The Jacobi Elliptic Equation Method for Solving Fractional Partial Differential Equations

Based on a nonlinear fractional complex transformation, the Jacobi elliptic equation method is extended to seek exact solutions for fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. For demonstrating the validity of this method, we apply it to solve the space fractional coupled Konopelchenko-Dubrovsky (KD) equations and the space-time fractional Fokas equation. As a result, some exact solutions for them including the hyperbolic function solutions, trigonometric function solutions, rational function solutions, and Jacobi elliptic function solutions are successfully found

Some New Oscillation Criteria for a Class of Nonlinear Fractional Differential Equations with Damping Term

We are concerned with oscillation of solutions of a class of nonlinear fractional differential equations with damping term. Based on a generalized Riccati function and inequality technique, we establish some new oscillation criteria for it. Some applications are also presented for the established results

Simple to Complex Cross-modal Learning to Rank

The heterogeneity-gap between different modalities brings a significant challenge to multimedia information retrieval. Some studies formalize the cross-modal retrieval tasks as a ranking problem and learn a shared multi-modal embedding space to measure the cross-modality similarity. However, previous methods often establish the shared embedding space based on linear mapping functions which might not be sophisticated enough to reveal more complicated inter-modal correspondences. Additionally, current studies assume that the rankings are of equal importance, and thus all rankings are used simultaneously, or a small number of rankings are selected randomly to train the embedding space at each iteration. Such strategies, however, always suffer from outliers as well as reduced generalization capability due to their lack of insightful understanding of procedure of human cognition. In this paper, we involve the self-paced learning theory with diversity into the cross-modal learning to rank and learn an optimal multi-modal embedding space based on non-linear mapping functions. This strategy enhances the model's robustness to outliers and achieves better generalization via training the model gradually from easy rankings by diverse queries to more complex ones. An efficient alternative algorithm is exploited to solve the proposed challenging problem with fast convergence in practice. Extensive experimental results on several benchmark datasets indicate that the proposed method achieves significant improvements over the state-of-the-arts in this literature.Comment: 14 pages; Accepted by Computer Vision and Image Understandin

Low complexity Reed–Solomon-based low-density parity-check design for software defined optical transmission system based on adaptive puncturing decoding algorithm

AbstractWe propose and demonstrate a low complexity Reed–Solomon-based low-density parity-check (RS-LDPC) code with adaptive puncturing decoding algorithm for elastic optical transmission system. Partial received codes and the relevant column in parity-check matrix can be punctured to reduce the calculation complexity by adaptive parity-check matrix during decoding process. The results show that the complexity of the proposed decoding algorithm is reduced by 30% compared with the regular RS-LDPC system. The optimized code rate of the RS-LDPC code can be obtained after five times iteration

Noisy Correspondence Learning with Meta Similarity Correction

Despite the success of multimodal learning in cross-modal retrieval task, the remarkable progress relies on the correct correspondence among multimedia data. However, collecting such ideal data is expensive and time-consuming. In practice, most widely used datasets are harvested from the Internet and inevitably contain mismatched pairs. Training on such noisy correspondence datasets causes performance degradation because the cross-modal retrieval methods can wrongly enforce the mismatched data to be similar. To tackle this problem, we propose a Meta Similarity Correction Network (MSCN) to provide reliable similarity scores. We view a binary classification task as the meta-process that encourages the MSCN to learn discrimination from positive and negative meta-data. To further alleviate the influence of noise, we design an effective data purification strategy using meta-data as prior knowledge to remove the noisy samples. Extensive experiments are conducted to demonstrate the strengths of our method in both synthetic and real-world noises, including Flickr30K, MS-COCO, and Conceptual Captions.Comment: Accepted at CVPR 202