Bowen entropy for actions of amenable groups

Bowen introduced a definition of topological entropy of subset inspired by Hausdorff dimension in 1973 \cite{B}. In this paper we consider the Bowen's entropy for amenable group action dynamical systems and show that under the tempered condition, the Bowen entropy of the whole compact space for a given F{\o}lner sequence equals to the topological entropy. For the proof of this result, we establish a variational principle related to the Bowen entropy and the Brin-Katok's local entropy formula for dynamical systems with amenable group actions.Comment: 13 page

Hierarchic Clustering Algorithm Used for Anomaly Detecting

AbstractThe popularity of using Internet contains some risks of network attacks. Intrusion detection is one major research problem in network security, whose aim is to prevent unauthorized access to system resources and data. This paper choose the clustering algorithm based on the hierarchical structure, to form normal behavior profile on the audit records and adjust the profile timely as the program behavior changed. The algorithm can convert the problem to resolve the problem of massive data processing to the hot research point of anomaly detection. Moreover, in order to improve the results of testing further, we choose data processing algorithm to get high-quality data source. As the experiment shown, we get effective experimental result

Chinese Herbal Medicines Facilitate the Control of Chemotherapy-Induced Side Effects in Colorectal Cancer: Progress and Perspective

Side effects, including nausea, vomiting, mucositis, peripheral neuropathy, and diarrhea, have been frequently reported in colorectal cancer (CRC) patients undergoing chemotherapy. Chinese Herbal Medicines (CHMs) display distinct clinical outcomes, as a result, they have been increasingly used as an adjuvant therapy to manage chemotherapy-induced side effects. In this review, we aim to intensively explore the molecular mechanisms of CHMs, underline the significance of CHMs in mitigating the side effects induced by chemotherapy, and examine the necessary studies required to understand the role of CHMs in alleviating chemotherapy-induced side effects. Specifically, ginger, Astragali Radix, and Liujunzi Decoction have been verified to ameliorate nausea and vomiting. Banxia Xiexin Decoction and Huangqin Decoction have been confirmed to be beneficial to mucositis and delayed-onset of diarrhea. Moreover, Niuche Shenqi Wan, Guilong Tongluo Decoction, Huangqi Guizhi Wuwu Decoction, and tumeric have been found to display potential therapeutic effects for preventing the genesis and development of peripheral neurotoxicity. These findings have further emphasized the pivotal role of CHMs in improving the outcomes of chemotherapy-induced side effects in CRC. Nonetheless, more molecular evidence is required to comprehensively understand and more appropriately apply CHMs in routine clinical practice for CRC

Optimal parameter for the SOR-like iteration method for solving the system of absolute value equations

The SOR-like iteration method for solving the absolute value equations~(AVE) of finding a vector $x$ such that $Ax - |x| - b = 0$ with $\nu = \|A^{-1}\|_2 < 1$ is investigated. The convergence conditions of the SOR-like iteration method proposed by Ke and Ma ([{\em Appl. Math. Comput.}, 311:195--202, 2017]) are revisited and a new proof is given, which exhibits some insights in determining the convergent region and the optimal iteration parameter. Along this line, the optimal parameter which minimizes $\|T_\nu(\omega)\|_2$ with $$T_\nu(\omega) = \left(\begin{array}{cc} |1-\omega| & \omega^2\nu \\ |1-\omega| & |1-\omega| +\omega^2\nu \end{array}\right)$$ and the approximate optimal parameter which minimizes $\eta_{\nu}(\omega) =\max\{|1-\omega|,\nu\omega^2\}$ are explored. The optimal and approximate optimal parameters are iteration-independent and the bigger value of $\nu$ is, the smaller convergent region of the iteration parameter $\omega$ is. Numerical results are presented to demonstrate that the SOR-like iteration method with the optimal parameter is superior to that with the approximate optimal parameter proposed by Guo, Wu and Li ([{\em Appl. Math. Lett.}, 97:107--113, 2019]). In some situation, the SOR-like itration method with the optimal parameter performs better, in terms of CPU time, than the generalized Newton method (Mangasarian, [{\em Optim. Lett.}, 3:101--108, 2009]) for solving the AVE.Comment: 23 pages, 7 figures, 7 table