A Specific Method for Solving Fractional Delay Differential Equation via Fraction Taylor’s Series

It is well known that the appearance of the delay in the fractional delay differential equation (FDDE) makes the convergence analysis very difficult. Dealing with the problem with the traditional reproducing kernel method (RKM) is very tricky. The feature of this paper is to gain a more credible approximate solution via fractional Taylor’s series (FTS). We use the FTS to deal with the delay for improving the accuracy of the approximate solutions. Compared with other methods, the five numerical examples demonstrate the accuracy and efficiency of the proposed method in this paper.

ANALISIS SENTIMEN ULASAN APLIKASI TIKTOK DI GOOGLE PLAY MENGGUNAKAN METODE SUPPORT VECTOR MACHINE (SVM) DAN ASOSIASI

Corona virus pandemic requires people to do activities from home so the number of internet usage in Indonesia has increased because information is carried out through social media. One of the popular social media in Indonesia is TikTok. However, the Tiktok’s popularity cannot be separated from the footsteps of TikTok in Indonesia which was blocked by government for committing many violations. Each application allows users to provide a review about the application. To find out the users TikTok’s sentiment, sentiment analysis was carried out to classify reviews into positive and negative sentiments. Classification is carried out using the Support Vector Machine (SVM) with kernel Radial Basis Function (RBF) method which is more effective classification algorithm and kernel function, seen from previous studies. The parameters used in the SVM gamma default 0.0004255 and the Cost (C) parameter experiment used is 0,01; 0,1; 1; 10; 100; 1000. The results can provide information that can be retrieved using the association method. The steps are scrapping data, data preprocessing, sentiment scoring, TF-IDF weighting, classifying using the SVM RBF kernel method and text association. Evaluation of the model using a confusion matrix with the value of accuracy and kappa. The greater the value of accuracy and kappa, the better the performance of the classification model. The review classification resulted in the best accuracy rate of 90.62% and the best kappa of 81.24% which means that it includes an almost perfect classification result. Based on the data association, positive reviews are given because users like and are comfortable with the current version of TikTok which contains funny videos on fyp. Meanwhile, negative reviews were given because the user failed to register and his account was blocked, so the user asked TikTok to continue to make improvements.

Exact tail asymptotics for a three-dimensional Brownian-driven tandem queue with intermediate inputs

In this paper, we consider a three-dimensional Brownian-driven tandem queue with intermediate inputs, which corresponds to a three-dimensional semimartingale reflecting Brownian motion whose reflection matrix is triangular. For this three-node tandem queue, no closed form formula is known, not only for its stationary distribution but also for the corresponding transform. We are interested in exact tail asymptotics for stationary distributions. By generalizing the kernel method, and using extreme value theory and copula, we obtain exact tail asymptotics for the marginal stationary distribution of the buffer content in the third buffer and for the joint stationary distribution.

MCKAT: a multi-dimensional copy number variant kernel association test

Background Copy number variants (CNVs) are the gain or loss of DNA segments in the genome. Studies have shown that CNVs are linked to various disorders, including autism, intellectual disability, and schizophrenia. Consequently, the interest in studying a possible association of CNVs to specific disease traits is growing. However, due to the specific multi-dimensional characteristics of the CNVs, methods for testing the association between CNVs and the disease-related traits are still underdeveloped. We propose a novel multi-dimensional CNV kernel association test (MCKAT) in this paper. We aim to find significant associations between CNVs and disease-related traits using kernel-based methods. Results We address the multi-dimensionality in CNV characteristics. We first design a single pair CNV kernel, which contains three sub-kernels to summarize the similarity between two CNVs considering all CNV characteristics. Then, aggregate single pair CNV kernel to the whole chromosome CNV kernel, which summarizes the similarity between CNVs in two or more chromosomes. Finally, the association between the CNVs and disease-related traits is evaluated by comparing the similarity in the trait with kernel-based similarity using a score test in a random effect model. We apply MCKAT on genome-wide CNV datasets to examine the association between CNVs and disease-related traits, which demonstrates the potential usefulness the proposed method has for the CNV association tests. We compare the performance of MCKAT with CKAT, a uni-dimensional kernel method. Based on the results, MCKAT indicates stronger evidence, smaller p-value, in detecting significant associations between CNVs and disease-related traits in both rare and common CNV datasets. Conclusion A multi-dimensional copy number variant kernel association test can detect statistically significant associated CNV regions with any disease-related trait. MCKAT can provide biologists with CNV hot spots at the cytogenetic band level that CNVs on them may have a significant association with disease-related traits. Using MCKAT, biologists can narrow their investigation from the whole genome, including many genes and CNVs, to more specific cytogenetic bands that MCKAT identifies. Furthermore, MCKAT can help biologists detect significantly associated CNVs with disease-related traits across a patient group instead of examining each subject’s CNVs case by case.

An Improved Approach for Solving Partial Differential Equation Based on Reproducing Kernel Method

The traditional reproducing kernel method (TRKM) cannot obtain satisfactory numerical results for solving the partial differential equation (PDE). In this study, for the first time, the abovementioned problems are solved by adaptive piecewise interpolation reproducing kernel method (APIRKM) to obtain the exact and approximate solutions of partial differential equations by means of series expansion using reconstructed kernel function. The highlight of this paper is to obtain more accurate approximate solution and save more time through adaptive discovery. Numerical solutions of the three examples show that the present method is more advantageous than TRKM.