In this paper, we find all Fibonacci and Lucas numbers written in the form $2^a+3^b+5^c+7^d$ , in non-negative integers $a,b,c,d$ , with $0\le \max \{a,b,c\}\le d$ .

Data augmentation, generating new data that are similar but not same with the original data by making a series of transformations to the original data, is one of the mainstream methods to alleviate the problem of insufficient data. Instead of augmenting input data, this paper proposes a method for augmenting features in the middle layers of deep models, called MEML (Mean Extrapolation in Middle Layers). It gets the features outputted by any middle layer of deep models and then creates new features by extrapolating some randomly selected features with their corresponding class mean. After that, it replaces these selected features with the new ones, and then let the new composed output continue to propagate forward. Experiments on two classic deep neural network models and three image datasets show that our MEML method can significantly improve the model classification accuracy and outperform the state-of-the-art feature space augmentation methods such as dropout and K Nearest Neighbors extrapolation in most experiments. Interestingly, when coupled with some input space augmentation methods, e.g., rotation and horizontal flip, MEML could further improve the performance of deep models, implying that the input space augmentation methods and MEML could complement each other.

Privacy protection, high labeling cost, and the varying characteristics of seizures among patients and at different times are the main obstacles to building seizure detection models. In light of these, we propose a novel Mentor-Student architecture for Patient-Specific seizure detection (MS4PS). It contains a new way of knowledge transferring named mentor-select-for-student, which exploits the knowledge of a Mentor model by using this model to select data for training a Student model, making it possible to avoid transferring patients’ data and the negative influence of transferring parameters/structures of pretrained models. It also contains a new way of active learning, which uses both an experienced Mentor model and a quick-learning Student model to select high-quality samples for doctors to label. Each of the two models is coupled with a particular sample selection strategy that combines the uncertainty/certainty and the distance between unlabeled samples and labeled seizure samples. The proposed method could quickly train a suitable detector for a patient at his/her first epilepsy diagnosis with the help of: (1) an experienced Mentor model that chooses the most category-certain electroencephalography (EEG) data segments; (2) a Student model (detector itself) that chooses the most category-uncertain EEG data segments; (3) doctors who label these data segments selected by both the Mentor model and Student model. By replacing or improving the Mentor model and refining the historical models of patients when they come next time, the MS4PS system could be sustainedly promoted. The proposed method is tested on CHB-MIT and NEO datasets and the results demonstrate its effectiveness and efficiency.

Image matting is an important vision problem. The main stream methods for it combine sampling-based methods and propagation-based methods. In this paper, we deal with the combination with a normalized weighting parameter, which could well control the relative relationship between information from sampling and from propagation. A reasonable value range for this parameter is given based on statistics from the standard benchmark dataset. The matting is further improved by introducing semi-supervised learning iterations, which automatically refine the trimap without user's interaction. This is especially beneficial when the trimap is coarse. The experimental results on standard benchmark dataset have shown that both the normalized weighting parameter and the semi-supervised learning iteration could significantly improve the matting performance.