2019 No. 1
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2019, (1): 1-12, 38.
doi: 10.3969/j.issn.1000-5641.2019.01.001
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Abstract:
A susceptible-infected-susceptible (SIS) epidemic model driven by spectrally positive α-stable processes is considered. Firstly, the uniqueness and the existence of the global positive solution are proved. Next, by using Khasminskii's lemma and the Lyapunov method, conditions for the existence of a unique stationary distribution are given. In addition, the model is shown to be exponentially ergodic. Finally, conditions for extinction of the model are given.
A susceptible-infected-susceptible (SIS) epidemic model driven by spectrally positive α-stable processes is considered. Firstly, the uniqueness and the existence of the global positive solution are proved. Next, by using Khasminskii's lemma and the Lyapunov method, conditions for the existence of a unique stationary distribution are given. In addition, the model is shown to be exponentially ergodic. Finally, conditions for extinction of the model are given.
2019, (1): 13-23.
doi: 10.3969/j.issn.1000-5641.2019.01.002
Abstract:
Traditional loss reserve models are mainly based on aggregate loss triangles, in which the entries are obtained by summations of individual loss data. The summation procedures inevitably cause wastage of information contained in the raw individual data. Though this method is simple, it results in a larger error in the estimate of loss reserves. Individual loss reserve models emerging in recent years have failed to consider dependencies between policies. This article assumes the existence of certain common random effects between policies in the same accident year. Thus, a hierarchical bayesian model is built for individual data loss reserves. Using the ideas of credibility theory, we get the credibility estimate of loss reserves in each accident year, and thus the total reserve. In addition, the estimation of structural parameters and development factors are discussed. And the statistical properties are derived for those estimators of structural parameters. Finally, a numerical example is given to show the calculations with our estimators, and simulations are done to compare the mean square of reserve estimator between an individual loss model and an aggregate data model.
Traditional loss reserve models are mainly based on aggregate loss triangles, in which the entries are obtained by summations of individual loss data. The summation procedures inevitably cause wastage of information contained in the raw individual data. Though this method is simple, it results in a larger error in the estimate of loss reserves. Individual loss reserve models emerging in recent years have failed to consider dependencies between policies. This article assumes the existence of certain common random effects between policies in the same accident year. Thus, a hierarchical bayesian model is built for individual data loss reserves. Using the ideas of credibility theory, we get the credibility estimate of loss reserves in each accident year, and thus the total reserve. In addition, the estimation of structural parameters and development factors are discussed. And the statistical properties are derived for those estimators of structural parameters. Finally, a numerical example is given to show the calculations with our estimators, and simulations are done to compare the mean square of reserve estimator between an individual loss model and an aggregate data model.
2019, (1): 24-31.
doi: 10.3969/j.issn.1000-5641.2019.01.003
Abstract:
This paper investigates a class of variable coefficient partial differential equations. By using the homogeneous balance method, the Bäcklund transformation is obtained, which leads to exact solutions for the equation. By applying Lie symmetry analysis, the symmetries and vector field of the equation are obtained. Then, by means of a similarity transformation, the partial differential equations are reduced to ordinary differential equations. Solving the reduced equations, we investigate the exact solutions to the equations concisely using the power series expansion method.
This paper investigates a class of variable coefficient partial differential equations. By using the homogeneous balance method, the Bäcklund transformation is obtained, which leads to exact solutions for the equation. By applying Lie symmetry analysis, the symmetries and vector field of the equation are obtained. Then, by means of a similarity transformation, the partial differential equations are reduced to ordinary differential equations. Solving the reduced equations, we investigate the exact solutions to the equations concisely using the power series expansion method.
2019, (1): 32-38.
doi: 10.3969/j.issn.1000-5641.2019.01.004
Abstract:
Based on the existence of random attractors in the plate equation with linear memory and additive noise, the upper semi-continuity of the random attractor is proved when the coefficient of the noise term goes to zero.
Based on the existence of random attractors in the plate equation with linear memory and additive noise, the upper semi-continuity of the random attractor is proved when the coefficient of the noise term goes to zero.
