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    25 November 2021, Volume 2021 Issue 6 Previous Issue   
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    Review Article
    The Chinese experience at the International Mathematical Olympiad
    Bin XIONG, Peijie JIANG
    2021, 2021 (6):  1-14.  doi: 10.3969/j.issn.1000-5641.2021.06.001
    Abstract ( 4 )   HTML ( 2 )   PDF (1371KB) ( 2 )   Save

    The International Mathematical Olympiad (IMO) is one of the most important and influential global youth intellectual competitions. However, there is little research on how to effectively organize the competition at the national level to help cultivate talent in mathematics, science, and technology. The Mathematical Olympiad originated from a competition to solve mathematical problems. Many outstanding mathematicians and scientists have been prior winners of the IMO and have reaped benefits subsequently to some extent. The Mathematical Olympiad helps to select and train gifted students in mathematics. China’s outstanding historical achievements in the IMO have attracted the attention of the world. Many of China’s students, who exhibited exceptional performance at the IMO, later became outstanding mathematicians, scientists, and technologists. These achievements need to be publicized, and the Chinese experience at the Mathematical Olympiad needs to be summarized and promoted. This article summarizes the history of the IMO and reviews the practices of the IMO in China based on the literature. China uses a number of strategies to ensure outstanding results in the IMO, including: the selection of contestants from existing domestic programs (National High School Mathematics Joint Competition, Chinese Mathematical Olympiad, and National Training Team); a multi-level educational system based on school training; and the accumulation and publication of relevant learning materials. The outbreak of the novel coronavirus has affected the normal proceedings of the IMO, but China has implemented effective countermeasures. There are still some misunderstandings about the Mathematical Olympiad in China. By introducing prior contestants, who have participated in the IMO and made outstanding contributions, China can help the public better appreciate the Mathematical Olympiad. At the same time, the Chinese experience at the IMO is an important reference for other countries in organizing competition training and selecting and nurturing gifted students in mathematics.

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    Mathematics
    The structure of 3-Lie-Rinehart algebras
    Ruipu BAI, Xiaojuan LI
    2021, 2021 (6):  15-23.  doi: 10.3969/j.issn.1000-5641.2021.06.002
    Abstract ( 5 )   HTML ( 0 )   PDF (674KB) ( 1 )   Save

    In this paper, we introduce a class of 3-ary algebras, called the 3-Lie-Rinehart algebra, and we discuss the basic structure thereof. The 3-Lie-Rinehart algebras are constructed using 3-ary differentiable functions, modules of known 3-Lie algebras, and inner derivatives of 3-Lie algebras.

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    Finite sums in higher order powers of shifted-harmonic numbers
    Qinglun YAN, Zhaofen WANG, Juan MI
    2021, 2021 (6):  24-32.  doi: 10.3969/j.issn.1000-5641.2021.06.003
    Abstract ( 2 )   HTML ( 0 )   PDF (430KB) ( 1 )   Save

    In this article, using methods such as the partial fraction method, we study a set of combined identities for an Euler-type summation. We calculate, furthermore, the finite summation form of the product of the high order shifted-harmonic number and the reciprocal of the binomial coefficient. By using special values for the parameters, interesting identities can be obtained.

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    Braided vector algebra $ V(R',R) $
    Hongmei HU
    2021, 2021 (6):  33-37.  doi: 10.3969/j.issn.1000-5641.2021.06.004
    Abstract ( 7 )   HTML ( 0 )   PDF (472KB) ( 3 )   Save

    Braided vector algebras are an important class of Hopf algebras in braided tensor categories. In this paper, it is shown that braided vector algebras are isomorphic to quantum vector spaces as associative algebras; hence, the algebraic structure of braided vector algebras and three equalities of the pair $ (R',R)$ are recovered from representations of quantized enveloping algebras $ U_q(\mathfrak g)$ .

