-
A Fast High Order Algorithm for 3D Helmholtz Equation with Dirichlet Boundary
Sheng An,
Gendai Gu,
Meiling Zhao
Issue:
Volume 7, Issue 4, August 2018
Pages:
180-187
Received:
26 July 2018
Accepted:
13 August 2018
Published:
11 September 2018
Abstract: Helmholtz equation is widely applied in the scientific and engineering problem. For the solution of the three-dimensional Helmholtz equation, the computational efficiency of the algorithm is especially important. In this paper, in order to solve the contradiction between accuracy and efficiency, a fast high order finite difference method is proposed for solving the three-dimensional Helmholtz equation. First, a traditional fourth order method is constructed. Then, fast Fourier transformation are introduced to generate a block-tridiagonal structure which can easily divide the original problem into small and independent subsystems. For large 3D problems, the computation of traditional discrete Fourier transformation is less efficient, and the memory requirements increase rapidly. To fix this problem, the transformed coefficient matrix is constructed as a sparse structure. In light of the sparsity, the algorithm presented in this paper requires less memory space and computational cost. This sparse structure also leads to independent solving procedure of any plane in the domain. Therefore, parallel method can be used to solve the Helmholtz equation with large grid number. In the end, three numerical experiments are presented to verify the effectiveness of the fast fourth-order algorithm, and the acceleration effect to use the parallel method has been demonstrated.
Abstract: Helmholtz equation is widely applied in the scientific and engineering problem. For the solution of the three-dimensional Helmholtz equation, the computational efficiency of the algorithm is especially important. In this paper, in order to solve the contradiction between accuracy and efficiency, a fast high order finite difference method is propose...
Show More
-
Peculiarities of the Rice Statistical Distribution: Mathematical Substantiation
Issue:
Volume 7, Issue 4, August 2018
Pages:
188-196
Received:
16 September 2018
Published:
18 September 2018
Abstract: The Rice statistical distribution has recently become a subject of increasing scientific interest due to its wide applicability in various fields of science and technology, such as the magnetic-resonance visualization and ultrasound diagnostics in medicine, the radio and radar signals’ analysis and processing, the optical measurements, etc. The common feature of the tasks that are adequately described by the Rician statistical model consists in the fact that the value to be measured and analyzed is an amplitude, or an envelope of the output signal which is composed as a sum of the initially determined informative component and a random noise component being formed by many independent normally-distributed summands. The efficient reconstruction of the Rician signal’s informative component against the noise background is shown to be achieved only on the basis of joint determination of both a priori unknown Rician parameters. The Rice statistical distribution possesses some peculiarities that allow solving rather complicated tasks connected with the stochastic data processing. The paper considers the issues of the strict mathematical substantiations of the Rice distribution properties that are meaningful for its efficient application, namely: the Rician likelihood function features and the stable character of the Rice distribution. There are provided the rigorous proofs of the mentioned properties.
Abstract: The Rice statistical distribution has recently become a subject of increasing scientific interest due to its wide applicability in various fields of science and technology, such as the magnetic-resonance visualization and ultrasound diagnostics in medicine, the radio and radar signals’ analysis and processing, the optical measurements, etc. The com...
Show More
-
Subjective Well-Being Prediction Using Data Mining Techniques: Evidence from Chinese General Social Survey
Leibao Zhang,
Yanli Fan,
Wenyu Zhang,
Shuai Zhang
Issue:
Volume 7, Issue 4, August 2018
Pages:
197-202
Received:
16 September 2018
Published:
18 September 2018
Abstract: Data mining techniques have attracted increasing attentions recently and played more and more important roles in various domains. However, few studies have used these prevalent techniques to explore the rules of subjective well-being for individuals. In this study, a prevalent data mining method, XGBoost, is applied to predict the subjective well-being according to various predictive factors. Feature selection step is implemented to further improve the prediction results and reduce the computational complex based on the importance calculated by XGBoost. An authoritative academic database, Chinese General Social Survey, is used for providing an evidence for classification prediction performance. Moreover, five benchmark models, i.e., logistic regression, support vector machine, decision tree, random forest, and gradient boosting decision tree, are used for comparative analysis based on three evaluation metrics, Accuracy, AUC and F-score. The experimental results indicate that XGBoost outperforms other benchmark models, and feature selection step can improve the prediction performance and reduce the computational time to some extent. In reality, using data mining methods can deeply explore the rule of subjective well-being based on various predictive features, and provide an overwhelming support for improving subjective well-being. Therefore, the methods used in this study are effective and the results provide a support for making society more harmonious.
Abstract: Data mining techniques have attracted increasing attentions recently and played more and more important roles in various domains. However, few studies have used these prevalent techniques to explore the rules of subjective well-being for individuals. In this study, a prevalent data mining method, XGBoost, is applied to predict the subjective well-b...
Show More
-
The Cordial Labeling for the Four-Leaved Rose Graph
Issue:
Volume 7, Issue 4, August 2018
Pages:
203-211
Received:
22 June 2018
Accepted:
31 August 2018
Published:
15 October 2018
Abstract: A cactus graph with four blocks which are all cycles, not necessarily be of the same size, is called four-leaved rose graph and denoted by Ln, m, k, s, where n, m, k and s represent she sizes of the four cycles. A cordial graph is a graph whose vertices and edges have 0-1 labeling in such a way that the number of vertices (edges) labelled with zeros and the number of vertices (edges) labelled with ones differ absolutely by at most one .In this paper, we study this graph in detail and show that any four-leaved rose graph is cordial for all n, m, k and s except possibly at n, m are odd with (k + s) = 0(mod4) or n, m are even with (k + s) = 2(mod4). Our technique depends on the methods that partition off the set of positive integers and then use suitable labeling in each division of the partition to achieve our results. AMS classification 05C76, 05C78
Abstract: A cactus graph with four blocks which are all cycles, not necessarily be of the same size, is called four-leaved rose graph and denoted by Ln, m, k, s, where n, m, k and s represent she sizes of the four cycles. A cordial graph is a graph whose vertices and edges have 0-1 labeling in such a way that the number of vertices (edges) labelled with zero...
Show More
-
Performance Evaluation of Machine Learning Methods for Breast Cancer Prediction
Issue:
Volume 7, Issue 4, August 2018
Pages:
212-216
Received:
17 October 2018
Published:
18 October 2018
Abstract: Breast cancer is the most common invasive cancer in women and the second main cause of cancer death in females, which can be classified Benign or Malignant. Research and prevention on breast cancer have attracted more concern of researchers in recent years. On the other hand, the development of data mining methods provides an effective way to extract more useful information from complex database, and some prediction, classification and clustering can be made according to extracted information. In this study, to explore the relationship between breast cancer and some attributes so that the death probability of breast cancer can be reduced, five different classification models including Decision Tree (DT), Random Forest (RF), Support Vector Machine (SVM), Neural Network (NN) and Logistics Regression (LR) are used for the classification of two different datasets related to breast cancer: Breast Cancer Coimbra Dataset (BCCD) and Wisconsin Breast Cancer Database (WBCD). Three indicators including prediction accuracy values, F-measure metric and AUC values are used to compare the performance of these five classification models. comparative experiment analysis shows that random forest model can achieve better performance and adaptation than other four methods. Therefore, the model of this study is approved to possess clinical and referential values in practical applications.
Abstract: Breast cancer is the most common invasive cancer in women and the second main cause of cancer death in females, which can be classified Benign or Malignant. Research and prevention on breast cancer have attracted more concern of researchers in recent years. On the other hand, the development of data mining methods provides an effective way to extra...
Show More