2019, (1): 39-47, 57.
doi: 10.3969/j.issn.1000-5641.2019.01.005
Abstract:
A Halin graph is a plane graph G=T ∪ C, where T is a tree with no vertex of degree 2 and at least one vertex of degree 3 or more, and C is a cycle connecting the leaves of T in the cyclic order determined by the drawing of T. After structural analysis of Halin graphs, we show that the L(2, 1)-labelling number of every Halin graph G with a maximum degree 7 is at most 10.
A Halin graph is a plane graph G=T ∪ C, where T is a tree with no vertex of degree 2 and at least one vertex of degree 3 or more, and C is a cycle connecting the leaves of T in the cyclic order determined by the drawing of T. After structural analysis of Halin graphs, we show that the L(2, 1)-labelling number of every Halin graph G with a maximum degree 7 is at most 10.
2019, (1): 48-57.
doi: 10.3969/j.issn.1000-5641.2019.01.006
Abstract:
Cyber-physical systems (CPS) are multi-dimensional complex systems that integrate computing, networks, and physical environments. The modelling for such heterogeneous systems is actively researched. However, there still lacks a systematic approach to model characteristics of CPS, such as heterogeneity, uncertainty, hardware/software coordination, and Non-Functional Properties (NFP). In this paper, we propose a co-modelling approach that relies on SysML (System Modeling Language)/MARTE (Modeling and Analysis of Real-Time and Embedded Systems)/pCCSL (p Clock Constraint Specification Language) to model different aspects of CPS from different points of view, including structure, behavior, clock constraints, and NFP. The novelty of our approach lies in the use of pCCSL to specify the interaction and synchronization to explicitly model the logical consistency between models. Meanwhile, to capture characteristics of CPS, such as stochastic behavior and continuous behavior, we build upon some meta-models of SysML/MARTE. Finally, to demonstrate the feasibility of our co-modelling approach, we present various models of an energy-aware building as a case study.
Cyber-physical systems (CPS) are multi-dimensional complex systems that integrate computing, networks, and physical environments. The modelling for such heterogeneous systems is actively researched. However, there still lacks a systematic approach to model characteristics of CPS, such as heterogeneity, uncertainty, hardware/software coordination, and Non-Functional Properties (NFP). In this paper, we propose a co-modelling approach that relies on SysML (System Modeling Language)/MARTE (Modeling and Analysis of Real-Time and Embedded Systems)/pCCSL (p Clock Constraint Specification Language) to model different aspects of CPS from different points of view, including structure, behavior, clock constraints, and NFP. The novelty of our approach lies in the use of pCCSL to specify the interaction and synchronization to explicitly model the logical consistency between models. Meanwhile, to capture characteristics of CPS, such as stochastic behavior and continuous behavior, we build upon some meta-models of SysML/MARTE. Finally, to demonstrate the feasibility of our co-modelling approach, we present various models of an energy-aware building as a case study.
2019, (1): 58-65.
doi: 10.3969/j.issn.1000-5641.2019.01.007
Abstract:
First, this paper introduces the rules of the game NoGo. Next, we review current methods of artificial intelligence and their respective shortcomings. Then, the article shows an analysis of the game theory characteristics of NoGo and proposes a value evaluation function. Based on this function, a multi-layer recursive algorithm to the artificial intelligence of NoGo can be constructed, which addresses the problem of high complexity in time and space in the present algorithm. Finally, the paper demonstrates the capability of this algorithm and provides results that the program against with the famous open source software OASE-NoGo, which achieved a winning rate of more than 90%. In a typical situation, it demonstrates that the algorithm is better than existing algorithms in computing, and proves the feasibility and effectiveness of this method.
First, this paper introduces the rules of the game NoGo. Next, we review current methods of artificial intelligence and their respective shortcomings. Then, the article shows an analysis of the game theory characteristics of NoGo and proposes a value evaluation function. Based on this function, a multi-layer recursive algorithm to the artificial intelligence of NoGo can be constructed, which addresses the problem of high complexity in time and space in the present algorithm. Finally, the paper demonstrates the capability of this algorithm and provides results that the program against with the famous open source software OASE-NoGo, which achieved a winning rate of more than 90%. In a typical situation, it demonstrates that the algorithm is better than existing algorithms in computing, and proves the feasibility and effectiveness of this method.
