A novel computer virus propagation model and its dynamics

By taking into account the fact that, in general, a computer immediately possesses infectivity as soon as it is infected, a novel computer virus propagation model, known as the SLBS model, is established. It is proved that the dynamic behaviour of the model is determined by a threshold R ₀. Specifically, the virus-free equilibrium is globally asymptotically stable if R ₀≤1, whereas the virulent equilibrium is globally asymptotically stable if 1<R ₀≤4. It is conjectured that the virulent equilibrium is also globally asymptotically stable if R ₀>4. These results suggest some effective strategies for eradicating computer viruses distributed in the Internet.     

一维传感网中混合数据传输的能量均衡

无线传感器网络的固有通信特征会引发能耗不均衡现象,进而产生能量空洞问题;混合数据传输是新近提出的一种能量空洞避免策略,其能量均衡性能主要取决于各节点的传输概率.然而,传输概率的设置还缺乏相关理论模型的指导,而且在节点传输距离受限的条件下能否通过混合传输策略实现全网能量均衡,还有待进一步研究.将一维网络中混合传输策略的能量均衡问题转化为传输概率的优化分配问题,通过相应的形式化模型,推导传输概率的精确表达.研究中发现:传输概率主要取决于节点的位置,但当网络片段的个数超过某一阈值时,传输概率的取值非法,无法应用混合传输策略均衡网络能耗.在此基础上,从理论上给出了全网能量均衡的条件,证明仅当网络片段数不超过n₀时全网能量均衡才能实现,n₀仅取决于一个文中新发现的系数α,α是通信系统的能耗溢价率.还分析了传输距离设置对能量均衡的影响,给出了一般情况下混合传输策略的能量均衡上限.通过仿真实验对所给出的能量均衡条件进行了验证,实验结果与理论分析表明:该条件下,基于所提方法设置传输概率,能够均衡所有节点的能耗.     

Dynamical behavior of a vector-host epidemic model with demographic structure

In the paper, we propose a model that tracks the dynamics of many diseases spread by vectors, such as malaria, dengue, or West Nile virus (all spread by mosquitoes). Our model incorporates demographic structure with variable population size which is described by nonlinear birth rate and linear death rate. The stability of the system is analyzed for the existence of the disease-free and endemic equilibria points. We find the basic reproduction number R₀ in terms of measurable epidemiological and demographic parameters is the threshold condition that determines the dynamics of disease infection: if R₀<1 the disease fades out, and for R₀>1 the disease remains endemic. The threshold condition provides important guidelines for accessing control of the vector diseases, and implies that it is an efficient way to halt the spread of vector epidemic by reducing the carrying capacity of the environment for the vector and the host. Moreover, sufficient conditions are also obtained for the global stability of the unique endemic equilibrium E^*.     

带可移动存储设备的P2G网络病毒传播模型

基于计算机病毒可以通过可移动存储设备传播和P2G网络病毒传播的特点,提出了带可移动存储设备的P2G网络病毒传播模型。利用微分动力学系统理论分析发现该模型只存在唯一的有病毒平衡点,这意味着网络中的病毒将无法根除,即病毒既有可能存在于计算机中,也有可能存在于移动存储设备中。同时,研究了此平衡点的动力学特性（局部稳定性和全局稳定性）。最后,通过数值仿真验证了理论分析的正确性。     

大规模网络的病毒群体免疫模型

由于计算机和Internet的普及,越来越多的人使用邮件,邮件病毒造成了巨大的损失和严重的破坏。传统的度免疫模型有一定的盲目性,没有考虑感染节点的位置,对整个网络中度高的节点进行免疫。把群体概念引入病毒预防控制领域中,提出群体免疫模型,在不同的病毒感染阶段,采用感染群体免疫或健康群体免疫,在降低节点感染密度的同时,把感染节点控制在一定群体内。度免疫无法将病毒控制在某些群体内,从而使得病毒分散在各个群体;而群体免疫能够将病毒集中到感染群体内部。两种免疫模型需要免疫的节点个数和群体感染比率的差别较大,所以群体免疫是原理上不同于度免疫的新型有效的免疫模型。     

