Table of Content

15 October 2021, Volume 38 Issue 5 Previous Issue   

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Gene Data Mining and Bioinformatics Analysis of Tuberculosis Based on Three Bayesian Methods ZHANG Xu, WU Peiwang, QIAO Feng 2021, 38 (5):  601-609.  doi: 10.3969/j.issn.1005-3085.2021.05.001 Abstract ( 53 )   PDF (965KB) ( 46 )   Save Identification of susceptible host genes plays a key role in the treatment and prevention of tuberculosis. So far, only a few genes have been confirmed to be related to it. Based on the gene chip dataset GSE54992 of peripheral blood mononuclear cells of tuberculosis patients, this paper selects the differentially expressed genes between normal samples and active tuberculosis samples by combing information prior Bayesian test and linear model empirical Bayesian method. 319 differentially expressed genes are recognized by both methods. These genes are modeled by using naive Bayes classifier based on the independent verification set GSE83456 where a high classification accuracy is obtained. Finally, the molecular mechanism of tuberculosis is analyzed from the biological point of view through GO function enrichment and KEGG pathway analysis. This study highlights the important roles of the three Bayesian methods in gene data analysis. It provides a new comprehensive strategy for exploring specific biomarkers of tuberculosis, and shows the important clues for the prevention, diagnosis and treatment of tuberculosis. Related Articles | Metrics

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A Scale Adaptive Discrete Unified Gas Kinetic Scheme XU Ding, LIU Xin, SUN Xiang 2021, 38 (5):  610-626.  doi: 10.3969/j.issn.1005-3085.2021.05.002 Abstract ( 55 )   PDF (852KB) ( 33 )   Save In this paper, a general discretization of Boltzmann-BGK model equation along the characteristic line is obtained, where the time integration of collision term is handled as a weighted average between the implicit and explicit part. Moreover, the value of weight factor depends on the local Knudsen number, which represents the local flow regime and scale. With the aid of this weight factor, a scale adaptive discrete unified gas kinetic scheme (SADUGKS) has been developed based on the existing discrete unified gas kinetic scheme (DUGKS). The range of the value of weight factor is analyzed mathematically, and discussed physically. It is found that the value of weight factor could adjust dynamically according to the local flow regime and scale. Finally, four numerical simulations, including Taylor vortex flow, lid-driven cavity flow, backward-facing step flows and micro-Couette flow, are performed to investigate the accuracy and validity of SADUGKS in both continuum and rarefied flow regimes. It is concluded that the present SADUGKS is a reliable and practical multiscale method for all Knudsen number gas flows. Related Articles | Metrics

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Microblog Emotion Classification Based on Target Domain Adaptive SVM Classifier HAO Xiaohong, XUE Baoju 2021, 38 (5):  627-636.  doi: 10.3969/j.issn.1005-3085.2021.05.003 Abstract ( 59 )   PDF (283KB) ( 150 )   Save At present, it is difficult to achieve cross domain sentiment classification in microblog data. Many feature-based and case-based methods have low classification accuracy and slow computing speed. To solve these problems, a model-based adaptive support vector machine (SVM) method is proposed, that is MASVM, which can directly apply existing models to new target domain data. Firstly, Based on the many-to-one SVM adaptive model, the classifier decision function trained by the source domain data set is modified, and a classifier adapted to the target domain is created. Then, we extend the multiple classifier adaptation framework, and learn the weight control of the basic classifier according to the allocation performance of the basic classifier in the smaller target domain tag set. Finally, the basic classifier trained by the general corpus is used to minimize the error of the emotional classification through domain adaptation. The experimental results show that the proposed method is better than the performance of the benchmark method and some similar methods in terms of accuracy and computational efficiency. In addition, the different proportions of the target domain label data will also affect the classification performance. As the performance of the proposed method is better than the basic model and domain adaptive method, it shows similar performance with the upper bound model in the domain, and has the advantage of computing speed, so it can be used as a fast microblog emotion classification method. Related Articles | Metrics

