Dissipativity and synchronization control of fractional‐order memristive neural networks with reaction‐diffusion terms

This paper deals with the dissipativity and synchronization control of fractional‐order memristive neural networks (FOMNNs) with reaction‐diffusion terms. By means of fractional Halanay inequality, Wirtinger inequality, and Lyapunov functional, some sufficient conditions are provided to ensure global dissipativity and exponential synchronization of FOMNNs with reaction‐diffusion terms, respectively. The underlying model and the obtained results are more general since the reaction‐diffusion terms are first introduced into FOMNNs. The given conditions are easy to be checked, and the correctness of the obtained results is confirmed by a living example.     

Accuracy,robustness and efficiency comparison in iterative computation of convection diffusion equation with boundary layers

Nine‐point fourth‐order compact finite difference scheme, central difference scheme, and upwind difference scheme are compared for solving the two‐dimensional convection diffusion equations with boundary layers. The domain is discretized with a stretched nonuniform grid. A grid transformation technique maps the nonuniform grid to a uniform one, on which the difference schemes are applied. A multigrid method and a multilevel preconditioning technique are used to solve the resulting sparse linear systems. We compare the accuracy of the computed solutions from different discretization schemes, and demonstrate the relative efficiency of each scheme. Comparisons of maximum absolute errors, iteration counts, CPU timings, and memory cost are made with respect to the two solution strategies. © 2000 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 16: 379–394, 2000     

A sufficient condition and a necessary condition for the diffusion approximations of multiclass queueing networks under priority service disciplines

We establish a sufficient condition for the existence of the (conventional) diffusion approximation for multiclass queueing networks under priority service disciplines. The sufficient condition relates to a sufficient condition for the weak stability of the fluid networks that correspond to the queueing networks under consideration. In addition, we establish a necessary condition for the network to have a continuous diffusion limit; the necessary condition is to require a reflection matrix (of dimension equal to the number of stations) to be completely-S. When applied to some examples, including generalized Jackson networks, single station multiclass queues, first-buffer-first-served re-entrant lines, a two-station Dai–Wang network and a three-station Dumas network, the sufficient condition coincides with the necessary condition.     

Network modeling of chromatography by stochastic phenomena of adsorption,diffusion and convection

The limitation of macroscopic models to represent structural parameters, such as topology and morphology, as well as population effects, i.e. multi-molecules movement, in the modeling of chromatography systems has implications on the understanding of the phenomenological aspects that contribute to the separation mechanisms in porous media. The representation of the porous structure of chromatographic columns by a three-dimensional cubic network of interconnected sites allows a better analysis of the structural characteristics of the porous column and its connection with the phenomena of adsorption, diffusion and convection. In the present work the application of an interconnected cubic network model associated with a stochastic modeling of the adsorption, diffusion and convection phenomena leads to the proper representation of the dynamic aspects of the breakthrough curves related to separation processes in chromatographic columns. Therefore, it is possible to study the dynamics of solute retention from the molecules distribution in the separation processes throughout the column. Among the mass transfer mechanisms investigated, the convection showed to be closely related to the separation dynamics of chromatography, with the diffusion having little effects. The adsorption influenced both the separation dynamics and solute retention.     

The value of information in energy harvesting sensor networks

We study optimal data collection in energy harvesting sensor networks. The sensed data-stream constitutes a sequence of stationary ergodic random variables and, assuming that timely data is valued more, the value of the data is discounted over time such that frequent collection is required to avoid a loss in value. However, unlimited data collection is constrained by both the cost of data collection and the availability of energy.     

On maximal 3-restricted edge connectivity and reliability analysis of hypercube networks

It is shown in this work that all n-dimensional hypercube networks for n ? 4 are maximally 3-restricted edge connected. Employing this observation, we analyze the reliability of hypercube networks and determine the first 3n − 5 coefficients of the reliability polynomial of n-cube networks.     