Global synchronised regions of linearly coupled Lur'e systems

This article addresses the global synchronisation problem of a network of coupled Lur'e systems from the perspective of global synchronised region. A decomposition approach is proposed to convert the synchronisation of high-dimensional Lur'e networks into the test of a set of matrix inequalities whose dimensions are the same as a single Lur'e node. The notion of global synchronised region is then introduced and analysed. A necessary and sufficient condition is derived for the existence of the inner-linking matrix to guarantee a desirable unbounded synchronised region. A multi-step design procedure is given for constructing such an inner-linking matrix, which maintains a favourable decoupling property. Furthermore, the global H _∞ synchronised region is characterised for evaluating the performance of a Lur'e network subject to external disturbances. The effectiveness of the theoretical results is demonstrated through a network of Chua's circuits.     

Dynamical behaviours and control measures of rumour-spreading model with consideration of network topology

A series of online rumours have seriously influenced the normal production and living of people. This paper aims to study the combined impact of psychological factor, propagation delay, network topology and control strategy on rumour diffusion over the online social networks. Based on an online social network, which is seen as a scale-free network, we model the spread of rumours by using a delayed SIS (Susceptible and Infected) epidemic-like model with consideration of psychological factor and network topology. First, through theoretical analysis, we illustrate the boundedness of the density of rumour-susceptible individuals and rumour-infected individuals. Second, we obtain the basic reproduction number R₀ and prove the stability of the non-rumour equilibrium point and the rumour-spreading equilibrium point. Third, control strategies, such as uniform immunisation control, proportional immunisation control, targeted immunisation control and optimum control, are put forward to restrain rumour diffusion. Meanwhile, we have compared the differences of these control strategies. Finally, some representative numerical simulations are performed to verify the theoretical analysis results.     

Stability and bifurcation of disease spreading in complex networks

A general nonlinear model of disease spreading is proposed, describing the effect of the new link-adding probability p in the topological transition of the N-W small-world network model. The new nonlinear model covers both limiting cases of regular lattices and random networks, and presents a more flexible internal nonlinear interaction than a previous model. Hopf bifurcation is proved to exist during disease spreading in all typical cases of regular lattices, small-world networks, and random networks described by this model. It is shown that probability p not only determines the topological transition of the N-W small-world network model, but also dominates the stability of the local equilibria and bifurcating periodic solutions, and moreover can be further applied to stabilize a periodic spreading behaviour onto a stable equilibrium over the network.     

自适应复杂网络中的病毒传播模型

提出了一个基于自适应复杂网络的病毒传播模型。模型中,易感节点为了不被感染,能够有意识地避开与感染节点的连接,此过程一方面使得网络结构发生了变化,另一方面网络结构的变化又反过来对病毒传播过程造成了影响。着重考查了模型中个体的躲避行为对病毒传播效果的影响,结果显示,在个体躲避行为的驱动下,系统的最终染病节点数会发生振荡,并且在一定的参数范围内系统出现了双稳状态。     

一种新的网络拓扑建模方法

网络拓扑结构能够很好地解决服从某种规律的网络传播行为问题,所以针对不同的预测和改善网络性能的目的,建立合适的网络拓扑模型是非常重要的。从复杂网络拓扑建模的角度出发,综合考虑了节点和链接的加入与消亡、节点的孤立、网络内新增的内部连接以及局域网内部的偏好连接等因素,提出了一个新的网络拓扑建模的方法NBSFN（New Base Scale Free Network）。运用Java和Matlab工具对结果进行了仿真研究,发现仿真结果能够很好地刻画出无标度、小世界等诸多特性。     

Connectivity in finite ad-hoc networks

Research on ad-hoc network connectivity has mainly focused on asymptotic results in the number of nodes in the network. For a one-dimensional ad-hoc network G1, assuming all the nodes are independently uniform distributed in a closed interval [0, Z]（z ∈ R^＋）, we derive a generic formula for the probability that the network is connected. The finite connected ad-hoc networks is analyzed. And we separately suggest necessary conditions to make the ad-hoc network to be connected in one and two dimensional cases, facing possible failed nodes （f-nodes）. Based on the necessary condition and unit-disk assumption for the node transmission, we prove that the nodes of the connected two-dimensional ad-hoc networks （G2） can be divided into at most five different groups. For an f-node no in either of the five groups, we derive a close formula for the probability that there is at least one route between a pair of nodes in G2 -- {no}.     

