659 research outputs 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
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
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
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
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
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