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    Picard-type theorems for entire functions of several complex variables with total derivatives
    Shengyao ZHOU, Liu YANG
    2021, 2021 (6):  38-46.  doi: 10.3969/j.issn.1000-5641.2021.06.005
    Abstract ( 5 )   HTML ( 0 )   PDF (607KB) ( 4 )   Save

    In this paper, we use the logarithmic derivative lemma for several complex variables to extend the Milloux inequality to differential polynomials of entire functions. As an application, we subsequently apply the concept to two Picard-type theorems: (1) Let $ f $ be an entire function in $\mathbb{C}^{n}$ and $a, b\;(\neq 0)$ be two distinct complex numbers. If $ f\neq a, {\cal{P}}\neq b, $ then $ f $ is constant. (2) If $ f^{s}D^{t_{1}}(f^{s_{1}})\cdots D^{t_{q}}(f^{s_{q}})\neq b $ and $ s+ $ $ \sum_{j = 1}^{q}s_{j}\geqslant 2+\sum_{j = 1}^{q}t_{j}, $ then $ f $ is constant, where $ D^{k}f $ is the $ k $ -th total derivative of $ f $ and $ {\cal{P}} $ is a differential polynomial of $ f $ with respect to the total derivative.

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    Ambrosetti-Prodi results for second-order discrete periodic boundary value problems
    Rui WANG, Yanqiong LU, Xiaomei YANG
    2021, 2021 (6):  47-57.  doi: 10.3969/j.issn.1000-5641.2021.06.006
    Abstract ( 6 )   HTML ( 0 )   PDF (801KB) ( 2 )   Save

    This paper explores the relationship between the number of solutions and the parameter $ s $ of second-order discrete periodic boundary value problems of the form           $\left\{ \begin{array}{ll} \Delta^{2} u(t-1)+f\Delta u(t)+g(t,u(t)) = s, \;t\in[1,T]_{\mathbb{Z}}, \\ u(0) = u(T-1),\;\Delta u(0) = \Delta u(T-1), \end{array} \right.$ where $g: [1,T]_{\mathbb{Z}}\times \mathbb{R}\to\mathbb{R}$ is a continuous function, $ f\geqslant0 $ is a constant, $ T\geqslant2 $ is an integer, and $ s $ is a real number. By using the upper and lower solution method and the theory of topological degree, we obtain the Ambrosetti-Prodi type alternatives which demonstrate the existence of either zero, one, or two solutions depending on the choice of the parameter $ s $ with fixed constant $ s_{0}\in \mathbb{R} $ .

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    Singularity indices of hyperelliptic fibrations
    Zhiming GUO
    2021, 2021 (6):  58-64.  doi: 10.3969/j.issn.1000-5641.2021.06.007
    Abstract ( 3 )   HTML ( 0 )   PDF (702KB) ( 3 )   Save

    Xiao introduced a series of singularity indices to survey hyperelliptic fibrations. However, it remains unknown whether the second singularity index, $ s_2 $ , is non-negative. In this paper, I demonstrate a series of examples of degeneration of curves where $s_2$ tends to $-\infty$ as the genus $g$ grows. Moreover, I obtain a lower bound for $s_2$ for a given genus $g$ , thereby confirming that the index $s_2$ of fibrations for genus $g=2,3,4$ is non-negative.

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    Computer Science
    A fast key points matching method for high resolution images of a planar mural
    Xinye ZHANG, Weiqing TONG, Haisheng LI
    2021, 2021 (6):  65-80.  doi: 10.3969/j.issn.1000-5641.2021.06.008
    Abstract ( 6 )   HTML ( 0 )   PDF (2053KB) ( 2 )   Save

    Existing methods of key points matching were invented for grayscale images and are not suitable for high resolution images. Mural images typically have very high resolution, and there may be areas with the same gray textures and different colors. For this special kind of image, this paper proposes a high-speed algorithm of key points matching for high-resolution mural images (NeoKPM for short). NeoKPM has two main innovations: (1) first, the homography matrix of rough registration for the original image is obtained by downsampling the image, which substantially reduces the time required for key points matching; (2) second, a feature descriptor based on gray and color invariants is proposed, which can distinguish different colors of texture with the same gray level, thereby improving the correctness of key points matching. In this paper, the performance of the NeoKPM algorithm is tested on a real mural image library. The experimental results show that on mural images with a resolution of 80 million pixels, the number of correct matching points per pair of images is nearly 100 000 points higher than that of the SIFT (Scale Invariant Feature Transform) algorithm, the processing speed of key points matching is more than 20 times faster than that of the SIFT algorithm, and the average error of dual images based on a single pixel of the image is less than 0.04 pixels.