Mixed H2/H∞ distributed robust model predictive control for polytopic uncertain systems subject to actuator saturation and missing measurements

In this paper, we discuss the mixed H₂/H_∞ distributed robust model predictive control problem for polytopic uncertain systems subject to randomly occurring actuator saturation and packet loss. The global system is decomposed into several subsystems, and all the subsystems are connected by a fixed topology network, which is the definition for the packet loss among the subsystems. To better use the successfully transmitted information via Internet, both the phenomena of actuator saturation and packet loss resulting from the limitation of the communication bandwidth are taken into consideration. A novel distributed controller model is established to account for the actuator saturation and packet loss in a unified representation by using two sets of Bernoulli distributed white sequences with known conditional probabilities. With the nonlinear feedback control law represented by the convex hull of a group of linear feedback laws, the distributed controllers for subsystems are obtained by solving an linear matrix inequality (LMI) optimisation problem. Finally, numerical studies demonstrate the effectiveness of the proposed techniques.     

基于吸引域的总体极小化问题的神经网络求解

神经网络求解优化问题具有非常强大的实时计算功用,因此近年来受到了密切的关注.这里考察了求解无约束总体极小化问题的神经网络方法,提出了一种新的网络求解模型.从基于吸引域分析方法为出发点证明了所给网络平稳点集合的全局吸引性.分析了网络的电路实现,并估计了各个平稳点的吸引域.这些理论分析与估计是构造所提神经网络模型的依据,同时也是网络可靠运行的基础.此外,数值模拟试验也充分揭示了这个网络模型在实际运行中都能够很好地求解总体极小化问题,是一个十分有效的神经网络系统.这里的结果表明:这里提出的网络模型无论从理论上还是实际运行中都能够可靠且稳定地求解总体极值问题,基于吸引域构造神经网络的方法是一种很有潜力的神经网络求解优化问题的研究方向.     

Genetic algorithm hybridized with multilayer perceptron to have an economical slope stability design

The present work aimed to evaluate and optimize the design of an artificial neural network (ANN) combined with an optimization algorithm of genetic algorithm (GA) for the calculation of slope stability safety factors (SF) in a pure cohesive slope. To make datasets of training and testing for the developed predictive models, 630 finite element limit equilibrium (FELE) analyses were performed. Similar to many artificial intelligence-based solutions, the database was involved in 189 testing datasets (e.g., 30% of the entire database) and 441 training datasets; for example, a range of 70% of the total database. Moreover, variables of multilayer perceptron (MLP) algorithm (for example, number of nodes in any hidden layer) and the algorithm of GA like population size was optimized by utilizing a series of trial and error process. The parameters in input, which were used in the analysis, consist of slope angle (β), setback distance ratio (b/B), applied stresses on the slope (F_y) and undrained shear strength of the cohesive soil (C_u) where the output was taken SF. The obtained network outputs for both datasets from MLP and GA-MLP models are evaluated according to many statistical indices. A total of 72 MLP trial and error (e.g., parameter study) the optimal architecture of 4 × 8 × 1 were determined for the MLP structure. Both proposed techniques result in a proper performance; however, according to the statistical indices, the GA–MLP model can somewhat accomplish the least mean square error (MSE) when compared to MLP. In an optimized GA–MLP network, coefficient of determination (R²) and root mean square error (RMSE) values of (0.975, and 0.097) and (0.969, and 0.107) were found, respectively, to both of the normalized training and testing datasets.

