相依网络的条件依赖群逾渗

相依网络鲁棒性研究多集中于满足无反馈条件的一对一依赖,但现实网络节点往往依赖于多节点构成的依赖群,即使群内部分节点失效也不会导致依赖节点失效.针对此现象提出了一种相依网络的条件依赖群逾渗模型,该模型允许依赖群内节点失效比例不超过容忍度γ时,依赖节点仍可正常工作.通过理论分析给出了基于生成函数方法的模型巨分量方程,仿真结果表明方程理论解与相依网络模拟逾渗值相吻合,增大γ值和依赖群规模可提高相依网络鲁棒性.本文模型有助于更好地理解现实网络逾渗现象,对如何增强相依网络鲁棒性有一定指导作用.     

Scaling of average receiving time and average weighted shortest path on weighted Koch networks

In this paper we present weighted Koch networks based on classic Koch networks. A new method is used to determine the average receiving time (ART), whose key step is to write the sum of mean first-passage times (MFPTs) for all nodes to absorption at the trap located at a hub node as a recursive relation. We show that the ART exhibits a sublinear or linear dependence on network order. Thus, the weighted Koch networks are more efficient than classic Koch networks in receiving information. Moreover, average weighted shortest path (AWSP) is calculated. In the infinite network order limit, the AWSP depends on the scaling factor. The weighted Koch network grows unbounded but with the logarithm of the network size, while the weighted shortest paths stay bounded.     

Sequences in neural networks with temporal association

We solve the dynamics of the strongly diluted version of a model recently proposed by Herz et al. to store sequences of patterns with spatio-temporal retrieval properties. We analyze the spurious sequence solutions and we find the region in the (,T) plane where the only relevant attractors are the learnt cycles.     

Mesoscale and clusters of synchrony in networks of bursting neurons

We study the role of network architecture in the formation of synchronous clusters in synaptically coupled networks of bursting neurons. We give a simple combinatorial algorithm that finds the largest synchronous clusters from the network topology. We demonstrate that networks with a certain degree of internal symmetries are likely to have cluster decompositions with relatively large clusters, leading potentially to cluster synchronization at the mesoscale network level. We also address the asymptotic stability of cluster synchronization in excitatory networks of Hindmarsh-Rose bursting neurons and derive explicit thresholds for the coupling strength that guarantees stable cluster synchronization.     

Engineered self-organization of neural networks using carbon nanotube clusters

A novel approach was developed to form engineered, electrically viable, neuronal networks, consisting of ganglion-like clusters of neurons. In the present method, the clusters are formed as the cells migrate on low affinity substrate towards high affinity, lithographically defined carbon nanotube templates on which they adhere and assemble. Subsequently, the gangliated neurons send neurites to form interconnected networks with pre-designed geometry and graph connectivity. This process is distinct from previously reported formation of clusterized neural networks in which a network of linked neurons collapses via neuronal migration along the inter-neuron links. The template preparation method is based on photo-lithography, micro-contact printing and carbon nanotube chemical vapor deposition techniques. The present work provides a new approach to form complex, engineered, interconnected neuronal network with pre-designed geometry via engineering the self-assembly process of neurons.     

Control of random Boolean networks via average sensitivity of Boolean functions

In this paper,we discuss how to transform the disordered phase into an ordered phase in random Boolean networks.To increase the effectiveness,a control scheme is proposed,which periodically freezes a fraction of the network based on the average sensitivity of Boolean functions of the nodes.Theoretical analysis is carried out to estimate the expected critical value of the fraction,and shows that the critical value is reduced using this scheme compared to that of randomly freezing a fraction of the nodes.Finally,the simulation is given for illustrating the effectiveness of the proposed method.     

An estimation formula for the average path length of scale-free networks

A universal estimation formula for the average path length of scale free networks is given in this paper. Different from other estimation formulas, most of which use the size of network, $N$, as the only parameter, two parameters including $N$ and a second parameter $\alpha $ are included in our formula. The parameter $\alpha $ is the power-law exponent, which represents the local connectivity property of a network. Because of this, the formula captures an important property that the local connectivity property at a microscopic level can determine the global connectivity of the whole network. The use of this new parameter distinguishes this approach from the other estimation formulas, and makes it a universal estimation formula, which can be applied to all types of scale-free networks. The conclusion is made that the small world feature is a derivative feature of a scale free network. If a network follows the power-law degree distribution, it must be a small world network. The power-law degree distribution property, while making the network economical, preserves the efficiency through this small world property when the network is scaled up. In other words, a real scale-free network is scaled at a relatively small cost and a relatively high efficiency, and that is the desirable result of self-organization optimization.     

