A coupled system of p-Laplacian implicit fractional differential equations depending on boundary conditions of integral type

The objective of this article is to investigate a coupled implicit Caputo fractional $p$-Laplacian system, depending on boundary conditions of integral type, by the substitution method. The Avery-Peterson fixed point theorem is utilized for finding at least three solutions of the proposed coupled system. Furthermore, different types of Ulam stability, i.e., Hyers-Ulam stability, generalized Hyers-Ulam stability, Hyers-Ulam-Rassias stability and generalized Hyers-Ulam-Rassias stability, are achieved. Finally, an example is provided to authenticate the theoretical result

On Some New Weighted Inequalities for Differentiable Exponentially Convex and Exponentially Quasi-Convex Functions with Applications

In this article, we aim to establish several inequalities for differentiable exponentially convex and exponentially quasi-convex mapping, which are connected with the famous Hermite–Hadamard (HH) integral inequality. Moreover, we have provided applications of our findings to error estimations in numerical analysis and higher moments of random variables

EDAfuse: A encoder–decoder with atrous spatial pyramid network for infrared and visible image fusion

Abstract Infrared and visible images come from different sensors, and they have their advantages and disadvantages. In order to make the fused images contain as much salience information as possible, a practical fusion method, termed EDAfuse, is proposed in this paper. In EDAfuse, the authors introduce an encoder–decoder with the atrous spatial pyramid network for infrared and visible image fusion. The authors use the encoding network which includes three convolutional neural network (CNN) layers to extract deep features from input images. Then the proposed atrous spatial pyramid model is utilized to get five different scale features. The same scale features from the two original images are fused by our fusion strategy with the attention model and information quantity model. Finally, the decoding network is utilized to reconstruct the fused image. In the training process, the authors introduce a loss function with saliency loss to improve the ability of the model for extracting salient features from original images. In the experiment process, the authors use the average values of seven metrics for 21 fused images to evaluate the proposed method and the other seven existing methods. The results show that our method has four best values and three second‐best values. The subjective assessment also demonstrates that the proposed method outperforms the state‐of‐the‐art fusion methods

Graph Embedding Method Based on Biased Walking for Link Prediction

Link prediction is an essential and challenging problem in research on complex networks, which can provide research tools and theoretical supports for the formation and evolutionary mechanisms of networks. Existing graph representation learning methods based on random walks usually ignore the influence of local network topology on the transition probability of walking nodes when predicting the existence of links, and the sampling strategy of walking nodes during random walks is uncontrolled, which leads to the inability of these methods to effectively learn high-quality node vectors to solve the link prediction problem. To address the above challenges, we propose a novel graph embedding method for link prediction. Specifically, we analyze the evolution mechanism of links based on triadic closure theory and use the network clustering coefficient to represent the aggregation ability of the network’s local structure, and this adaptive definition of the aggregation ability of the local structure enables control of the walking strategy of nodes in the random walking process. Finally, node embedding generated based on biased walking paths is employed to solve the link prediction problem. Extensive experiments and analyses show that the TCW algorithm provides high accuracy across a diverse set of datasets

On Local Generalized Ulam–Hyers Stability for Nonlinear Fractional Functional Differential Equation

We discuss the existence of positive solution for a class of nonlinear fractional differential equations with delay involving Caputo derivative. Well-known Leray–Schauder theorem, Arzela–Ascoli theorem, and Banach contraction principle are used for the fixed point property and existence of a solution. We establish local generalized Ulam–Hyers stability and local generalized Ulam–Hyers–Rassias stability for the same class of nonlinear fractional neutral differential equations. The simulation of an example is also given to show the applicability of our results

Infrared and Visible Image Fusion Combining Interesting Region Detection and Nonsubsampled Contourlet Transform