Volume growth and escape rate of symmetric diffusion processes

We give an upper rate function, in terms of the volume growth of the underlying state space, for the symmetric diffusion process associated with a symmetric, strongly local regular Dirichlet form. It extends the main result of Hsu and Qin [Ann. Probab. 38(4) 2010], where an upper rate function was given for Brownian motion on Riemannian manifold.     

神经网络在复杂自相关预测过程中的应用及对比研究

由于PM_(2.5)日均浓度值受外界多重复杂因素的影响,其较强的自相关性使得时间序列模型ARIMA构建难以实现,因此,给出高映射能力的非线性神经网络预测模型,并分别建立基于BP神经网络和GRNN神经网络的预测模型,进行PM_(2.5)浓度预测实验.结果表明,BP神经网络回检过程和检测过程存在不稳定性,预测残差波动较大,而GRNN神经网络检测残差呈完全U型,回检过程和检测过程较稳定,并且GRNN神经网络回检数据拟合度、预测数据精度和运算速度均优于BP神经网络,建模过程更为方便,易于实际应用.     

A structure-preserving finite element approximation of surface diffusion for curve networks and surface clusters

We consider the evolution of curve networks in two dimensions (2d) and surface clusters in three dimensions (3d). The motion of the interfaces is described by surface diffusion, with boundary conditions at the triple junction points lines, where three interfaces meet, and at the boundary points lines, where an interface meets a fixed planar boundary. We propose a parametric finite element method based on a suitable variational formulation. The constructed method is semi-implicit and can be shown to satisfy the volume conservation of each enclosed bubble and the unconditional energy-stability, thus preserving the two fundamental geometric structures of the flow. Besides, the method has very good properties with respect to the distribution of mesh points, thus no mesh smoothing or regularization technique is required. A generalization of the introduced scheme to the case of anisotropic surface energies and non-neutral external boundaries is also considered. Numerical results are presented for the evolution of two-dimensional curve networks and three-dimensional surface clusters in the cases of both isotropic and anisotropic surface energies.     

Laminar flamelet modeling of a turbulent CH4/H2/N2 jet diffusion flame using artificial neural networks

The laminar flamelet concept is used in the prediction of mean reactive scalars in a non-premixed turbulent CH₄/H₂/N₂ flame. First, a databank for temperature and species concentrations is developed from the solutions of counter-flow diffusion flames. The effects of flow field on flamelets are considered by using mixture fraction and scalar dissipation rate. Turbulence-chemistry interactions are taken into account by integrating different quantities based on a presumed probability density function (PDF), to calculate the Favre-averaged values of scalars. Flamelet library is then generated. To interpolate in the generated library, one artificial neural network (ANN) is trained where the mean and variance of mixture fraction and the scalar dissipation rate are used as inputs, and species mean mass fractions and temperature are selected as outputs. The weights and biases of this ANN are implemented in a CFD flow solver code, to estimate mean values of the scalars. Results reveal that ANN yields good predictions and the computational time has decreased as compared to numerical integration for the estimation of mean thermo-chemical variables in the CFD code. Predicted thermo-chemical quantities are close to those from experimental measurements but some discrepancies exist, which are mainly due to the assumption of non-unity Lewis number in the calculations.     

Perturbations of finite networks and asymptotic periodicity of flow semigroups

We consider a transport process on a finite network and introduce a new special transformation of the underlying graph that is then used to yield an alternative proof of the main theorem on asymptotic periodicity of the flow semigroup proven in Kramar and Sikolya (Math. Z. 249:139–162, 2005). The perturbation technique we develop allows us to prove this theorem starting from a special case, thus greatly simplifying the proof. This technique is in Kunszenti-Kovács (Perturbations of networks and asymptotic periodicity of recurrent flows: the infinite case, Preprint, 2008) adapted to infinite networks, where it allows for significant generalisations of previous results.     