Implantation of size-selected silver clusters into graphite

We report on a systematic study of the implantation of size-selected Ag_N ⁺ clusters on a graphite sample, for different cluster sizes (N = 1,3,7,9,13) and different impact energies (E = 1-30 keV). Results show that the implantation depth scales linearly with the momentum of the cluster, with a stopping power which depends on cluster size. We have particularly investigated the effects of the size and the geometry of the cluster on the implantation into the graphite substrate. A sort of universal behavior, which unifies different elements and different cluster geometries, can be recognized by scaling the momentum with the cluster projected surface. The stopping power of the cluster while penetrating the HOPG surface has been investigated for each cluster size, and a molecular effect is recognized, meaning that the stopping power is not additive in the number of atoms of the cluster.Received: 24 November 2003, Published online: 10 February 2004PACS: 61.46. + w Nanoscale materials: clusters, nanoparticles, nanotubes, and nanocrystals - 68.55.Ln Defects and impurities: doping, implantation, distribution, concentration, etc. - 79.20.Rf Atomic, molecular, and ion beam impact and interactions with surfaces - 81.05.Uw Carbon, diamond, graphite     

The role of small clusters in the transformation of two-ring clusters into fullerenes

Possible reactions by which small carbon molecules C₂ and C₃ can join a cluster at an intermediate assembly stage from a two-ring cluster to a fullerene are considered. For analysis of the separate stages of this type of reaction, methods of quantum chemistry are used. The generalized reaction probabilities obtained are then included into the general scheme of assembly kinetics alongside monomolecular reactions. It has been shown that at a small cluster concentration of about 10¹⁴ cm⁻³ the assembly time drops severalfold. Also given are generalized results of the effect on the assembly time of the multiplicity of paths of fullerene assembly from two-ring clusters.     

基于节点间依赖度的社团结构划分方法

本文提出了一种基于节点间依赖度的在复杂网络中划分社团结构的算法,定义了节点对其邻居的依赖度以及节点对社团的依赖度和条件依赖度.算法的基本要点是优先将最大依赖度不小于其他节点且有惟一依赖节点的节点划分到社团,并将对社团的依赖度或条件依赖度达到一定值的节点吸收进社团,直到所有节点都得到准确的社团划分.本算法在几个实际网络的测试上,都成功地划分出了满足条件的社团,并且对社团结构已知的网络的划分结果符合实际情况.     

Efficient methods for grouping vectors into low-rank clusters

We present a few practical algorithms for sorting vectors into low-rank clusters. These algorithms rely on a subdivision scheme applied to the space of projections from d-dimensions to 1-dimension. This subdivision scheme can be thought of as a higher-dimensional generalization of quicksort. Given the ability to quickly sort vectors into low-rank clusters, one can efficiently search a matrix for low-rank sub-blocks of large diameter. The ability to detect large-diameter low-rank sub-blocks has many applications, ranging from data-analysis to matrix-compression.     

Spontaneous alloying of tin atoms into nanometer-sized gold clusters and phase stability in the resultant alloy clusters

Alloying behavior and phase stability has been studied in situ by transmission electron microscopy using clusters in the Au-Sn system. When tin atoms are vapor-deposited onto nm-sized gold clusters, rapid dissolution of tin atoms into gold clusters takes place and as a result Au-rich solid solution, amorphous-like Au-Sn alloy and AuSn compound clusters are formed depending upon the concentration of tin. The remarkable enhancement of solubility has been observed in Au-rich solid solution and AuSn compound. It becomes more difficult to form two phases in the interior of individual clusters even if the composition of alloy clusters falls in the two-phase region in the phase diagram for the bulk alloy and as a result amorphous-like phase is stabilized in nm-sized Au-Sn alloy clusters. Received 2 August 1999 and Received in final form 8 November 1999     

Statistical indicators of collective behavior and functional clusters in gene networks of yeast

We analyze gene expression time-series data of yeast (S. cerevisiae) measured along two full cell-cycles. We quantify these data by using q-exponentials, gene expression ranking and a temporal mean-variance analysis. We construct gene interaction networks based on correlation coefficients and study the formation of the corresponding giant components and minimum spanning trees. By coloring genes according to their cell function we find functional clusters in the correlation networks and functional branches in the associated trees. Our results suggest that a percolation point of functional clusters can be identified on these gene expression correlation networks.