2019, (1): 66-75.
doi: 10.3969/j.issn.1000-5641.2019.01.08
Abstract:
A multi-strategy gravitational search algorithm based on dynamic grouping is proposed in this paper. At the initial stage of the algorithm iteration, adaptive grouping strategies are used to optimize populations. Only the least-optimal individuals are updated in each group. The cloud model theory is used to improve the evolutionary behavior of the optimal individuals. In the later part of the algorithm iteration, the populations are divided into dominant and extension subgroups. The differential mutation operator is subsequently used to update the dominant subgroups to improve the precision and speed of the optimization. Tent chaos theory is used to update the extension subgroups to complete the individual variation. Typical complex function tests show that the algorithm has good convergence accuracy and computational speed.
A multi-strategy gravitational search algorithm based on dynamic grouping is proposed in this paper. At the initial stage of the algorithm iteration, adaptive grouping strategies are used to optimize populations. Only the least-optimal individuals are updated in each group. The cloud model theory is used to improve the evolutionary behavior of the optimal individuals. In the later part of the algorithm iteration, the populations are divided into dominant and extension subgroups. The differential mutation operator is subsequently used to update the dominant subgroups to improve the precision and speed of the optimization. Tent chaos theory is used to update the extension subgroups to complete the individual variation. Typical complex function tests show that the algorithm has good convergence accuracy and computational speed.
2019, (1): 76-82, 92.
doi: 10.3969/j.issn.1000-5641.2019.01.009
Abstract:
Fortran source code for calculating the integer order of Bessel functions of the first kind with complex arguments is presented. The method is based on the backward recurrence relation of Bessel functions. Values of the Bessel function generated by our program are in-agreement with the values generated by Matlab to at least 12 significant digits. We use the program to calculate the integer order of Bessel functions of the first kind with pure imaginary arguments, provided by Xu Shiliang's Fortran algorithm assembly. The results show that the first 6 significant digits are accurate. We also analyze the algorithm for calculating Bessel functions with complex arguments, which use the infinite sum of the product of the real arguments of the Bessel function and the pure imaginary arguments of the Bessel function, provided by Xu Shiliang's algorithm assembly. The results show that this algorithm does not always get accurate values for Bessel functions with complex arguments. The reason lies with the fact that the term in the sum larger than the function value causes the loss of significant digits.
Fortran source code for calculating the integer order of Bessel functions of the first kind with complex arguments is presented. The method is based on the backward recurrence relation of Bessel functions. Values of the Bessel function generated by our program are in-agreement with the values generated by Matlab to at least 12 significant digits. We use the program to calculate the integer order of Bessel functions of the first kind with pure imaginary arguments, provided by Xu Shiliang's Fortran algorithm assembly. The results show that the first 6 significant digits are accurate. We also analyze the algorithm for calculating Bessel functions with complex arguments, which use the infinite sum of the product of the real arguments of the Bessel function and the pure imaginary arguments of the Bessel function, provided by Xu Shiliang's algorithm assembly. The results show that this algorithm does not always get accurate values for Bessel functions with complex arguments. The reason lies with the fact that the term in the sum larger than the function value causes the loss of significant digits.
2019, (1): 83-92.
doi: 10.3969/j.issn.1000-5641.2019.01.010
Abstract:
In this study, we used calculations to determine the solvation free energies of 13 side chain analogs of neutral amino acids in water to compare the performance of equilibrium and nonequilibrium molecular dynamic simulations on high-performance computers. We found that nonequilibrium molecular dynamic simulations have the same accuracy as equilibrium molecular dynamic simulations in calculations for solvation free energies. From the perspective of efficiency and computational cost, the nonequilibrium method is more efficient and requires less computational time.
In this study, we used calculations to determine the solvation free energies of 13 side chain analogs of neutral amino acids in water to compare the performance of equilibrium and nonequilibrium molecular dynamic simulations on high-performance computers. We found that nonequilibrium molecular dynamic simulations have the same accuracy as equilibrium molecular dynamic simulations in calculations for solvation free energies. From the perspective of efficiency and computational cost, the nonequilibrium method is more efficient and requires less computational time.