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    Research on large-field microscopic images based on the best stitching path
    Yang XU, Hongying LIU, Quanjie ZHUANG
    2021, 2021 (6):  81-87.  doi: 10.3969/j.issn.1000-5641.2021.06.009
    Abstract ( 8 )   HTML ( 1 )   PDF (861KB) ( 1 )   Save

    Image stitching technology is one of the key technologies in the application of large-field microscopic digital images. The existing traditional image stitching method is to stitch in a fixed order after image registration, and once there is an error, it will be accumulated along a fixed path, thereby causing problems such as misalignment of subsequent images. In this study, through experimental analysis, a method for optimizing the stitching path of the large-field image was proposed, which greatly optimized the problems caused by error accumulation and registration failure, and effectively improved the stitching quality of the large-field microscopic digital image. This method can be used not only for the stitching of large-field microscopic images, but also for other types of stitching.

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    Research on joint computation offloading and resource allocation strategy for mobile edge computing
    Dongqing HUANG, Liyang YU, Jue CHEN, Tongquan WEI
    2021, 2021 (6):  88-99.  doi: 10.3969/j.issn.1000-5641.2021.06.010
    Abstract ( 4 )   HTML ( 0 )   PDF (1073KB) ( 1 )   Save

    With the emergence of low-latency applications such as driverless cars, online gaming, and virtual reality, it is becoming increasingly difficult to meet users’ demands for service quality using the traditional centralized mobile cloud computing model. In order to make up for the shortages of cloud computing, mobile edge computing came into being, which provides users with computing and storage resources by migrating computing tasks to network edge servers through computation offloading. However, most of the existing work processes only consider single-objective performance optimization of delay or energy consumption, and do not consider the balanced optimization of delay and energy consumption. Therefore, in order to reduce task delay and equipment energy consumption, a multi-user joint computation offloading and resource allocation strategy is proposed. In this strategy, the Lagrange multiplier method is used to obtain the optimal allocation of computing resources for a given offloading decision. Then, a computation offloading algorithm based on a greedy algorithm is proposed to obtain the optimal offloading decision; the final solution is obtained through continuous iteration. Experimental results show that, compared with the benchmark algorithm, the proposed algorithm can reduce system costs by up to 40%.

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    Network anomaly traffic detection based on ensemble feature selection
    Qiwen HUANG, Liying LI, Fuke SHEN, Tongquan WEI
    2021, 2021 (6):  100-111.  doi: 10.3969/j.issn.1000-5641.2021.06.011
    Abstract ( 6 )   HTML ( 0 )   PDF (1321KB) ( 3 )   Save

    With the continuous development of Internet technology, network security is garnering increasing attention. Network anomalous traffic detection can provide an effective guarantee for blocking network attacks. However, to accurately detect anomalous traffic in a network, analyzing large volumes of data is usually required. Analyzing this data not only consumes substantial computational resources and reduces real-time detection capability, but it may also reduce the overall accuracy of detection. To solve these problems, we propose a network anomaly traffic detection method based on ensemble feature selection. Specifically, we use five different feature selection algorithms to design a voting mechanism for selecting feature subsets. Three different machine learning algorithms (Naive Bayesian, Decision Tree, XGBoost) are used to evaluate the feature selection algorithm, and the best algorithm is selected to detect abnormal network traffic. The experimental results show that the runtime of the proposed method is 84.38% less than the original data set on the optimal feature subset selected by the proposed approach, and the average accuracy is 16.93% higher than that of the single feature selection algorithm.

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    Research on an Edge-Cloud collaborative acceleration mechanism of deep model based on network compression and partitioning
    Nuo WANG, Liying LI, Dongwei QIAN, Tongquan WEI
    2021, 2021 (6):  112-123.  doi: 10.3969/j.issn.1000-5641.2021.06.012
    Abstract ( 5 )   HTML ( 1 )   PDF (966KB) ( 1 )   Save

    The advanced capabilities of artificial intelligence (AI) have been widely used to process large volumes of data in real-time for achieving rapid response. In contrast, conventional methods for deploying various AI-based applications can result in substantial computational and communication overhead. To solve this problem, a deep model Edge-Cloud collaborative acceleration mechanism based on network compression and partitioning technology is proposed. This technology can compress and partition deep neural networks (DNN), and deploy artificial intelligence models in practical applications in the form of an Edge-Cloud collaboration for rapid response. As a first step, the proposed method compresses the neural network to reduce the execution latency required and generates a new layer that can be used as a candidate partition point. It then trains a series of prediction models to find the best partitioning point and partitions the compressed neural network model into two parts. The two parts obtained are deployed in the edge device and the cloud server, respectively, and these two parts can collaborate to minimize the overall latency. Experimental results show that, compared with four benchmarking methods, the proposed scheme can reduce the total delay of the depth model by more than 70%.