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Representative Research on Census Micro-records Sample HU Guihua, CHI Lujie 2021, 38 (5):  637-652.  doi: 10.3969/j.issn.1005-3085.2021.05.004 Abstract ( 48 )   PDF (240KB) ( 32 )   Save After each census, the governmental statistical departments of various countries issue items on the development and utilization of census data, in order to maximize the role of census data in social and economic development. The governmental statistical department often only provides item's successful bidders with the sample census micro-records. If the sample census micro-records are not representative of those of the population, the wrong analysis conclusions will be drawn. Few scholars or relevant personnel of governmental statistical departments pay attention to the representativeness of the sample census micro-records, which is reflected in the direct use of the census micro-records to draw statistical analysis conclusions. To solve this problem, the IPUMS database established by the Population Center of the Uni-versity of Minnesota is applied as the data source, the stratified double sampling method is adopted to construct the linear estimator, the ratio estimator and their sampling variance estimators of the number of men and women, the representativeness of 1% sample micro-records in Chongqing, China in 2000 is studies. The research results show that the linear estimator and the ratio estimator estimating the numbers of men and women obey or asymptotically obey the normal distribution, and the sample census micro-records are representative. Moreover, all the confidence intervals include the corresponding true value, and the estimated results are close to the true value, the estimation precision is high. This work helps scholars pay attention to and study the representativeness of the sample census micro-records, and test their representativeness before using sample census micro-records for statistical analysis. Also, it provides scientific basis for census data users to decide whether or to what extent to use census data. Related Articles | Metrics

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Persistence and Global Existence of Positive Solutions for Water-plant Stochastic Model WANG Jingnan, CHEN Hui, YANG Dezhong, LU Chaoyi, TAN Yuli 2021, 38 (5):  653-661.  doi: 10.3969/j.issn.1005-3085.2021.05.005 Abstract ( 72 )   PDF (411KB) ( 28 )   Save Land desertification caused by human over-exploitation and destruction of nature has become one of the severest ecological problems of China inland basin. In order to learn about the situation of the sustainable growth of plants in desertification areas, we establish a new water-plant model with stochastic effects to study the effect of the random water supply on plant growth in this paper. Through phase diagram analysis and It$\hat{\rm o}$ formula, we prove the global existence of the positive solution for water-plant stochastic model. By the average integral method, It$\hat{\rm o}$ formula and the strong large numbers law of local martingales, we obtain the sufficient conditions for the strong persistence in the mean of plants. The numerical simulations show the effect of the random water supply on plant growth. The results of theoretical and numerical simulations provide the theoretical basis for the control over the desertification problem. Related Articles | Metrics

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The Spatial Distribution Pattern of an Algae-mussel Model with Nonlocal Predation Effect LI Jing, SUN Guiquan 2021, 38 (5):  662-678.  doi: 10.3969/j.issn.1005-3085.2021.05.006 Abstract ( 48 )   PDF (5966KB) ( 40 )   Save Mussel population is a key link in the food chain network of coastal ecosystem, and its spatial distribution pattern plays an important role in the healthy development of coastal ecosystem. The current researches ignore that the increase of mussel biomass in one location is caused by the mussels of other locations moving to this location and preying on algae. In this paper, an algae-mussel spatial diffusion model with nonlocal predation effect is established. Firstly, the existences of two equilibria in the non-diffusion system are calculated and the corresponding conditions of locally asymptotic stability are given. Then, the conditions for Turing instability of the diffusion system near the mussel survival equilibrium are derived based on Turing instability theory. Furthermore, the spatial distribution pattern of mussel population with time evolution was demonstrated by numerical simulations, which eventually formed a high density spot distribution structure. Finally, the parameter sensitivity analysis shows that the diffusion rates of the two populations significantly affect the spatial distribution pattern of the mussel population, which indicates that the changes of the movement laws of two populations may destroy the stable evolution of the coastal ecosystem; While the influence of nonlocal predation effect is not obvious, which is more conducive to the sustainable survival of mussel population. This work helps people to better understand the evolution law of mussel population from the mathematical level, and provides theoretical support for the rational development and utilization of coastal ecosystem resources. Related Articles | Metrics

