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Volume 4, 2021

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Mathematical Foundations of Computing

May 2021 , Volume 4 , Issue 2

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Semi-Supervised classification of hyperspectral images using discrete nonlocal variation Potts Model
Linyao Ge, Baoxiang Huang, Weibo Wei and Zhenkuan Pan
2021, 4(2): 73-88 doi: 10.3934/mfc.2021003 +[Abstract](286) +[HTML](127) +[PDF](928.41KB)

The classification of Hyperspectral Image (HSI) plays an important role in various fields. To achieve more precise multi-target classification in a short time, a method for combining discrete non-local theory with traditional variable fraction Potts models is presented in this paper. The nonlocal operator makes better use of the information in a certain region centered on that pixel. Meanwhile, adding the constraint in the model can ensure that every pixel in HSI has only one class. The proposed model has the characteristics of non-convex, nonlinear, and non-smooth so that it is difficult to achieve global optimization results. By introducing a series of auxiliary variables and using the alternating direction method of multipliers, the proposed classification model is transformed into a series of convex subproblems. Finally, we conducted comparison experiments with support vector machine (SVM), K-nearest neighbor (KNN), and convolutional neural network (CNN) on five different dimensional HSI data sets. The numerical results further illustrate that the proposed method is stable and efficient and our algorithm can get more accurate predictions in a shorter time, especially when classifying data sets with more spectral layers.

Hermite-Hadamard type inequalities for harmonical $ (h1,h2)- $convex interval-valued functions
Ruonan Liu and Run Xu
2021, 4(2): 89-103 doi: 10.3934/mfc.2021005 +[Abstract](234) +[HTML](119) +[PDF](338.1KB)

We introduce the concept of interval harmonical \begin{document}$ (h1,h2)- $\end{document}convex functions, establish some new Hermite-Hadamard type inequalities on interval Riemann integrable functions, and generalize the results of Noor et al. 2015 and Zhao Dafang et al. 2019.

New explicit and exact traveling wave solutions of (3+1)-dimensional KP equation
Yuanqing Xu, Xiaoxiao Zheng and Jie Xin
2021, 4(2): 105-115 doi: 10.3934/mfc.2021006 +[Abstract](132) +[HTML](88) +[PDF](892.63KB)

In this paper, we investigate explicit exact traveling wave solutions of the generalized (3+1)-dimensional KP equation

describing the dynamics of solitons and nonlinear waves in the field of plasma physics and fluid dynamics, where \begin{document}$ \alpha, \beta, \gamma, \delta $\end{document} are nonzero constants. By using the simplified homogeneous balance method, we get one single soliton solution and one double soliton solution of (1). Moreover, we use the extended tanh method with a Riccati equation and the simplest equation method with Bernoulli equation to obtain seven sets of explicit exact traveling wave solutions. When \begin{document}$ \delta = 0 $\end{document} or \begin{document}$ \gamma = 0 $\end{document}, (1) reduces to (2+1)-dimensional KP equation. Therefore, we can get some exact traveling wave solutions of (2+1)-dimensional KP equation.

Global attractors of the 3D micropolar equations with damping term
Xiaojie Yang, Hui Liu and Chengfeng Sun
2021, 4(2): 117-130 doi: 10.3934/mfc.2021007 +[Abstract](166) +[HTML](88) +[PDF](318.18KB)

The 3D micropolar system with a damping term is considered by the uniform estimates. In this paper, global attractors of the 3D micropolar equations with damping term are proved for \begin{document}$ 3<\beta<5 $\end{document} with any \begin{document}$ \sigma>0 $\end{document}.

Evaluation of parallel and sequential deep learning models for music subgenre classification
Miria Feng and Wenying Feng
2021, 4(2): 131-143 doi: 10.3934/mfc.2021008 +[Abstract](179) +[HTML](87) +[PDF](666.64KB)

In this paper, we evaluate two deep learning models which integrate convolutional and recurrent neural networks. We implement both sequential and parallel architectures for fine-grain musical subgenre classification. Due to the exceptionally low signal to noise ratio (SNR) of our low level mel-spectrogram dataset, more sensitive yet robust learning models are required to generate meaningful results. We investigate the effects of three commonly applied optimizers, dropout, batch regularization, and sensitivity to varying initialization distributions. The results demonstrate that the sequential model specifically requires the RMSprop optimizer, while the parallel model implemented with the Adam optimizer yielded encouraging and stable results achieving an average F1 score of \begin{document}$ 0.63 $\end{document}. When all factors are considered, the optimized hybrid parallel model outperformed the sequential in classification accuracy and system stability.



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