Scale-free network provides an optimal pattern for knowledge transfer

We study numerically the knowledge innovation and diffusion process on four representative network models, such as regular networks, small-world networks, random networks and scale-free networks. The average knowledge stock level as a function of time is measured and the corresponding growth diffusion time, τ is defined and computed. On the four types of networks, the growth diffusion times all depend linearly on the network size N as τN, while the slope for scale-free network is minimal indicating the fastest growth and diffusion of knowledge. The calculated variance and spatial distribution of knowledge stock illustrate that optimal knowledge transfer performance is obtained on scale-free networks. We also investigate the transient pattern of knowledge diffusion on the four networks, and a qualitative explanation of this finding is proposed.     

A stochastic model of tweet diffusion on the Twitter network

We introduce a stochastic model which describes the information diffusion on the network of a popular web service, Twitter. Restricting our attention to the daily diffusion from a popular account, we model the information diffusion as a random multiplicative process. We justify our model by directly observing the statistics of the multiplicative factors in the Twitter data.     

Information diffusion on adaptive network

Based on the adaptive network, the feedback mechanism and interplay between the network topology and the diffusive process of information are studied. The results reveal that the adaptation of network topology can drive systems into the scale-free one with the assortative or disassortative degree correlations, and the hierarchical clustering. Meanwhile, the processes of the information diffusion are extremely speeded up by the adaptive changes of network topology.     

A spatiotemporal master equation model of morphogen transport: Local accumulation times,noise measurement and diffusion force

Morphogen, a class of signaling molecules to direct and control pattern formation of cell and tissue, is first synthesized in a local region and then conveyed to other regions or degraded. In the previous studies, this transport process was modeled by deterministic models of ordinary differential equations. In microcosmic environments, however, the process is often affected by stochastic fluctuations (or the noise). It remains unclear how this noise affects morphogen gradients. Here, we build a spatiotemporal master equation model for the process of morphogen transport in a finite developmental field, from which we derive the first-order moment equations of this master equation. We derive the analytical expression of the local accumulation time that the morphogens reach a steady state, and find that this time is nonlinear with respect to the cell positions. We also derive the approximate expressions of the steady-state variances, the Fano factors and the local accumulation time of the variance. Interestingly, we find that the local accumulation time for the variance of the morphogen number is shorter than that of its corresponding second-order moment. Moreover, the noise in the morphogen number is almost not affected by the distance from the cellular position to morphogen source. In addition, we further study some quantities (e.g., potential energy and diffusion force) from the view of physical-chemical mechanisms, and uncover that the diffusion force is a key factor for the formation of the morphogen gradient. Our results provide insights on morphogen diffusion.     

Method of analyzing the influence of network structure on information diffusion

Social phenomena are affected by the structure of networks consisting of personal relationships. In the present paper, the diffusion of information among people is examined. In particular, the relationship between the network structure and the dynamics is studied. First, several networks are generated using the proposed network model and other network models, such as the WS model and the KE model. By changing the parameters of the network models, networks with different structures are generated. The parameters of the network models determine the topology of the networks and the statistical indicators.     

A model of modulated diffusion. I. Analytical results

We introduce an integrable isochronous system and perturb its frequency by an external-deterministic or purely random-noise. Under the perturbation the action variable evolves in time: the corresponding diffusion coefficient is exactly computed and its dependence on the magnitude of the perturbation is carefully investigated. Different behaviors are found and justified: the quasilinear approximation, the superlinear regime, and the ballistic motion.     

A model of modulated diffusion. II. Numerical results on statistical properties

We investigate numerically the statistical properties of a model of modulated diffusion for which we have already computed analytically the diffusion coefficientD. Our model is constructed by adding a deterministic or random noise to the frequency of an integrable isochronous system. We consider in particular the central limit theorem and the invariance principle and we show that they follow wheneverD is positive and for any magnitude of the noise; we also investigate the asymptotic distribution in a case whenD=0.     