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    SQLite-CC based on non-volatile memory cache
    Yaoyi HU, Huiqi HU, Xuan ZHOU, Aoying ZHOU
    2021, 2021 (6):  124-134.  doi: 10.3969/j.issn.1000-5641.2021.06.013
    Abstract ( 4 )   HTML ( 0 )   PDF (999KB) ( 1 )   Save

    In recent years, non-volatile memory (NVM) has developed rapidly. Its advantages, among others, include: persistence, large capacity, low latency, byte addressing, high density, and low energy consumption — all of which have impacted current database system architecture. SQLite is a lightweight relational database widely used in embedded fields such as mobile platforms. It operates as a serverless, zero-configuration, transactional SQL database engine. It maintains a cache for each connection, which results in problems with large space overhead and data consistency detection. At the same time, it adopts a relatively simple serialized single-write transaction execution method and page-based logging, which offers low performance and write amplification in the journal mode and a storage space requirement in the WAL mode during execution. In order to address the above challenges, a new scheme of SQLite Cache based on non-volatile memory, SQLite-CC (Copy Cache), is constructed, which fully considers the hardware characteristics of non-volatile memory and ensures the atomicity of transactions using a CC-manager and by adding an updated page index to ensure the consistency of database files and cache. Benchmarking tests show that it can achieve the same concurrency performance as SQLite-WAL mode. Compared with the rollback mode, it improves the execution performance of transactions by 3 times, reduces latency by 40%, and effectively solves the issue of write amplification on disks.

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    Anomaly detection of transformer loss data based on a robust random cut forest
    Guofang ZHANG, Lili WEN, Meng WU, Tongyu LIU, Kuanyun ZHENG, Fuxing HUANG, Peisen YUAN
    2021, 2021 (6):  135-146.  doi: 10.3969/j.issn.1000-5641.2021.06.014
    Abstract ( 6 )   HTML ( 0 )   PDF (1002KB) ( 2 )   Save

    With the rapid development of smart grids, the construction of new digital infrastructure has become one of the core businesses of power companies. Power companies’ governance and intelligent analytical capabilities enable opportunities for business model innovation, such as platform operation and value-added data realization. In the context of power digitization and intelligent governance, we use the robust random cut forest in this paper for transformer loss data anomaly intelligence detection. The algorithm divides sample points by random cutting to construct a random cut forest structure model by inserting and removing sample points in the structure; the anomaly score of a sample point is then given by the influence of complexity. This method is suitable for anomaly detection on real-time loss data and offers a high degree of credibility, effectiveness, and efficiency. An experiment of anomaly detection on real transformer loss data shows that the method is efficient and flexible. The accuracy, recall, and efficiency of the proposed method, moreover, is substantially better than alternatives.

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    Unsupervised author name disambiguation based on heterogeneous networks
    Chenliang GUO, Xin LIN, Yue YIN
    2021, 2021 (6):  147-160.  doi: 10.3969/j.issn.1000-5641.2021.06.015
    Abstract ( 7 )   HTML ( 0 )   PDF (983KB) ( 6 )   Save

    Author name disambiguation is an important step in constructing an academic knowledge graph. The issue of ambiguous names is widely prevalent in academic literature due to the presence of missing data, ambiguous names, or abbreviations. This paper proposes an unsupervised author name disambiguation method, based on heterogenous networks, with the goal of addressing the problems associated with inadequate information utilization and cold-start; the proposed method automatically learns the features of papers with the ambiguous authors’ name. As a starting point, the method preprocesses strings of authors, organizations, titles, and keywords by lemmatization. The algorithm then learns the embedded representation of text features by the word2vec and TF-IDF methods and learns the embedded representation of structural features using the meta-path random walk and word2vec methods. After merging features by similarity of structure and text, disambiguation is done by a DBSCAN clustering algorithm and merging isolated papers. Experimental results show that the proposed model significantly outperforms existing models in a small dataset and in engineering applications for cold-start unsupervised author name disambiguation. The data indicates that the model is effective and can be implemented in real-world applications.