2019, (1): 93-104, 114.
doi: 10.3969/j.issn.1000-5641.2019.01.011
Abstract:
With pentahydrate bismuth nitrate (Bi(NO3)35H2O), potassium iodide (KI), and MIL-125(Ti) as raw materials, ethylene glycol as solvent, and citric acid as the structural inducer, heterojunction structure light catalyst MIL-125(Ti)/BiOI was prepared through one-step coprecipitation. The effect of photocatalytic degradation of Rhodamine B in visible light was also tested. By a series of measurements, including XRD, PL, SEM, BET and UV-Vis, we researched the relationships between structure, morphology, spectrum and the catalytic performance of the catalyst. Furthermore, the catalytic mechanism was analysized via energy band structure. The results indicated that by adjusting the ratio of Ti/Bi, MIL-125(Ti)/BiOI has a good degradation effect on Rhodamine B under visible light radiation, which is stable and can be applied to industrial applications.
With pentahydrate bismuth nitrate (Bi(NO3)35H2O), potassium iodide (KI), and MIL-125(Ti) as raw materials, ethylene glycol as solvent, and citric acid as the structural inducer, heterojunction structure light catalyst MIL-125(Ti)/BiOI was prepared through one-step coprecipitation. The effect of photocatalytic degradation of Rhodamine B in visible light was also tested. By a series of measurements, including XRD, PL, SEM, BET and UV-Vis, we researched the relationships between structure, morphology, spectrum and the catalytic performance of the catalyst. Furthermore, the catalytic mechanism was analysized via energy band structure. The results indicated that by adjusting the ratio of Ti/Bi, MIL-125(Ti)/BiOI has a good degradation effect on Rhodamine B under visible light radiation, which is stable and can be applied to industrial applications.
2019, (1): 105-114.
doi: 10.3969/j.issn.1000-5641.2019.01.012
Abstract:
The parallel method of moments (MoM) is successfully optimized using the MPI+OpenMP hybrid programming strategy, based on the second-generation Intel Xeon Phi many-core processor platform, codenamed Knights Landing (KNL). Using OpenMP programming technology, the utilization rate of the CPU (Center Processing Unit) is increased, and the computing resources of KNL are fully utilized. The introduction of threads substantially reduces the inter-process redundant integrals in the filling matrix process. In order to give full play to the advantage of KNL's 512-bit vector width, the efficiency of the loop structure is further enhanced through vector optimization. For the matrix solution process, which typically requires intensive computation and high CPU utilization, MPI (Message Passing Interface) communication time is reduced and the solution process is accelerated by introducing an OpenMP programming strategy. Numerical results show that the efficiency of solving complex electromagnetic problems by parallel MoM is greatly improved through optimization on the KNL many-core processor platform.
The parallel method of moments (MoM) is successfully optimized using the MPI+OpenMP hybrid programming strategy, based on the second-generation Intel Xeon Phi many-core processor platform, codenamed Knights Landing (KNL). Using OpenMP programming technology, the utilization rate of the CPU (Center Processing Unit) is increased, and the computing resources of KNL are fully utilized. The introduction of threads substantially reduces the inter-process redundant integrals in the filling matrix process. In order to give full play to the advantage of KNL's 512-bit vector width, the efficiency of the loop structure is further enhanced through vector optimization. For the matrix solution process, which typically requires intensive computation and high CPU utilization, MPI (Message Passing Interface) communication time is reduced and the solution process is accelerated by introducing an OpenMP programming strategy. Numerical results show that the efficiency of solving complex electromagnetic problems by parallel MoM is greatly improved through optimization on the KNL many-core processor platform.
2019, (1): 115-123.
doi: 10.3969/j.issn.1000-5641.2019.01.013
Abstract:
Position information is nonlinear in the node localization of wireless sensor networks (WSN). Based on the robust ability of multivariate linear regression of partial least squares (PLS), and in combination with nonlinear data dimension reduction of manifold learning, a novel kernel matrix ISOMAP (Isometric Feature Mapping) algorithm is proposed. Geodesic distances between nodes are used as a measure of dissimilarity, and the contribution rate is then used to find and delete the "short circuit" edge. The matrix constructed by a double-centered transformation and the kernel transformation trick is mapped to a high dimensional feature space; finally, the relative position is obtained by PLS. Compared with the traditional ISOMAP algorithm and the multidimensional scale method (MDS), simulation results indicate that the proposed algorithm has good topology stability, generalization properties, robustness, positioning accuracy, and lower computational complexity.