扩散理论对RLA模型中交换作用的研究

以扩散理论为基础，建立以“基本微观过程” 为核心的新模型，引入交换比的概念，对存在表面活化剂时薄膜生长的微观过程进行Kinetic Monte Carlo模拟.模拟发现，活化层原子和沉积原子都会发生跨层间的扩散，跨层扩散主要是单个原子的扩散，层间扩散的原子数目随着温度的升高或沉积厚度的增加而增多.RLA模型中的“交换作用”只是若干个“基本微观过程”的组合，大多数交换不是位置的“完全交换”，交换比也并非恒为1.     

扩散理论对RLA模型中交换作用的研究

以扩散理论为基础,建立以“基本微观过程” 为核心的新模型,引入交换比的概念,对存在表面活化剂时薄膜生长的微观过程进行Kinetic Monte Carlo模拟.模拟发现,活化层原子和沉积原子都会发生跨层间的扩散,跨层扩散主要是单个原子的扩散,层间扩散的原子数目随着温度的升高或沉积厚度的增加而增多.RLA模型中的“交换作用”只是若干个“基本微观过程”的组合,大多数交换不是位置的“完全交换”,交换比也并非恒为1. 关键词： 扩散理论 薄膜生长 交换作用 RLA     

基于脉冲耦合神经网络和图像熵的各向异性扩散模型研究

在图像去噪过程中, 大部分基于偏微分方程的各向异性扩散模型均使用梯度信息检测边缘, 当边缘部分被噪声严重污染时, 这些方法不能有效检测出这些边缘, 因而无法保留边缘特征. 为了较完整的保留图像的区域信息, 用脉冲耦合神经网络(PCNN)能使具有相似输入的神经元同时产生脉冲的性质对噪声图像做处理, 得到图像熵序列, 并将图像熵序列作为边缘检测算子引入到扩散方程中, 不仅能克服仅用梯度作为边缘检测算子易受噪声影响的弊端, 而且能较完整地保留图像的区域信息. 然后, 用最小交叉熵准则搜索使去噪前后图像信息量差异最小的阈值, 设计最佳阈值控制扩散强度, 建立基于脉冲耦合神经网络与图像熵改进的各向异性扩散模型(PCNN-IEAD). 分析与仿真结果表明, 该模型与经典模型相比, 保留了更多的图像信息, 能够兼顾去除图像的噪声和保护图像的边缘纹理等细节信息, 较完整的保留了图像的区域信息, 性能指标同样也证实了新模型的优越性. 另外, 该模型的运行时间较经典模型的短, 因此, 该模型是一个理想的模型.     

A random field model for anomalous diffusion in heterogeneous porous media

Heterogeneity, as it occurs in porous media, is characterized in terms of a scaling exponent, or fractal dimension. A feature of primary interest for two-phase flow is the mixing length. This paper determines the relation between the scaling exponent for the heterogeneity and the scaling exponent which governs the mixing length. The analysis assumes a linear transport equation and uses random fields first in the characterization of the heterogeneity and second in the solution of the flow problem, in order to determine the mixing exponents. The scaling behavior changes from long-length-scale dominated to short-length-scale dominated at a critical value of the scaling exponent of the rock heterogeneity. The long-length-scale-dominated diffusion is anomalous.     

A generalised model of hydrogen diffusion in metals with multiple trap types

Continuum modelling of hydrogen diffusion in metals, which accounts for both trapping and an imposed force field, is revisited. A generalised model of hydrogen diffusion and trapping is developed as a continuous interpretation of the discrete random-walk theory. A system of nonlinear equations describing the phenomenon of diffusion with multiple types of traps is derived without the assumption of a local equilibrium among hydrogen populations in dissimilar positions. Lattice-trap interchange kinetics can degenerate into local equilibrium as a limit case. Moreover, certain terms in general equations may be negligible in specific situations. By removing these terms, known particularised models of hydrogen diffusion and trapping are recovered. Determining the terms, which are disregarded in reduced models, enables a straightforward assessment of the applicability of these models. The advantages and limitations of particularised models applied to hydrogen embrittlement analyses are discussed.     