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    Enabling self-attention based multi-feature anomaly detection and classification of network traffic
    Yuting HUANGFU, Liying LI, Haizhou WANG, Fuke SHEN, Tongquan WEI
    2021, 2021 (6):  161-173.  doi: 10.3969/j.issn.1000-5641.2021.06.016
    Abstract ( 5 )   HTML ( 0 )   PDF (1174KB) ( 6 )   Save

    Network traffic anomaly detection based on feature selection has attracted great research interest. Most existing schemes detect anomalies by reducing the dimensionality of traffic data, but ignore the correlation between data features; this results in inefficient detection of anomaly traffic. In order to effectively identify various types of attacks, a model based on a self-attentive mechanism is proposed to learn the correlation between multiple features of network traffic data. Then, a novel multi-feature anomalous traffic detection and classification model is designed, which analyzes the correlation between multiple features of the anomalous traffic data and subsequently identifies anomalous network traffic. Experimental results show that, compared to two benchmark methods, the proposed technique increased the accuracy of anomaly detection and classification by a maximum of 1.65% and reduced the false alarm rate by 1.1%.

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    Estuary and Coastal Research
    Analysis of the long-term evolution of saltwater intrusion in the Changjiang Estuary
    Jinghua GU, Jianrong ZHU, Cheng QIU, Rui YUAN, Zhipeng LI, Wei QIU, Zhi JIN
    2021, 2021 (6):  174-186.  doi: 10.3969/j.issn.1000-5641.2021.06.017
    Abstract ( 5 )   HTML ( 0 )   PDF (1563KB) ( 125 )   Save

    In this study, we analyzed the evolution of saltwater intrusion in Changjiang Estuary since the 1970s based on: salinity data collected at the Wusong, Gaoqiao, and Baogang stations; days of saltwater intrusion at the water intakes of the Wusong water plant, Chenhang reservoir, and Qingcaosha reservoir; river discharges at Datong station; and satellite remote sensing data of estuarine topography changes. The measured salinity changes at Wusong, Gaoqiao, and Baogang stations in the dry seasons showed that the saltwater intrusion in the Changjiang Estuary was serious in the 1970s, became weak in the 1980s, and was weak from 1990 to 1996. The peak salinity at Baogang station occurred prior to Wusong station, and the peak salinity at Wusong station occurred prior to Gaoqiao station; these observations indicate that the saltwater intrusion originated from upstream saltwater spilling over from the North Branch. The annual days of saltwater intrusion at the water intakes of the Wusong water plant, Chenhang reservoir, and Qingcaosha reservoir indicate that the saltwater intrusion was serious from 1974 to 1981 and particularly acute in 1974, 1979 and 1980; in these cases, the days of saltwater intrusion at the water intake of Wusong water plant exceeded 70 days. The saltwater intrusion was relatively weak from 1982 to 1995. The saltwater intrusion intensified from 1996 to 2002, and serious saltwater intrusion occurred in 1996, 1999, and 2001. The saltwater intrusion from 2003 to 2020 decreased significantly. The construction of the Three Gorges reservoir in 2003 and the cascade reservoirs in the upper reaches of the Changjiang Basin after 2003 resulted in a significant increase in river discharge during the dry season; this phenomenon was the main driver for the weakening saltwater intrusion. The changes in estuarine topography from 1974 to 2013 were detected by satellite remote sensing images; in particular, the North Branch was a wide river in the 1970s. With the successive reclamations of Yonglongsha, Xinglongsha, and Xincunsha, as well as the reclamation of the south shoal in the lower reaches of the North Branch, the North Branch became narrow and the tidal capacity decreased; the sequence of events subsequently led to the gradual weakening of saltwater spillover from the North Branch into the South Branch in a long time scale. The topography changes of the North Branch also explain the drivers for the serious saltwater intrusion that occurred in the 1970s and the relative weakening of saltwater intrusion over time, particularly since the beginning of this century. River discharge and estuarine topography changes are the main drivers for the long-term changes in saltwater intrusion in the Changjiang Estuary. With the construction of more reservoirs in the upper reaches of the Changjiang River and further shrinkage of the North Branch, saltwater intrusion will continue to weaken. These changes are conducive to the safety of freshwater resources in the Changjiang Estuary.

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