Position information is nonlinear in the node localization of wireless sensor networks (WSN). Based on the robust ability of multivariate linear regression of partial least squares (PLS), and in combination with nonlinear data dimension reduction of manifold learning, a novel kernel matrix ISOMAP (Isometric Feature Mapping) algorithm is proposed. Geodesic distances between nodes are used as a measure of dissimilarity, and the contribution rate is then used to find and delete the "short circuit" edge. The matrix constructed by a double-centered transformation and the kernel transformation trick is mapped to a high dimensional feature space; finally, the relative position is obtained by PLS. Compared with the traditional ISOMAP algorithm and the multidimensional scale method (MDS), simulation results indicate that the proposed algorithm has good topology stability, generalization properties, robustness, positioning accuracy, and lower computational complexity.
2019, (1): 124-135, 143.
doi: 10.3969/j.issn.1000-5641.2019.01.014
Abstract:
The R programming language offers powerful statistical analysis, data processing, and visualization capabilities, which can run on Windows, Linux, and Mac operating systems; the software allows users to show scientific research data through graphics by writing new code or adjusting existing code. However, it is difficult to learn R's programming code and use R packages, so R is not commonly favored by novices in the scientific research community. Based on the context of bioscience fields and data from published papers, public databases, and the National Bureau of Statistics, this study demonstrates how to plot high quality maps, heat maps, functional networks, Venn diagrams, and column charts using R, R Studio, and R-packages. To facilitate the use of R, we offer detailed scripts for biological researchers. After comparing R with other graphing software, this study provides good examples and discussions of how to reasonably and intuitively present results in biological research. We hope R will become the preferred plotting tool for elementary biological researchers in their learning and research activities.
The R programming language offers powerful statistical analysis, data processing, and visualization capabilities, which can run on Windows, Linux, and Mac operating systems; the software allows users to show scientific research data through graphics by writing new code or adjusting existing code. However, it is difficult to learn R's programming code and use R packages, so R is not commonly favored by novices in the scientific research community. Based on the context of bioscience fields and data from published papers, public databases, and the National Bureau of Statistics, this study demonstrates how to plot high quality maps, heat maps, functional networks, Venn diagrams, and column charts using R, R Studio, and R-packages. To facilitate the use of R, we offer detailed scripts for biological researchers. After comparing R with other graphing software, this study provides good examples and discussions of how to reasonably and intuitively present results in biological research. We hope R will become the preferred plotting tool for elementary biological researchers in their learning and research activities.
2019, (1): 136-143.
doi: 10.3969/j.issn.1000-5641.2019.01.015
Abstract:
The proposal of the Water Saving Society (WSS) and the strictest water resource management system introduced clearer and stricter requirements for water use in China. To calculate the constraint of the set objectives on water use, this study defined Objective Constraint Strength (OCS) for water regulation, and further compared OCS of agricultural and industrial water-use efficiency for 31 provincial regions in China. The study also carried out scenario analysis on seven different types of areas and proposed advice on WSS construction.
The proposal of the Water Saving Society (WSS) and the strictest water resource management system introduced clearer and stricter requirements for water use in China. To calculate the constraint of the set objectives on water use, this study defined Objective Constraint Strength (OCS) for water regulation, and further compared OCS of agricultural and industrial water-use efficiency for 31 provincial regions in China. The study also carried out scenario analysis on seven different types of areas and proposed advice on WSS construction.
2019, (1): 144-155.
doi: 10.3969/j.issn.1000-5641.2019.01.016
Abstract:
Growth and photosynthesis characteristics of native Phragmites australis and exotic Spartina alterniflora, the dominant salt marsh species in China's coastline, grown under elevated temperature and waterlogging conditions, were investigated. The results showed that elevated temperature increased the shoot height, leaf area, maximum rate of photosynthesis, and the apparent quantum yield of P. australis under non-waterlogging (Non-W) and shallow-waterlogging (S-W) conditions. However, the effect was negligible for the growth and photosynthesis parameters of P. australis in deep-waterlogging (D-W) conditions. The shoot height of P. australis reached a maximum, but the leaf area was lowest in a D-W state, indicating morphological adaption to waterlogging. D-W conditions significantly decreased the photosynthesis and chlorophyll fluorescence parameters of P. australis during the middle and later growth periods, compared to Non-W and S-W conditions. Both temperature elevation and waterlogging increased the growth, photosynthesis and chlorophyll fluorescence parameters of S. alterniflora, and the degree of increase under elevated temperature was greater than that of P. australis. Differences in growth and photosynthesis of S. alterniflora between the waterlogging treatments were not notable throughout the growing period. Analysis of variance showed that the effect of elevated temperature on the eco-physiological characters of P. australis was season-dependent, and the impact of waterlogging treatment was more notable with some interaction between the treatments. The effect of temperature elevation on photosynthesis parameters of S. alterniflora was notable, but not for the waterlogging treatment. We suggest that anticipated climate warming and rises in sea level might be beneficial to the exotic marsh species.