A new local-world evolving network model

In some real complex networks, only a few nodes can obtain the global information about the entire networks, but most of the nodes own only local connections therefore own only local information of the networks. A new local-world evolving network model is proposed in this paper. In the model, not all the nodes obtain local network information, which is different from the local world network model proposed by Li and Chen (LC model). In the LC model, each node has only the local connections therefore owns only local information about the entire networks. Theoretical analysis and numerical simulation show that adjusting the ratio of the number of nodes obtaining the global information of the network to the total number of nodes can effectively control the valuing range for the power-law exponent of the new network. Therefore, if the topological structure of a complex network, especially its exponent of power-law degree distribution, needs controlling, we just add or take away a few nodes which own the global information of the network.     

Observation of diffusion through ion irradiated Makrofol KG

The features of the latent track in polycarbonate can be analysed by measuring the diffusion constant under ultra high vacuum conditions. Stacks of 30 μm Makrofol KG foils were irradiated with uranium ions of 11.4 MeV/u at the GSI Darmstadt, Germany. We used different fluences from 3·10¹⁰ to 5·10¹¹ ions/cm². The diffusion constant was determined by the time-lag-method [1]. A quadrupole mass filter was used to observe the diffusion of the gas. We measured the diffusion of argon through different foils of each stack at room temperature. In all cases also unirradiated foils were measured. The dependence of the permeability and the diffusion constant on the ion fluence and the energy loss of the ions will be given and indications on the size of latent ion tracks concerning gas diffusion will be discussed.     

Neural network approach to diffusion of B and N adatoms on the Pt(111) surface

Artificial neural network boasts an outstanding class in terms of its performance and efficiency and is being spread widely in most fields of physics. We report our investigation of the diffusions of boron and nitrogen adatoms on the Pt(111) surface by performing molecular dynamics simulations equipped with machine-learned potentials. Platinum is commonly used as a substrate for the growth of hexagonal boron nitride (h-BN) thin films, and the diffusion of B and N atoms on the substrate, which are decomposed from the precursor molecules, plays important roles in the initial stages of h-BN growth. The two-dimensional potential energy surfaces and the trajectories of the B and N adatoms are consistent with the DFT calculation. The Arrhenius plots of the diffusion coefficients produce the diffusion barriers of the B and N adatoms on Pt(111), which agree well with the DFT barriers.     

A jump diffusion model for spot electricity prices and market price of risk

We construct a jump-diffusion model with seasonality, mean-reversion, time-dependent jump intensity and heteroskedastic disturbance for electricity spot prices, while keeping the analytical tractability of futures prices. We find that the jump component plays a considerably larger role than the diffusion component in the variance of spot prices. Moreover, the jump intensity is much higher during summer and winter. We also explore the seasonal market price of risk (MPR) with different maturities, from one month to five months. Our results show that the diffusion risk and the jump risk are priced quite differently.     

一种可大范围调节聚类系数的加权无标度网络模型

在Barrat, Barthélemy 和 Vespignani (BBV)加权无标度网络模型的基础上，提出了一种可大范围调节聚类系数的加权无标度网络模型——广义BBV模型(GBBV模型).理论分析和仿真实验表明，GBBV模型保留了BBV模型的许多特征，节点度、节点权重和边权值等都服从幂律分布.但是，GBBV模型克服了BBV模型只能小范围调节聚类系数的缺陷，从而可以用于具有大聚类系数网络的建模. 关键词： 无标度网络 加权网络 聚类系数     

一类高聚类系数的加权无标度网络及其同步能力分析

针对真实世界中大规模网络都具有明显聚类效应的特点, 提出一类具有高聚类系数的加权无标度网络演化模型, 该模型同时考虑了优先连接、三角结构、随机连接和社团结构等四种演化机制. 在模型演化规则中, 以概率p增加单个节点, 以概率1–p增加一个社团. 与以往研究的不同在于新边的建立, 以概率φ在旧节点之间进行三角连接, 以概率1–φ进行随机连接. 仿真分析表明, 所提出的网络度、强度和权值分布都是服从幂律分布的形式, 且具有高聚类系数的特性, 聚类系数的提高与社团结构和随机连接机制有直接的关系. 最后通过数值仿真分析了网络演化机制对同步动态特性的影响, 数值仿真结果表明, 网络的平均聚类系数越小, 网络的同步能力越强. 关键词： 无标度网络 加权网络 聚类系数 同步能力