tremendous increasing among international students to study in Chinese universities, where who may experience considerable difficulties and challenges, particularly during the first-year study. However, there is still incipient research in this area. Thus, it is high time to explore the factors that might affect the international students' learning performances and outcomes of Mathematics courses. The investigation is based on a sample of 140 undergraduate students from different disciplines at Zhejiang University of Science and Technology. The finding constitutes a range of contributory factors which affect their adaptions and opens new paths for future research on the international education.
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