The most fundamental purpose of infrared (IR) and visible (VI) image fusion is to integrate the useful information and produce a new image which has higher reliability and understandability for human or computer vision. In order to better preserve the interesting region and its corresponding detail information, a novel multiscale fusion scheme based on interesting region detection is proposed in this paper. Firstly, the MeanShift is used to detect the interesting region with the salient objects and the background region of IR and VI. Then the interesting regions are processed by the guided filter. Next, the nonsubsampled contourlet transform (NSCT) is used for background region decomposition of IR and VI to get a low-frequency and a series of high-frequency layers. An improved weighted average method based on per-pixel weighted average is used to fuse the low-frequency layer. The pulse-coupled neural network (PCNN) is used to fuse each high-frequency layer. Finally, the fused image is obtained by fusing the fused interesting region and the fused background region. Experimental results demonstrate that the proposed algorithm can integrate more background details as well as highlight the interesting region with the salient objects, which is superior to the conventional methods in objective quality evaluations and visual inspection

Predictions of Apoptosis Proteins by Integrating Different Features Based on Improving Pseudo-Position-Specific Scoring Matrix

Apoptosis proteins are strongly related to many diseases and play an indispensable role in maintaining the dynamic balance between cell death and division in vivo. Obtaining localization information on apoptosis proteins is necessary in understanding their function. To date, few researchers have focused on the problem of apoptosis data imbalance before classification, while this data imbalance is prone to misclassification. Therefore, in this work, we introduce a method to resolve this problem and to enhance prediction accuracy. Firstly, the features of the protein sequence are captured by combining Improving Pseudo-Position-Specific Scoring Matrix (IM-Psepssm) with the Bidirectional Correlation Coefficient (Bid-CC) algorithm from position-specific scoring matrix. Secondly, different features of fusion and resampling strategies are used to reduce the impact of imbalance on apoptosis protein datasets. Finally, the eigenvector adopts the Support Vector Machine (SVM) to the training classification model, and the prediction accuracy is evaluated by jackknife cross-validation tests. The experimental results indicate that, under the same feature vector, adopting resampling methods remarkably boosts many significant indicators in the unsampling method for predicting the localization of apoptosis proteins in the ZD98, ZW225, and CL317 databases. Additionally, we also present new user-friendly local software for readers to apply; the codes and software can be freely accessed at https://github.com/ruanxiaoli/Im-Psepssm

Network Representation Learning Algorithm Based on Complete Subgraph Folding

Network representation learning is a machine learning method that maps network topology and node information into low-dimensional vector space. Network representation learning enables the reduction of temporal and spatial complexity in the downstream data mining of networks, such as node classification and graph clustering. Existing algorithms commonly ignore the global topological information of the network in network representation learning, leading to information loss. The complete subgraph in the network commonly has a community structure, or it is the component module of the community structure. We believe that the structure of the community serves as the revealed structure in the topology of the network and preserves global information. In this paper, we propose SF-NRL, a network representation learning algorithm based on complete subgraph folding. The algorithm preserves the global topological information of the original network completely, by finding complete subgraphs in the original network and folding them into the super nodes. We employ the network representation learning algorithm to study the node embeddings on the folded network, and then merge the embeddings of the folded network with those of the original network to obtain the final node embeddings. Experiments performed on four real-world networks prove the effectiveness of the SF-NRL algorithm. The proposed algorithm outperforms the baselines in evaluation metrics on community detection and multi-label classification tasks. The proposed algorithm can effectively generalize the global information of the network and provides excellent classification performance

Facial Feature Extraction Using Frequency Map Series in PCNN

Pulse coupled neural network (PCNN) has been widely used in image processing. The 3D binary map series (BMS) generated by PCNN effectively describes image feature information such as edges and regional distribution, so BMS can be treated as the basis of extracting 1D oscillation time series (OTS) for an image. However, the traditional methods using BMS did not consider the correlation of the binary sequence in BMS and the space structure for every map. By further processing for BMS, a novel facial feature extraction method is proposed. Firstly, consider the correlation among maps in BMS; a method is put forward to transform BMS into frequency map series (FMS), and the method lessens the influence of noncontinuous feature regions in binary images on OTS-BMS. Then, by computing the 2D entropy for every map in FMS, the 3D FMS is transformed into 1D OTS (OTS-FMS), which has good geometry invariance for the facial image, and contains the space structure information of the image. Finally, by analyzing the OTS-FMS, the standard Euclidean distance is used to measure the distances for OTS-FMS. Experimental results verify the effectiveness of OTS-FMS in facial recognition, and it shows better recognition performance than other feature extraction methods