Growth and photosynthesis characteristics of native Phragmites australis and exotic Spartina alterniflora, the dominant salt marsh species in China's coastline, grown under elevated temperature and waterlogging conditions, were investigated. The results showed that elevated temperature increased the shoot height, leaf area, maximum rate of photosynthesis, and the apparent quantum yield of P. australis under non-waterlogging (Non-W) and shallow-waterlogging (S-W) conditions. However, the effect was negligible for the growth and photosynthesis parameters of P. australis in deep-waterlogging (D-W) conditions. The shoot height of P. australis reached a maximum, but the leaf area was lowest in a D-W state, indicating morphological adaption to waterlogging. D-W conditions significantly decreased the photosynthesis and chlorophyll fluorescence parameters of P. australis during the middle and later growth periods, compared to Non-W and S-W conditions. Both temperature elevation and waterlogging increased the growth, photosynthesis and chlorophyll fluorescence parameters of S. alterniflora, and the degree of increase under elevated temperature was greater than that of P. australis. Differences in growth and photosynthesis of S. alterniflora between the waterlogging treatments were not notable throughout the growing period. Analysis of variance showed that the effect of elevated temperature on the eco-physiological characters of P. australis was season-dependent, and the impact of waterlogging treatment was more notable with some interaction between the treatments. The effect of temperature elevation on photosynthesis parameters of S. alterniflora was notable, but not for the waterlogging treatment. We suggest that anticipated climate warming and rises in sea level might be beneficial to the exotic marsh species.
2019, (1): 156-165.
doi: 10.3969/j.issn.1000-5641.2019.01.017
Abstract:
Tidal creeks are identified as an important pathway for carbon exchange between coastal wetlands and the adjacent environment. This study investigated the seasonal variations in dissolved organic carbon (DOC) and particulate organic carbon (POC) in tidal creeks within typical vegetation communities (Poaceae and Cyperaceae) in the coastal wetlands of the Yangtze Estuary. The results showed that during ebb the concentrations of organic carbon components changed gradually along the altitude gradient from high marsh to low-lying shallow water areas outside the creeks. Generally, spring tides increased the organic carbon abundance in both creeks, relative to neap tide. In the Poaceae creek, with high plant biomass and soil carbon stocks, the DOC concentrations were significantly higher compared to the Cyperaceae creek during ebb across all seasons. In contrast, the POC contents were lower in the Poaceae creek compared to the Cyperaceae creek. The results of this study indicated that the Poaceae creek functioned as a net export (source) of DOC throughout the year but as a net sink of POC, and the Cyperaceae creek functioned as a net source of organic carbon over all seasons.
Tidal creeks are identified as an important pathway for carbon exchange between coastal wetlands and the adjacent environment. This study investigated the seasonal variations in dissolved organic carbon (DOC) and particulate organic carbon (POC) in tidal creeks within typical vegetation communities (Poaceae and Cyperaceae) in the coastal wetlands of the Yangtze Estuary. The results showed that during ebb the concentrations of organic carbon components changed gradually along the altitude gradient from high marsh to low-lying shallow water areas outside the creeks. Generally, spring tides increased the organic carbon abundance in both creeks, relative to neap tide. In the Poaceae creek, with high plant biomass and soil carbon stocks, the DOC concentrations were significantly higher compared to the Cyperaceae creek during ebb across all seasons. In contrast, the POC contents were lower in the Poaceae creek compared to the Cyperaceae creek. The results of this study indicated that the Poaceae creek functioned as a net export (source) of DOC throughout the year but as a net sink of POC, and the Cyperaceae creek functioned as a net source of organic carbon over all seasons.