考虑对象属性信息的复杂网络社团结构发现算法

针对社团结构发现算法仅考虑对象间相互关系的密集程度,忽视对象间属性特征差异的不足,提出考虑属性信息的复杂网络社团结构发现算法.算法引入属性特征相似度、基于属性特征相似度的有权网络、内聚度3个核心概念,迭代选取使内聚度指标上升最快的合并操作,自底向上实现社团聚集.由于考虑了属性信息,算法输出的社团结构具有更高准确度,更具应用价值.     

Dynamical behavior of solutions of a reaction–diffusion model in river network

In this paper, we study the long-time behavior of solutions of a reaction–diffusion model in a one-dimensional river network, where the river network has two branches, and the water flow speeds in each branch are the same constant $\beta$. We show the existence of two critical values $c_0$ and 2 with $0<c_0<2$, and prove that when $-c_0\le \beta <2$, the population density in every branch of the river goes to 1 as time goes to infinity; when $-2<\beta <-c_0$, then, as time goes to infinity, the population density in every river branch converges to a positive steady state strictly below 1; when $\left|\beta \right|\ge 2$, the species will be washed down the stream, and so locally the population density converges to 0. Our result indicates that only if the water-flow speed is suitably small (i.e., $\left|\beta \right|<2$), the species will survive in the long run.     

On the law of the iterated logarithm in open queueing networks

An open queueing network model in heavy traffic is developed. Such models are mathematical models of computer networks in heavy traffic. Laws of the iterated logarithm for the virtual waiting time of the customer in open queueing networks and homogeneous computer networks are proved.     

具有时滞和非时滞耦合的复杂动态网络的自适应同步

对于同时具有时滞耦合和非时滞耦合的复杂动态网络,以时滞动力系统的稳定性理论为基础,设计了全新的自适应控制器,同时给出了一些简单而又一般的网络同步化准则.对由三个节点组成的动态网络的同步化进行了数值模拟,使得理论分析与数值模拟得到了相互验证.     

面向集群创新网络异质企业的知识扩散建模及仿真研究

基于合作的集群创新网络知识扩散已经成为企业实现知识创新的重要手段,而集群创新网络知识扩散的动力学过程强烈依赖于异质企业间知识扩散能力的影响,为此,本文综合考虑了企业间不同接触数量、知识吸收和传播能力、知识淘汰率等异质性因素,建立了基于传染病理论的知识扩散模型,验证了由各异质因素构成的知识扩散再生数对知识扩散均衡和扩散效果的影响,并结合仿真实验进一步得出:在知识扩散前期,集群创新网络应发挥hub节点及异质网络的优势加快知识扩散,在中后期应注意企业关系发展的均衡性及企业接触邻居的规模性;相比过于强调知识交流的广泛性,加强企业传播能力和吸收能力的培养对网络知识扩散效果的提升更具意义;随着时间演化,企业知识淘汰率也会影响网络知识扩散的收敛情况。     

Neural networks for of continuous optimal approximation functions in R^d

Using some regular matrices we present a method to express any multivariate algebraic polynomial of total order n in a normal form. Consequently, we prove constructively that, to approximate continuous target functions defined on some compact set of ? ^d , neural networks are at least as good as algebraic polynomials.     

Stability and Hopf bifurcation of a delayed reaction–diffusion neural network

In this paper, a delayed reaction–diffusion neural network with Neumann boundary conditions is investigated. By analyzing the corresponding characteristic equations, the local stability of the trivial uniform steady state is discussed. The existence of Hopf bifurcation at the trivial steady state is established. Using the normal form theory and the center manifold reduction of partial function differential equations, explicit formulae are derived to determine the direction and stability of bifurcating periodic solutions. Numerical simulations are carried out to illustrate the main results. Copyright © 2011 John Wiley & Sons, Ltd.     

复杂金融网络收益率加权和的不变性研究

对包含两个子网络的复杂金融网络进行了分析,研究了网络中各节点收益率与资金流通量之间的关系.通过建立数学模型,证明了网络中各节点收益率加权和的不变性.