     

动态演化的互联网病毒建模与分析

互联网是一个不断生长的无标度网络,在其生长过程中伴随着计算机病毒的传播。基于此,兼顾静态和动态网络上的病毒传播过程,建立了含有拓扑结构演化的计算机病毒传播模型,研究了网络增长速度、网络平均度以及计算机连接度对病毒传播的影响。实验结果表明,网络演化速度越快,病毒传播也越快。同时平均度较高的网络更有助于病毒的传播。此外,病毒在爆发期间主要集中在连接度较大的计算机上。所得结论对控制病毒传播意义重大。     

基于最大后验估计的谣言源定位器

随着互联网的普及,信息能够通过互联网以极快的速度被传播给大众。但同时,一些虚假信息比如谣言也借助网络的级联效应泛滥成灾,因此如何在传播网络中快速准确地确定谣言传播源成为一个亟待解决的问题。文章针对社交网络提出了一种谣言源定位的方法,与现有的基于最大后验(Maximum-a-posteriori,MAP)概率估计的方法不同,该方法首先考虑全局和局部感染点、非感染点的影响,使用效果更优的MAP先验概率估计(Prior Probability Estimation,PPE)计算方式。然后基于最小生成树贪心算法来稀疏化社交网络,让MAP中的似然估计(Likelihood Estimation,LE)计算更符合真实的传播结构。最后,采用新的MAP值来估计传播网络中节点为传播源的可能性,从而更准确地定位谣言源点。将所提方法与现有的几种方法分别在模型网络和真实网络中进行了对比,实验结果表明,所提方法优于现有的谣言源定位方法。     

基于异质移动网络的破坏性病毒传播模型

针对现有研究没有考虑移动网络节点异质性与没有构建破坏性病毒传播模型的问题,提出一个基于异质移动网络的破坏性病毒传播模型。通过考虑移动网络节点的异质性,进一步将易感染状态划分为新系统状态和旧系统状态,并结合破坏性病毒的潜伏与爆发特性将感染状态划分为潜伏状态和爆发状态。计算了模型的平衡点与传播阈值,并指出当传播阈值大于1时,模型在正平衡点处不稳定;当传播阈值小于1时,模型在正平衡点处局部渐近稳定。在NW小世界网络和BA无标度网络上进行仿真对比实验,仿真结果表明,两个网络的病毒传播速度不同,NW网络存在病毒完全消除的情况,而BA网络中的病毒不会被完全清除。     

Nonstandard numerical methods for a mathematical model for influenza disease

In this paper we construct and develop two competitive implicit finite difference scheme for a deterministic mathematical model associated with the evolution of influenza A disease in human population. Qualitative dynamics of the model is determined by the basic reproduction number, _R0$R_0$. Numerical schemes developed here are based on nonstandard finite difference methods. Our aim is to transfer essential properties of the continuous model to the discrete schemes and to obtain unconditional stable schemes. The proposed numerical schemes have two fixed points which are identical to the critical points of the continuous model and it is shown that they have the same stability properties. Numerical simulations with different initial conditions, parameters values and time step sizes are developed for different values of parameter _R0$R_0$, convergence to the disease free equilibrium point when _R0<1$R_0<1$ and to the endemic equilibrium point when _R0>1$R_0>1$ are obtained independent of the time step size. These numerical integration schemes are useful since can reproduce the dynamics of original differential equations.     

Approximate analysis of exponential queueing systems with blocking

Summary A network of service stations Q ₀ Q ₁,...,Q_M is studied. Requests arrive at the centers according to independent Poisson processes; they travel through (part of) the network demanding amounts of service, with independent and negative exponentially distributed lengths, from those centers which they enter, and finally depart from the network. The waiting rooms or buffers at each service station in this exponential service system are finite. When the capacity at Q _i is reached, service at all nodes which are currently processing a request destined next for Q _i is instantaneously interrupted. The interruption lasts until the service of the request in the saturated node Q _i is. completed. This blocking phenomenon makes an exact analysis intractable and a numerical solution computationally infeasible for most exponential systems. We introduce an approximation procedure for a class of exponential systems with blocking and show that it leads to accurate approximations for the marginal equilibrium queue length distributions. The applicability of the approximation method may not be limited to blocking systems.Mathematical Sciences Department Postdoctoral Fellow 1978–79.