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Bifurcation Structures for a Class of Ratio-type Holling-Leslie Chemotaxis Models ZHANG Wang, LI Yanling, ZHOU Hao 2021, 38 (5):  679-690.  doi: 10.3969/j.issn.1005-3085.2021.05.007 Abstract ( 46 )   PDF (1644KB) ( 31 )   Save In this paper, a kind of rate-dependent Holling-Leslie predator-prey chemotaxis model is studied by using linearization method and local bifurcation theory. We discuss the structure of the normal positive equilibrium point in detail in two dimensional space with the prey-tactic sensitivity coefficient as bifurcation parameter and the bifurcation direction is determined near the bifurcation point. The theoretical results show that chemotactic rejection has an unstable effect and can lead to local bifurcation solutions. Finally, the theoretical prediction is verified by numerical simulation, and it is explained that the biochemical system would change from a homogeneous stable state to an unstable biological phenomenon. Related Articles | Metrics

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The Correspondence between the Dual NLS Hierarchy and the Derivative NLS Hierarchy GUO Mingyue, KANG Ting, WANG Yunbo 2021, 38 (5):  691-699.  doi: 10.3969/j.issn.1005-3085.2021.05.008 Abstract ( 57 )   PDF (141KB) ( 40 )   Save In this paper, we study the one-to-one correspondence between the dual NLS hierarchy and derivative NLS hierarchy, and associated Hamiltonian conservation laws. The first part, we give the correspondence between these two recursion operators according to the gauge transformation between the dual NLS and derivative NLS equations. And base on these relationships, we prove that these two equation hierarchies have the same gauge transformation. The sencond part, we propose the correspondence between these two equation hierarchies about the variation derivative of Hamiltonian functional. And then, we obtain to the relationship about their associated Hamiltonian conservation laws. Related Articles | Metrics

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Existence and Uniqueness of Solutions for Boundary Value Problems of Fractional Differential Equations with Delay LI Shuai, ZHANG Zhixin, JIANG Wei 2021, 38 (5):  700-708.  doi: 10.3969/j.issn.1005-3085.2021.05.009 Abstract ( 59 )   PDF (154KB) ( 43 )   Save The time delay factor has an important influence on the solution of the fractional differential system. The change of the system solution not only depends on the current state, but also is constrained by the past state. Therefore, it is of great significance to consider the delay effect in the fractional differential system. In this paper, the existence and uniqueness of solutions for a class of boundary value problem of fractional order differential equation with delay are disscussed. Firstly, the equivalent equation of fractional order differential equation with delay is given by constructing the Green function and the relevant properties of the fractional calculus. Then, the problem of solving this equivalent equation is transformed into a fixed point problem in Banach space. By applying Banach contraction mapping principle and Schauder fixed point theorems, some sufficient conditions ensure that the uniqueness and the existence of solutions of boundary value problem for fractional order differential equation with delay are obtained respectively. Finally, two examples are presented to verify the theoretical results. In this paper, we use a special norm in Banach space to obtain sufficient conditions for the existence and uniqueness of the solution of the system, which is simpler than the previous results. This method is novel and can be used to discuss the existence and uniqueness of positive solutions for boundary value problems of fractional Langevin equations with time delay. Related Articles | Metrics

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A Dijkstra Shortest Path Optimization Method Based on Binary Heap WANG Zhilin, QIAO Xinhui, MA Xu, YAN Yan 2021, 38 (5):  709-720.  doi: 10.3969/j.issn.1005-3085.2021.05.010 Abstract ( 66 )   PDF (323KB) ( 45 )   Save This paper is concerned with the problem that the calculations of Dijkstra algorithm increase rapidly with the amount of data. First of all, the minimum binary heap as the auxiliary data structure of Dijkstra shortest path algorithm is proposed, which can effectively reduce the  calculations and improve the operation efficiency. Then, the distance data and train accessibility data of 31 provincial capitals in China (excluding Hong Kong, Macao and Taiwan) are chosen in the numerical simulations. Finally, the results indicate that it is much faster to find the shortest path by applying the binary heap optimization algorithm than the traditional algorithms, and it is more obvious when increasing scale of the problem. It is conclued that the binary heap optimization algorithm is able to significantly improve the computational efficiency. Related Articles | Metrics

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Neighbor Expanded Sum Distinguishing Total Colorings of Some Cartesian Product Graphs WANG Guoxing 2021, 38 (5):  721-730.  doi: 10.3969/j.issn.1005-3085.2021.05.011 Abstract ( 47 )   PDF (205KB) ( 30 )   Save Based on the structure of Cartesian product graphs, we apply the constructional coloring functions to prove that the neighbor expanded sum distinguishing total chromatic indexes (NESDTC) of graphs $P_m\Box C_n$, $P_m\Box W_{n} (n\geq 9)$ and $P_m\Box K_n$ equal to 2. Those results show that the NESDTC-conjecture proposed by Flandrin {\sl et al} is correct for graphs $P_m\Box C_n$, $P_m\Box W_{n} (n\geq 9)$ and $P_m\Box K_n$. Related Articles | Metrics

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Some Limit Theorems for Nonhomogeneous Bifurcating Markov Chains Indexed by a Binary Tree LI Shilin, YANG Weiguo, SHI Zhiyan 2021, 38 (5):  731-739.  doi: 10.3969/j.issn.1005-3085.2021.05.012 Abstract ( 44 )   PDF (166KB) ( 39 )   Save Recently, the structural properties and limit properties of many complex systems such as tree graphs or tree networks have become hot topics in research, especially in the field of tree-index Markov chains. A large number of domestic and foreign scholars have obtained numerous significant research results. The non-homogeneous bifurcating Markov chain indexed by a binary tree is a special kind of tree-index Markov chain, and its limit properties have been extensively studied by scholars and applied to many fields such as biodynamics and information theory. This paper is devoted to the limit theorem of the transition probability for non-homogeneous bifurcating Markov chains indexed by a binary tree and the relationship between this theorem and the tree-index Markov chain model. First of all, under new conditions, we present a strong limit theorem for non-homogeneous branch Markov chains indexed by a binary tree taking values in a finite state space. Moreover, the strong limit theorem for the harmonic average of its random transition probabilities has been obtained. Finally, by using the equivalent of the above two models and the mean inequality, we extend the limit theorem of the random transition probability for the non-homogeneous Markov chain indexed by a tree. Related Articles | Metrics

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Likelihood Ratio Tests for Homogeneity of Multiple Populations in a Parametric Family QIN Yongsong, HUANG Meiqing 2021, 38 (5):  740-750.  doi: 10.3969/j.issn.1005-3085.2021.05.013 Abstract ( 41 )   PDF (1986KB) ( 26 )   Save The test for the homogeneity of several populations is a common issue in many application fields. The well-known results related to this issue include the analysis of variance (ANOVA) for normal populations and the Kruskal Wallis Test (KWT) for nonparametric populations, but there is no general result on the test for the homogeneity of parametric populations. In this paper, the likelihood ratio test (LRT) statistic is constructed to test for the homogeneity of several populations which are the members of a parametric family. It is shown that under some regularity conditions and the null hypothesis all distribution functions of the populations are the same, and the limiting distribution of the LRT statistic  is chi-squared distribution. This result fills in a gap between ANOVA for normal populations and KWT for nonparametric populations. Related Articles | Metrics